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[WSG23] Daily Study Group: Multivariable Calculus

Posted 8 months ago

A Wolfram U Daily Study Group previewing our upcoming Introduction to Multivariable Calculus course begins on Monday, September 11, 2023.

Join me and a cohort of fellow enthusiasts to learn multivariable calculus from the ground up. Learn how to use Wolfram Language to understand and visualize vectors, dot and cross products, curves, surfaces and the differential and integral calculus that can be done once free from the confines of "the x-axis." The three-week span of this study group will allow a large number of topics to be covered, including vector operations, multivariable and vector functions, gradients, coordinate transformations, line integrals and the "three great theorems" that come out of multivariable vector calculus.

enter image description here

The Introduction to Multivariable Calculus interactive course will soon be added to the Wolfram U catalog, and this Study Group offers early access to course lessons and resources. You will be able to participate in live Q&A, review your understanding through interactive in-session polls and even complete quizzes at the end of the study group to get a certificate of program completion.

This Study Group runs September 11–29, 2023, 11am-12pm CT (4-5pm GMT).

REGISTER HERE

Please use this thread to share ideas and questions about this material with your fellow learners.

We have put a lot of work into this course, and look forward to seeing you online!

enter image description here

POSTED BY: Arben Kalziqi
174 Replies
Posted 5 months ago

I can't join this group? I have joined it, but this group does not show in my groups...

POSTED BY: Soomi Cheong
Posted 5 months ago

Hello, Soomi. When you post a message to a group, you should get notifications whenever any new messages are posted to that group. This Daily Study Group ended about a month ago; most of the discussion from those daily sessions has ended. The Multivariable Calculus course taught during that DSG has now been released as an interactive course and is available for anyone to take and earn completion certificates: https://www.wolframcloud.com/obj/online-courses/introduction-to-multivariable-calculus/what-is-multivariable-calculus.html

If you have any questions during that course, this would be an excellent place to ask them. There also may be older entries in this discussion that may be helpful in learning the material. Good luck!

--phil (Not a Wolfram staffer; just a fellow student.)

POSTED BY: Phil Earnhardt

Hi;

Working on Lesson 34, I seem to be having an issue with getting my answer to even come close to any of the suggested answers - please see attached. The solution that I am using should work but obviously is not producing an answer that is close to any of the suggested answers. Please look over my attached notebook and help me understand what I am doing incorrectly.

Thanks,

Mitch Sandlin

Attachments:
POSTED BY: Mitchell Sandlin

Hi Mitch—try using CubeRoot rather than ^(1/ 3). (You may see why this is, now that I mention...)

POSTED BY: Arben Kalziqi

Hi Arben;

I tried using the CubeRoot[] function instead of ^1/3 and interestingly enough, I calculated a different answer - see attached. Also, when I equated = = = the two different results ie.
CubeRoot[]=== ^1/3 I received a "False" results - also see attached.

At the bottom of the attached, I tried using the SurfaceIntegrate[] function without any success. I believe the problem lies in my inability to setup the parametric equation correctly. Does Mathematica have a function that converts either a cartesian or polar coordinate equation into a parametric equation? In any event, it would help me if you could walk me through converting a cartesian or parametric equation into a parametric equation.

I enjoyed your class and passed the final exam today but would still like to obtain a better understanding of this problem. After spending the amount of time on this problem that I have, I actually feel like I own it.

Thanks,

Mitch Sandlin

Attachments:
POSTED BY: Mitchell Sandlin

Hi Mitch—if you could remind me of this next Wednesday, I would be happy to take a thorough look. I'm off for the next ~week, so can't check in the meantime. What I can at least say re: your comment is that CubeRoot and ^1/3 shouldn't return the same thing for either == or ===. The former explicitly gives the real cube root, whereas the latter refers to the more general cube root... at least when it's applied to a variable. For example, think about the cube root of 27—there's 3, obviously, but 3 e^(i 2 Pi /3) and 3 e^(i 4 Pi /3) both also give 3 if you cube them. When dealing with equations that have a ^(1/3), these latter types of roots are kept as possibilities whereas CubeRoot only keeps the real-valued one.

POSTED BY: Arben Kalziqi

Hi Arben;

Actually, I am traveling myself for the next month, so please take your time getting back to the problem and enjoy your vacation.

I actually worked the problem using both CubeRoot[] function and ^1/3 and both methods produced substantially different results, and of course none of the results matched the suggested answers.

In the end, what I would like to see is the textbook solution to the problem in question, since I have tried a bunch of different approaches without any clear success. Additionally, it seems that this problem is somewhat of a lynchpin to other problems, so it is important to fully understand the method used in solving it.

Thanks,

Mitch Sandlin

POSTED BY: Mitchell Sandlin

Hi Arben;

In this response, I have attached a notebook outlining exactly what I hope to accomplish with this problem, which is understanding how to perform these calculations using Mathematica. The attached notebook shows 5 or 6 different methods to solve this problem in Mathematica all of which I seem to be having trouble mastering. Hopefully, you can help me understand what I am doing incorrectly. For now, enjoy your vacation and we can work on this when your get back to your desk and me back from traveling.

Thanks,

Mitch Sandlin

Attachments:
POSTED BY: Mitchell Sandlin

HI Arben!

Thanks for a fun run through of multivariate calculus. My favorite phrase from the recordings:

I'm not going to go through the details but it looks nice!

I also enjoyed your video of the card deck toss because it reminded me of young me tossing a deck and realizing that some ways were easier than others and OH!, I knew about centers of mass before I knew about centers of mass.

Even though it wasn't necessary, I watched the videos in the framework because I like seeing all that orange. Did you realize that you speak so clearly that listening at twice the speed was an easy review? Try it, LOL!

Be safe. Be well. ON TO DISCRETE MATH!

Lori

P.S. Yes, I earned both certificates :-D

POSTED BY: Lori Johnson

On the Final Exam Lesson Eleven the domain of Log[Log[(x+y+x)^2 + 1]] does not include the endpoints so answers should only use "<" or ">".

POSTED BY: Thomas Rike

Hi Thomas—this question has been updated on our end. If it's a "blocker", you may have to get a new copy of the exam for it to deploy to you.

POSTED BY: Arben Kalziqi
Posted 6 months ago

I downloaded the final exam yesterday and I don't think that the proposed answers to Question 11 have been fixed in response to the prior posting: 'On the Final Exam Lesson Eleven the domain of Log[Log[(x+y+x)^2 + 1]] does not include the endpoints so answers should only use "<" or ">".'

Also, it appears that the second listed answer to that question does not actually offer a choice: x+y+z<=-1 or x+y+z<=-1. Is that intentional? Thanks

POSTED BY: Richard Sweney

Hi Arben;

In solving for a surface using the given equation Double integral x + y^2 + z^3 dS, one would need to convert z^3 into values of x and y for g[x,y}. Personally, I would simply use Solve[x + y^2 == z^3, z] which would equal (-x - y^2)^1/3. This value causes problems for mathematica in later calculations for the actual surface area. Do you see where I am going wrong with my calculation for g[x,y}?

Thanks,

Mitch Sandlin

POSTED BY: Mitchell Sandlin
Posted 6 months ago

In Lesson 7 "Vector Functions and Space Curves", Tim mentions torque with the "Twisted Cubic" curve. This is a discussion of the twisting forces at a particular place in the curve. It was a casual reference, and he didn't go into details.

In the YouTube video: "Torsion: How curves twist in space, and the TNB or Frenet Frame", Mathematics Professor Dr. Trefor Bazett provides a few more details. The torsional vector of a space curve is the binormal vector: the cross product of the tangent vector and the normal vector. Look at around 3:10 into Trefor's video if you'd like to see it graphically. While I consider myself slow to understand the "big picture" of multivariable stuff, this image and calculation makes perfect sense to me. I'm sure Arben, Luke, and the other Wolfram staff are familiar with the concept of the double-normal vector of a curve and its significance.

Why does this mathematical torque matter? It matters because it corresponds to physical torque for objects following a particular curve! In a lateral jump-rope movement called "RMT Ropes" (AKA "Flow Ropes"), the midline of the rope follows Viviani's Curve (with the rope criss-crossing over the rope-jumper's head). The rope's torque is obviously present and the front-most and rear-most movements of the rope. The frontmost torque is rope-over-the-top; the rearmost is rope-under-the-bottom. I'd felt this for many years of dragon-rolling; it was #!$$ exciting to see that the geometry of space-curves notes the same torsional forces. The rope-forces are noteworthy because they reflect the torsional forces in the musculoskeletal network of the human body. The math gives us insight how the rope moves and forces exist; the rope gives us insight in how a body driving those movements must also work. As a society, we have never understood how torsional forces are manifested and used in our bodies. That should change -- it must change!

I guess we're here for different purposes; I'm trying to understand use computational movement to visualize human movement a bit better. And anyone interested in getting a hands-on visualization to an interesting space-curve can try RMT Ropes.

I hope all are doing well with their progress with quizzes and the final.

POSTED BY: Phil Earnhardt

Thanks for this insight, Phil—though my training is in physics, I've never had that good of an intuition about "physical" objects and have felt much more at home with things like fields, so it's good to have a bit of a counterbalance here :).

POSTED BY: Arben Kalziqi

On Quiz 3 problem 4, where f(x,y)= e^(-x-y), I think the first three answers are all correct. Taking a partial with respect to x or y just multiplies the function by -1. So all combinations of third partial derivatives will be the same; i.e. the negative of the function.

POSTED BY: Thomas Rike

Indeed—there was a bit of a miscommunication when editing this problem to fix a previous error. We've fixed that on our end now and it should show up when we next redeploy the quiz notebooks!

POSTED BY: Arben Kalziqi

I didn't notice anyone else pointing this out. A minor typo in Practice Problem Set 2 Problem 13, The coordinate for A should be (0,2) instead of (0,-2).

POSTED BY: Thomas Rike

Hi Thomas—forgive my asking, but why is that?

POSTED BY: Arben Kalziqi

The problem ends by saying, "You can see that the curve starts at the red point (point A), then crosses the blue point (point C) and finally crosses the green point (point B)."
The curve r[t] = {-3 Sin[2pi t], 2 Cos[2pi t]} starting at t= 0 starts at (0,2). I agree that using A = (0, -2) is a nicer problem but would require more editing to have a correct solution. [C,A,B]

POSTED BY: Thomas Rike

Oh, of course—sometimes you stare at something but just totally miss the issue! Fixed.

POSTED BY: Arben Kalziqi

Hi Arben;
Is the following answer correct? The processing took forever to complete and created several errors - see below. Additionally, when I replaced //N with //Simplify, I really got a strange looking answer.

Thanks,
Mitch Sandlin

Attachments:
POSTED BY: Mitchell Sandlin

Hi Mitch—I suspect that the issue comes from either working with a double exponential (which can be numerically tricky) or from the fact that the region of integration includes a point where the function is undefined—as you can see, one of the error messages does say: "suspect one of the following: singularity [...]".

I would naïvely expect that you should get 0 for the result if anything, though, just by the FTC? If you look at the indefinite integral for x^y^x with respect to x and y, I think you'll see where some of the difficulty might come in. Is there a particular answer you're expecting, or is this an integral I ought to know?

POSTED BY: Arben Kalziqi

Dear Arben:

On quiz 5, problem 5, answers are in terms of b and none seem to be correct.

Also, is there something off here? enter image description here

Thanks again.

Best,

Juan Ariel

Posted 7 months ago

Hint : Lesson 30, Slide 4.

POSTED BY: M Firdaus

(I think you may mean Lesson 31...)

POSTED BY: Arben Kalziqi

Thank you both.

On exercise 5 quiz 5, I suggest to have b instead of 1 in the figure.

And in the other problem, I wrote the equations wrong and was not getting a simple curve, hence no Green.

Plenty of Green now.

Thank you, Thank you.

Are you seeing a 1? In both my source notebooks and the deployed version I'm seeing this:

enter image description here

POSTED BY: Arben Kalziqi

Arben, it shows as a 1. Spooky framework. one instead of b

Thank you Juan! We'll look into this.

POSTED BY: Arben Kalziqi

Hi Juan—there's no issue with Quiz 5 Problem 5; I've just computed the answer and checked that it both is one of the presented options and is marked as the correct answer in the key. There's also no problem with the answers being in terms of b; the path C in question is simply made up of four "legs" of length b.

There is also nothing wrong with the screenshot you provided. Hint: both of these misunderstandings stem from the same place! :)

POSTED BY: Arben Kalziqi

In the Framework, Lines and Planes, on the lessons view pane,

under Equation of a Plane, would it be worth appending " , represents an equation of the plane." to the first paragraph.

under the example of Equation of a Plane, the Dot Product symbol is missing between the two vectors ie it should read "therefore , <...> . <-3,1,4> = ... "

POSTED BY: John Burgers

Thanks for the millionth time, John :). I've added a small note to the end of that paragraph and inserted the dot.

POSTED BY: Arben Kalziqi

In the Framework under Cross Product, in the lesson view pane, all the Graphics have their WL code visible.

I must say the explanation of Magnus Effect and the referenced You Tube video is a high point in course applications.

POSTED BY: John Burgers

Not sure how this one happened, but it's been fixed. (Of all the code to be revealed, that lesson has some nasty stuff to make the custom images!)

And thanks for the comment about the Magnus force discussion—it's quite enlightening!

POSTED BY: Arben Kalziqi

In the framework, under Dot Product, in the lesson view pane under section Vector Projection, there is the WL statement SetOptions[ EvaulateNotebook[], ShowCellBracked->True ]

POSTED BY: John Burgers

You've got a real eagle eye! This is now fixed on our end; that's my fault for forgetting to remove it when we were testing out showing cell brackets for everybody so that they could see the code.

POSTED BY: Arben Kalziqi

Perhaps already caught by others, In the framework for Dot Product, in the lesson view pane, the image under "Angles between Vectors" is blank.

POSTED BY: John Burgers

Thanks again, John—this was fixed earlier this week on our end and should show up in the framework next time we deploy.

POSTED BY: Arben Kalziqi

In the lesson on Vectors I noticed that the description of what a vector is might be improved. Vectors are introduced as "Each vector contains two important pieces of information: its length (or magnitude) and the direction in which it points.". Then under the heading "Algebraic Representation of Vectors" we see that a vector can be written as <3,2> where in both entries are orthogonal distances that encode both the magnitude and direction. This leaves the student asking "what is the magnitude and direction then?". Later in the "Application" section we see a vector written as 50<cos(30),sin(30)> which is a magnitude and unit direction algebraic definition.

My question is whether it would be helpful to the student to see right away the magnitude * unit vector definition first followed up by an explanation that this is equivalent to the <distance, distance> Algebraic form ie. what the student sees in the application example ... 50 <cos(30),sin(30)> = 50 < sqrt(3)/2, 1/2> = <25 sqrt(3), 25>

I understand that it also requires the introduction of a unit vector, which is well done in the lesson as a decomposition of the <distance,distance> form.

I bring it up as something to think about.

Regards John

POSTED BY: John Burgers

Thanks John—I see where you're coming from, and will consider this as we make our final edits to the course.

POSTED BY: Arben Kalziqi

Your welcome Arben,
This framework is fundamental to many fields, so I'm willing to assist your call for comment. We're all tolerant to the most reasonable result within the time budget and the present condition of this framework is indeed quite good. I myself can only devote so much time to the call for comment.

Linear algebra introduces an arbitrary system of j linear equations in i unknowns xi as the sum over i and j of [aij xi] = bi, which is decomposed to A X = B, where a matrix is defined as A = [a11, ... a1j, a21, .... a2j, ... , ai,1, ... aij], and vectors defined as X=[x1, ... xj] and B = [b1, ... bj]. So a vector is defined simply as a row of matrix, a column of a matrix or more simply as a list of two or more scalars.

Applying vectors to Euclidean space whether (n= 2, 3) or to higher dimension, the concept of orthogonality is introduced, wherein the it understood that a change in any unknown, say xi, does not affect other unknowns, ie, in Euclidean 3D a change delta x does not change y or z. This is simply understood for 2D and 3D Euclidean space as we humans can visualize the orthogonal directions and associated unit vectors, but we need help to understand any applications of this beyond n=3.

That help is the concept of an orthonormal bases. For instance say we want to decompose a list of words describing colour. In literature all the colours are given a word or word combination (orange, white, bluish green, ...) where-in the word combinations are unique. Fields of study such as artificial intelligence, AI, might chose to model these assuming words and word combinations although unique as spelled are unique in meaning, that is can be modelled mathematically as orthogonal, ie that each colour word or word combination is orthogonal, however physicists study of light reveals colour is truly orthogonal as vector representation in the primary colours of <Red,Green,Blue>, ie. RGB as an n=3 orthonormal bases of colour. Fortunately the Gram-Schmidt process helps us determine an orthonormal basis when the xi are themselves not mutually orthogonal. I think this is an important thought as AI applications deepen beyond our comprehension of uniqueness.

In physics and engineering where the techniques of linear algebra, calculus, are well developed for conserved fields (read conservation of mass, momentum and energy) where the physics can be described in Euclidean space as orthogonal, it is preferred to keep separate the force vector functions and displacement vector functions, so the "physics" is more readable in the equations. An example of this would be the application example I liked and supplied for which I supplied a reworked notebook in a previous post, and should have separated the forces from the distances in all the equations. That way we would have seen an equation of the form f . d = mg <0,h> where mg is a force and the distance vector is <0,h> instead of f.d = mgh

Keep going Arben and team, You're doing well.
John

POSTED BY: John Burgers
Posted 7 months ago

Arben: I was interested in the area of the Möbius strip in Lesson 33, so I tried to use its formula in place of the one for the torus whose area was calculated. When I tried to evaluate the integral, Mathematica froze with the message (Running ...) and never produced an answer. See the attached pdf. Can you explain why it did not work and show us how to get an answer?

Attachments:
POSTED BY: Gerald Oberg
Posted 7 months ago

I left it running overnight and in the morning had some answers. It evaluated the inner integral but left a horrific mess for the integrand of the outer integral. However, it did get a numeric integral for the area. Arben, how can I ask it to show how long it took for each result?

Möbius Strip Area

POSTED BY: Gerald Oberg

Thank you for the interesting links about the Möbius strip! I will try to look into this question of area more—by some conventions, the lack of orientability of the strip means it doesn't have a well-defined area, but I think that that does feel a bit like a copout physically.

For example, the following code will return Undefined quite quickly:

r[u_, v_] := {(5 + u Cos[v/2]) Cos[v], (5 + u Cos[v/2]) Sin[v], 
  u Sin[v/2]} 
SurfaceArea[
 Region@ParametricRegion[r[u, v], {{u, -1, 1}, {v, 0, 2 \[Pi]}}]]

However, I have found a nice way to do this very quickly while recapturing your result:

rN[u_, v_] := {(5. + u Cos[v/2]) Cos[v], (5. + u Cos[v/2]) Sin[v], 
  u Sin[v/2.]} 
RegionMeasure[
 Region@ParametricRegion[rN[u, v], {{u, -1, 1}, {v, 0, 2 \[Pi]}}]]

We can use AbsoluteTiming here to see how long it took from my pressing shift+enter to getting a result:

In[16]:= AbsoluteTiming@
 RegionMeasure@
  Region@ParametricRegion[rN[u, v], {{u, -1, 1}, {v, 0, 2 \[Pi]}}]

Out[16]= {2.27812, 62.9377}

Generally, RepeatedTiming will give you more accurate timing results, but it is repeated so for a (possibly) lengthy calculation, you really might not want to repeat it.

I do have some other suggestions which are also much faster—the key point seems to be using the correct simplification assumptions and then doing a numerical integral, regardless of where you make the "conversion" to numerics:

In[42]:= 
rN[u_, v_] := {(5. + u Cos[v/2]) Cos[v], (5. + u Cos[v/2]) Sin[v], 
  u Sin[v/2.]} 
integrandN = 
  FullSimplify[Norm[D[rN[u, v], u]\[Cross]D[rN[u, v], v]], 
   Assumptions -> {-1 <= u <= 1, 0 <= v <= 2 \[Pi]}];
AbsoluteTiming@NIntegrate[integrandN, {u, -1, 1}, {v, 0, 2 \[Pi]}]

Out[44]= {0.002396, 62.9377}
In[50]:= 
r[u_, v_] := {(5 + u Cos[v/2]) Cos[v], (5 + u Cos[v/2]) Sin[v], 
  u Sin[v/2]}
integrand = 
  FullSimplify[Norm[D[r[u, v], u]\[Cross]D[r[u, v], v]], 
   Assumptions -> {-1 <= u <= 1, 0 <= v <= 2 \[Pi]}];
AbsoluteTiming@NIntegrate[integrand, {u, -1, 1}, {v, 0, 2 \[Pi]}]

Out[52]= {0.002543, 62.9377}
POSTED BY: Arben Kalziqi

Dear Arben, in Practice Problem Set 1, Problem 12, I guess that the slope of a line with eq. y = -5x + 3 is -5 and not -3. Therefore, the vector parallel to the line should be v = <1,-5> and not <1,-3>. The acute angle that results from the problem is 37.875 degrees and not 45 degrees. Best regards, Ruben.

Thank you Ruben—I've modified the equation in the prompt such that the slope is in fact -3 and the numbers stay a bit more tractable :).

POSTED BY: Arben Kalziqi

The method of Lagrange multipliers was skipped and the physical example of the lesson notebook is not covered in the video.

Liking this example, but finding it terse in explanation I've reworked in in the attached file. That so it might be considered for inclusion in the course framework.

Regards, John

Attachments:
POSTED BY: John Burgers

How does the person hold the weight up on a friction-less surface?

;-)

POSTED BY: Carl Hahn

Very carefully.

POSTED BY: Arben Kalziqi
Posted 7 months ago

Arben, Here is what I think is an interesting problem related to today's Lesson 27 on Change of Variables in Multiple Integrals as well as the upcoming Lesson 33 on Areas of Parametric Surfaces. Please see the attached pdf.
enter image description here

Attachments:
POSTED BY: Gerald Oberg

Very interesting! If you'd like to recreate this in a notebook—perhaps with some of the functionality we'll learn about later this week, even—here's a start on the visualization aspect at least!

POSTED BY: Arben Kalziqi

The recording for the lesson on Limits and Continuity, Partial Derivatives behaves oddly at poll questions. It on previous recordings it is possible to answer the poll question and submit then discharges it from view. In this recording it is not possible to dismiss the poll question by submitting an answer. The final poll question is also not answerable, and additionally we loose Arben's interpretation of the poll. Cassidy's is the next voice heard.

I'll assume that recordings are only for this study group and although content feedback may help, more feedback of their behaviour is not helpful for the framework development.

Regards, John

POSTED BY: John Burgers

Thanks for noting, John—we'll look into this.

POSTED BY: Arben Kalziqi

Arben - The Lesson and Exercises have cell brackets hidden. How can I display the cell input and output brackets? I have a good grasp of multi-variable math, but I wanted to learn new ways to use the WL to display graphics. This is the main reason for me taking this course, but I can't see the input code.

POSTED BY: Charles Glover

Hi Charles—most probably we will update all of the notebooks this week to have visible cell brackets, which means that you will be able to reverse open/close them and see how any given output was made, even in the cloud. For now, you can download any given notebook and run the following line of code anywhere in the notebook:

SetOptions[EvaluationNotebook[], ShowCellBracket -> True]

This will make the cell brackets visible again, at which point you can open them up to your heart's content.

POSTED BY: Arben Kalziqi

Arben - Thanks for the info

POSTED BY: Charles Glover

Any time! Tim's visualizations in the lessons are generally much nicer than mine in the exercises, but they do require correspondingly more work to make. We could say that this disparity is intentional in that it offers guidance to people at multiple levels of programming skill ;).

POSTED BY: Arben Kalziqi

Hi Charles—following up to say that we have updated all of the notebooks in the framework so that you should be able to examine the code freely even in the cloud. Of course, if you want to go in there and edit it for your own purposes, you'll want to download a copy or make a copy into your own cloud account.

POSTED BY: Arben Kalziqi

Arben - Thanks; I initially couldn't find the option ShowCellBracket in the Option Inspector. I knew it had to be somewhere in there. After you sent the one line of code, I finally found it.

POSTED BY: Charles Glover

Dear Arben:

On Quiz 4, can you confirm that the answers for problems 4 (missing a 1) and 10 (wrong limit of integration) are correct? Or maybe I am seeing them wrong.

Best,

Juan Ariel

Hi Juan—let me check.

  • For Problem 4, I can confirm that the correct answer is among the choices but was not marked as the correct answer in the key. I have updated this.
  • For Problem 10, I can confirm that the inequality should be ≤ rather than ≥ in order for the solution and graphic to match the given region.

Thanks for pointing these out!

POSTED BY: Arben Kalziqi

Thanks Arben. That makes sense.

In slide 8 of the Cylindrical Coordinate lecture on the "pencil and paper" solution on slide 8, I found the transition from line 2 to line 3 very cryptic. This essentially drops the r^2 Sin[theta] + r^2Cos[theta] terms because after integrating wrt r from 1 to 2 and then wrt theta from 0 to 2pi they result in zero. For someone encountering this the first time, this can be very frustrating and time consuming. (And of course, the constant 3 coming outside the integral in the same step turns the transition into a magic show.) A sentence explaining what happens to terms with sine and cosine functions as factors when evaluated from 0 to 2pi would be helpful.

POSTED BY: Thomas Rike

Thanks for the comment, Thomas—would an addendum right after the calculation like this suffice?enter image description here

POSTED BY: Arben Kalziqi

Yes, that is just what I had in mind.

POSTED BY: Thomas Rike

Great—it's implemented!

POSTED BY: Arben Kalziqi
Posted 7 months ago

For those interested in more input on unstable rotation about the axis with the mean moment of inertia, here are some links:

Still, it's impressive that you achieved the effect with a simple deck of cards under the influence of gravity. :-)

POSTED BY: lara wag

There is also an interesting post about Dzhanibekov effect here: https://community.wolfram.com/groups/-/m/t/2243140

POSTED BY: Ahmed Elbanna
Posted 7 months ago

There is a typo in final solution to Lesson 2 Exercise 4 (equation of the sphere); ...(x-3)^2... should be ...(y-3)^2...

POSTED BY: Graham Gyatt

This is corrected on our end; it may just not be deployed to the framework yet.

POSTED BY: Arben Kalziqi

In a lecture long past, lesson 4 on the dot product, in the section "dot product of 2 different vectors", I guess that the difference vector u-v points in the wrong direction in the 3D image, it points from u to v, and should point from v to u. In lesson 3 on vectors, in the section "vector subtraction", in the 2D image the vector difference u-v does point in the correct direction, from v to u.lesson 4 on the dot product

lesson 3 on vectors

Posted 7 months ago

Agreed - I was just about to post the same bug

POSTED BY: Graham Gyatt

I also was preparing to post as well.

POSTED BY: Charles Glover

Thanks Ruben—I've fixed this on our end and also fixed two dynamic interfaces that were broken in that lesson. These fixes will be available the next time notebooks are deployed.

POSTED BY: Arben Kalziqi

Hi Arben!

I have refreshed the page hoping this would be fixed but, no. The scratch notebook obscures the middle panel. It happens in Firefox, Safari, and Chrome. It does not happen with quizzes, only Practice Problems.

Examples: Chrome enter image description here Safari enter image description here Firefox enter image description here

Please let me know if you need more information! Thank you!

POSTED BY: Lori Johnson

Hi Lori—yes, if you could please email wolfram-u at wolfram dot com (very effective spam filter technique here, I'm sure) about this, that would be helpful. I can't quite see how this is happening, so more info would be good. Thanks!

POSTED BY: Arben Kalziqi

Thank you, Arben, I will! :-D

POSTED BY: Lori Johnson
Posted 7 months ago

Since you're running on a Mac, you could even take a short video to submit to Wolfram U. That may be better than a screenshot.

--phil

POSTED BY: Phil Earnhardt

Hello! Congratulations for this course! I'd like to know if the notebooks of classes are disponible.

Yes, they are "available" ;-)

POSTED BY: Carl Hahn

Thank you! Yes, you should be able to download them from the framework we shared or directly from the amoeba link that we pin/sticky every day.

POSTED BY: Arben Kalziqi
Posted 7 months ago

Arben: I used to explain the Average Value Theorem with ant farms. Suppose the surface of sand in an ant farm (before ants are put in) is made to conform to a given function. The farm is set on a vibrating plate and the vibration turned on. The sand will gradually flatten out to a depth equal to the average value of the function. I would like to see an animation of that process that can be done for any given (reasonable) function.
Suppose instead that the sand is replaced by a fluid with the surface held in place by a piece of hard plastic conforming to the given function. If the plastic is suddenly removed, the fluid will settle to a level surface. Water would slosh around a lot, but the higher the viscosity, the less sloshing. Could you make an animation of that process for a given function and viscosity? https://en.wikipedia.org/wiki/Viscosity shows something along these lines.
Finally, extend both of these from two to three dimensions as in a fish tank with the surface conforming to a function z = f(x,y).

Sand Ant Farm Gel Ant Farm

POSTED BY: Gerald Oberg

Gerald—this is a very nice way to demonstrate the idea. Unfortunately, I think developing such a simulation is a bit beyond the scope of this course (though if I knew how to do it mostly off the top of my head, I would admittedly still do it).

POSTED BY: Arben Kalziqi
Posted 7 months ago

Arben: Okay, let’s forget about any physical interpretation. Please read the attached pdf.

Attachments:
POSTED BY: Gerald Oberg
Posted 7 months ago

Adding a bit to the file ...

Attachments:
POSTED BY: Gerald Oberg

Thank Gerald! I've given this a skim and hopefully I can put something together this week.

POSTED BY: Arben Kalziqi
Posted 7 months ago

Interesting. First, I think you should show the single-variable calculus average value problem first in a very narrow tank, then expand it to a fish bowl proper. You could provide beautiful visualizations of both problems and show how they're related.

I also was thinking from a MAKE context of a museum exhibit. Have physical 2-D and 3-D tanks, and have a head like a printer head on a 3D Printer. Allow the user to specify a function to lay out bits of sand in the tank; the head rapidly distributes the sand into the curves. Then ask the average value question. Then have the vibration plates shake the sand down until it's flat. Was the operator able to guess the height of the sand -- the mean value?

Have you run across MAKE:Calculus (and its sister books MAKE:Geometry and MAKE:Trigonometry)? These are from a couple of makers -- and a reformed rocket scientist -- who think that 3DP objects can have a huge impact for students to understand these subjects. I like their work -- I think anyone here would like it, too. There are 3 episodes in the Make:Cast podcast -- including a suspicious blank section in the discussion about the calculus book! What was said that was deleted? If you dig hard enough in the Internet Archive, you can find it.

I think a physical demonstration would be great. IMHO, physicality trumps animations.

POSTED BY: Phil Earnhardt

Dear Arben:

There might by a typo on Problem 1,part 2, Lesson 17: g_{xx} is repeated.

Thanks for the eagle-eyed catch, Juan—I've updated the notebook on our side. I'll look into your question about the quiz after today's session as well.

POSTED BY: Arben Kalziqi
Posted 7 months ago

Several questions about the beta framework for the course:

  1. When we do exercises in the framework, where should students be showing/storing our work? In the Elementary Introduction to the Wolfram Language (EIWL) interactive course -- something that seems rather similar -- each chapter's exercise was a scratch Notebook proper that allowed (actually, required) the entering of WL code to answer the exercises. In this course, the exercise pages don't appear to be interactive Notebooks; I don't see any mechanism for entering any text into the "exercises" notebook in this framework. Unless I'm missing something, the only alternative seems to be to download the exercises notebook and work with the Notebook in my standalone Mathematica app. This seems to defeat the advantages of the entire interactive framework for working through the course; students that are familiar with the EIWL framework will be confused by this interactive course.

  2. Will transcripts be provided of the sessions? EIWL provided a "transcripts" tab with a transcript of the presentation (I presume that transcript was generated with one of the transcript-generating AIs out there). This was highly useful in that course; students here (and future students using this interactive course) would benefit from having those transcripts.

  3. Now that the interactive course beta has been published, what Notebooks that have been provided via the notebook code dump are not part of that course? AFAICT, the only Notebook which is only provided in the download code blob is the Week 1 review notebooks -- one Notebook so far. Is this a correct presumption: are all the other notebooks of this course included in the online course beta?

POSTED BY: Phil Earnhardt

Hi Phil—in order:

  1. Unlike the simple exercises in EIWL, there is—unfortunate as it may be—a 0% chance that we (or anybody, I think) could write code that would appropriately grade solutions to this type/level of exercise. In some cases, there is a strict numeric answer that could be entered and checked, but I don't think it makes sense to have an "enter your input here" only for some portion of the exercises. You can still work on the exercises in the scratch cloud notebook that you have available in the interface simultaneously with the exercises. I do, however, think that the lesson and exercise notebooks are best interacted with locally—we've made serious improvements to cloud such that it's even possible to host and interact with lots of the graphics and interfaces here, but when it comes down to it these are generally heavy notebooks and a local interface is always going to handle them noticeably better than a cloud interface.

  2. They are indeed being worked on, but are not yet ready. The transcripts are actually done by a person!

  3. All of the lesson and exercise notebooks are deployed to the beta course and should be in working order. The review notebooks are written as we go through the DSG in response to the questions people submit at the end-of-session surveys and are "DSG-exclusive", so to speak, on account of needing that context.

POSTED BY: Arben Kalziqi
Posted 7 months ago

Unlike the simple exercises in EIWL, there is—unfortunate as it may be—a 0% chance that we (or anybody, I think) could write code that would appropriately grade solutions to this type/level of exercise.

You may have misunderstood my question. I noted that EIWL answers are submitted via "exercises", but I wasn't asking for this course to work that way. I was simply asking if the "exercises" tab could each be a scratch notebook. It would be a place to hold work and store each response in context.

The problem with the separate scratch notebook is that it provides no way to store the student's work in context. There is a single scratch notebook for the entire framework; storing any entries one has made in the scratch notebook is problematic. There is no way to work on problems, make notes, and resume the work later.

I presume it would be rather easy to have regions in the "exercises" tab simply be scratch areas to enter WL code of the student's choosing.

One side note: you can say that the auto-grading of exercises in EIWL is rather easy, but I was thoroughly impressed with the code of the grading engine to determine the correctness of answers. Arbitrary code could be submitted. I was thoroughly impressed with the ability of the code to grade responses. I'd sometimes deliberately obfuscate my response; the error was able to ferret out what was happening.

But -- to repeat -- this is NOT what I'm suggesting for this particular course. All I want is a bunch of places in the "exercises" tab for me to enter and interpret my own WL code. Can you see the value in providing those work-spaces? Isn't this easy to do in the framework?

POSTED BY: Phil Earnhardt

I wouldn't say much of anything is particularly easy to do in the framework :'). But I see what you mean and will ask the person who handles our cloud deployment whether this is possible.

POSTED BY: Arben Kalziqi
Posted 7 months ago

How are the course designers visualizing that students work through the examples in the framework? How did beta testers using the framework go through the examples? If the "scratch" window in the framework is like other interactive courses, I don't see how it can be used to take notes and create a record of working through the problems. What did the beta testers find -- how did they work through this in the framework? How did they use the scratch notebook? Were they able to save their work?

I wouldn't say much of anything is particularly easy to do in the framework :').

You noted: that the difficulty in imitating what the EIWL course did was auto-grading. Don't auto-grade. Simply providing an interpreter in the exercises window should be easy.

I just can't quite visualize how we're supposed to generate organized notes as we work through the exercises. I don't see how this course framework provides any way to do that. That's why I'm curious how the beta testers used the framework in their testing. Working through the course in a standalone Mathematica notebooks isn't bad, but it doesn't seem to gybe with the intent of an interactive course. To use a metaphor, it's a bit of an impedance mismatch.

POSTED BY: Phil Earnhardt

You noted: that the difficulty in imitating what the EIWL course did was auto-grading. Don't auto-grade. Simply providing an interpreter in the exercises window should be easy.

Right, I said that doing auto-grading for something like this was impossible—but that's not to say that tasks simpler than that are trivial or even easy to accomplish; they're two orthogonal statements, so to speak. It's just that the auto-grading in particular is rather impossible; other notebook deployment possibilities which are sub-impossible can still span the range between "we'll trivially do that ASAP" and "that's a lot of work." Adding interactive portions to complex notebooks which auto-save, live, per-account and per-lesson, then are shown to each respective user each time seems like it falls closer to the latter to me—it would require modifying the framework such that the exercises aren't static notebooks, but auto-saving notebooks which display on a per-account basis.

...and that's excluding any responsiveness issues that might arise from having users not only typing into notebooks with complex 3D graphics and Manipulates and so on, but trying to generate their own such objects and save them to their own cloud copies of the notebooks. Then we have to worry about users making these objects in these notebooks but not making them in a way that runs well on cloud, and the support tickets that would be generated from people who have barely-functional things in their notebooks... I just mean to say that there are a lot of moving parts here that may not be fully visible to the end user. (Which is as it should be, but it's worth keeping in mind when imagining that something might be easy to implement!)

POSTED BY: Arben Kalziqi
Posted 7 months ago

...and that's excluding any responsiveness issues that might arise from having users not only typing into notebooks with complex 3D graphics and Manipulates and so on, but trying to generate their own such objects and save them to their own cloud copies of the notebooks.

Auto-grader aside, the EIWL exercises run through a rather thorough repertoire of things in their course. I rapidly got in the habit of using the exercise window for scratch code, and I wasn't shy about how I used it. I thought it was a rocking good way to have all of the coursework in one place.

Wouldn't the hypothetical problems you describe also apply to the scratch notebook in the framework? How in general did the course designers intend for students to use the framework? Did they want everyone to do all their work in the framework? Were the beta testers able to do that?

POSTED BY: Phil Earnhardt

Hi Phil,

The problem with the separate scratch notebook is that it provides no way to store the student's work in context.

I agree with you. My solution is to copy/paste the exercises into notebooks on my desktop, and then program my solutions/answers into these. Keyboard shortcuts in the desktop version make programming so much faster and these are unavailable in the online framework. In the end, it's easier to retrieve my work on my device, organized to my liking.

For those without access to the desktop version, there is always the Wolfram Cloud: use a free account to create notebooks, save to the desktop, and access with the free Wolfram Player later. It wouldn't take much to have two browser tabs open in a vertically split screen, one with exercises or quizzes, and another with the Wolfram Cloud notebook.

Maybe one of these solutions could work for you. The second option is especially good because it makes every part of these study groups cost nothing to participants. It's so hard to beat.

POSTED BY: Lori Johnson
Posted 7 months ago

Maybe one of these solutions could work for you. The second option is especially good because it makes every part of these study groups cost nothing to participants. It's so hard to beat.

The "for you" is not my focus. I'm asking how a Man from Mars would use the course and work the exercises. How would someone relatively new to the Mathematica app, the Wolfram Cloud, etc., figure out how to use the tools. If the framework is designed so that a [relative] newbie can work the course, it will be just fine for me.

For those without access to the desktop version, there is always the Wolfram Cloud: use a free account to create notebooks, save to the desktop, and access with the free Wolfram Player later.

Alternatively, I could work in the scratch notebook in the framework and save that notebook to my Cloud account. I hadn't thought about archiving the scratch-area that way. That is my point: some newbie -- some Man from Mars -- is not going to figure out how to do that in the course. To have a fighting chance, the framework would have to support it. That's why I was curious what the internal beta-testers speculated/noted on how students would manage the workflow of the exercises and quizzes.

As an aside, the "Man from Mars" reference is from the novel Stranger in a Strange Land (1961): a person who grew up on Mars absent from any humans returns as an adult to Earth; he is completely disoriented by many things he sees. The question of how a Man from Mars would cope with something was an idiom in certain circles for many years; I suspect that has waned in recent years, but it seemed perfect in this context.

POSTED BY: Phil Earnhardt

Hi Phil—I recall Feynman using that, yes :). I can only say that we will look into trying to implement this functionality, but can't offer any promises. As for testers, it's basically us on the Wolfram U team testing all of this stuff out. Admittedly, I'm not sure that we considered the perspective of someone new with no local installation that wanted everything in one editable auto-saved notebook per exercise set. It might be that the difficulties I mentioned—and others that I did not—precluded that consideration, or it might be that I personally think that these lessons and exercises all work best locally. (It's hard to say after the fact.)

POSTED BY: Arben Kalziqi

If or when this fictitious student/man (person) form Mars has a problem, a) the clever student, say a student from, oohhh, let’s say from MIT, would certainly be able to find any of the perfectly good solutions we have both mentioned B) the less nerdy but willing-to-ask learner would be helped by the very friendly, capable, and ever willing-to-help Wolfram folks. They really good about that!

POSTED BY: Lori Johnson
Posted 6 months ago

If or when this fictitious student/man (person) form Mars has a problem, a) the clever student, say a student from, oohhh, let’s say from MIT [...]

"Man from Mars" refers to someone who is a complete beginner with something -- not someone who has gone through several Wolfram U courses (like me). Why do you presume that someone with essentially zero background would guess there was some way to save a scratch notebook?

the less nerdy but willing-to-ask learner would be helped by the very friendly, capable, and ever willing-to-help Wolfram folks

Except that most are not willing-to-ask. Someone won't ask how to do something if they don't even know that it's possible. I "SAVE NOTEBOOK" button in the framework would be a Captain Obvious way to inform students that it was possible to save a notebook. Without an explicit bread crumb like that, you will only have a tiny percentage of students figuring out something like that. They wouldn't even know to ask the question.

POSTED BY: Phil Earnhardt

Hello Arben:

About Problem 4 on Quiz 3, are there more than one correct answer?

Hi Juan—yes, there's clearly an issue with this question. I'll modify it such that it makes sense and have it redeployed.

POSTED BY: Arben Kalziqi

Practice Problem Set 1 - Problem 4: I believe the equation to be entered into CountourPlot3D[] should be: 4x^2 + 4y^2 + 3z^2 -26z + 35 == 0. Correct?

POSTED BY: James Kralik

That is indeed correct, James—thanks for the catch!

POSTED BY: Arben Kalziqi

Dear Arben:

Thanks a lot for all your work. I truly appreciate it over many courses and webinars.

On Lesson 12, Exercise 5, what does it mean "join those regions together?"

Best, Juan Ariel

Hi Juan—thank you for your kind comments. In that exercise, the idea is that the function is a product of one function of x and y and another function of z. This means that you can find where the whole function is continuous in the x-y plane by looking at that first function, find out where it's continuous "out of the plane" (i.e. where z != 0) by looking at the second function, and then find the full 3D region where the whole function is continuous by taking the intersection of these two regions. ("Join" is a little imprecise there, I agree. I will update the notebook now to specify "intersection".)

For example, imagine a situation where f(x,y,z) = sqrt(x^2 + y^2 - 1) ln(1-z).

  • You can say that g(x,y) = sqrt(x^2 + y^2 - 1) and h(z) = ln(1-z), so that f(x,y,z) = g(x,y) h(z).
  • g(x,y) is continuous as long as its argument is non-negative, so you need that x^2 + y^2 - 1 ≥ 0, or x^2 + y^2 ≥ 1. This corresponds to the whole plane with the unit circle centered at the origin cut out.
  • h(z) is continous as long as its argument is positive, so you need 1 - z > 0, or z < 1.
  • In total, f(x,y,z) must be continuous only where x^2 + y^2 ≥ 1 and z < 1 at the same time. That looks like:

enter image description here

POSTED BY: Arben Kalziqi

Thank you Arben. Perhaps join was for the conditions, and intersection is better for regions.

You're welcome, of course! Maybe that's how I had intended it, but your comment made me realize that it was a bit unclear, so I'm glad that I could update it.

POSTED BY: Arben Kalziqi

In the Lesson 10 exercises notebook in Exercise 2 I notice the word problem states a function of cosines, whereas the solution uses a function of sines.

Regards, John Burgers.

POSTED BY: John Burgers

Thanks John—this is also fixed now.

POSTED BY: Arben Kalziqi
Posted 7 months ago

never mind thanks, i found the folder, i just can't access it 8-(

hello arben, i'm admittedly a little late to the course and trying to catch up, can you please (re)share the link to the course material folder? thanks, tom

POSTED BY: Tom Pearce

If you have the link, you should be able to access it. You should get the link in your reminder emails each day, and it's of course put up in the chat during each course. If the link isn't working for you, please email us (with the link) at wolfram-u at wolfram dot com and we'll figure out what's going on.

POSTED BY: Arben Kalziqi
Posted 7 months ago

You should get the link in your reminder emails each day, and it's of course put up in the chat during each course. If the link isn't working for you,

The link to the downloadable code blob should be put up in the chat every day, but it hasn't been posted in the BigMarker chat panel the past 2 days. The only thing posted on the chat page was a link to this discussion page. I don't need the URL, but I noticed that the download URL was missing. I posted a note that it was missing in the BigMarker comments area that pop up after the session. The link for the data blog has been regularly included in the reminder e-mails before the session, and the e-mails noting that each video is available for download.

POSTED BY: Phil Earnhardt

That's surprising to me—I've entered the preview room for tomorrow's lecture and the link is already pre-populated. I recall seeing a sticky link there in today's class, though I didn't need to click it (for obvious reasons). That link should be pre-populated for the entire study group series, so I don't see any reason that it shouldn't have been there on Friday or today. Also, that link works when I'm fully logged out and in incognito mode, so there should be no permissions issues.

I'll keep an eye out tomorrow, but something seems fishy!

POSTED BY: Arben Kalziqi

Indeed, this is what I'm seeing here:

enter image description here

POSTED BY: Arben Kalziqi
Posted 7 months ago

@Arben Kalziqi , here's a screenshot 3 minutes before the course is scheduled to start today, September 19, 2023:

enter image description here

The community forum link is noted, but there is no link for the download blob. Something is unhappy in the workflow....

POSTED BY: Phil Earnhardt

Hi Phil—please see attached :)

enter image description here

POSTED BY: Arben Kalziqi
Posted 7 months ago

Here's the long answer: "We used to explicitly post the URL for the download materials and the community forum URL in the Chat panel. We have changed this: while we still explicitly note the URL of the community forum, we now place the DOWNLOAD link behind a label. There are good reasons for this change! Sorry for any confusion this change may have caused." :)

POSTED BY: Phil Earnhardt
Posted 7 months ago

i have yet to see the download link for the code blob

POSTED BY: Tom Pearce

Hi Tom—it's in the same place for all DSGs, at the top of the chat panel in a light cyan color. You can see it explicitly circled in red in the screenshot within this thread.

POSTED BY: Arben Kalziqi
Posted 7 months ago

hello, i am not seeing that at all; i only seem to be "getting" the same link to the community group or more recently a link regarding the course framework enter image description here

POSTED BY: Tom Pearce
Posted 7 months ago

@tom pearce , e-mails from the "Wolfram U Team" should have the URL of the code blob. I just verified: the e-mail sent at 11AM EDT this (Thursday) morning definitely has the link the code blob. I recommend keeping all e-mails from the "Wolfram U Team" in your e-mail archive.

The e-mail sent out at 5:34 PM EDT today (Thursday) noting that today's video was available for viewing has the URL for the beta version of the interactive framework for the course. All videos and exercises are accessible from that.

I believe that each e-mail from "Wolfram U Team" should have both of these URLs, but each e-mail today was missing one of the links. The links do not change; once you have both of them, you should be fine.

The links that Arben mentioned in the BigMarker presentation are only viewable (and accessible) during the live presentation of the course. AFAICT, they are not available in the replay of the course. But you should be good if you kept the e-mails from "Wolfram U Team" today. That should get you running tonight.

POSTED BY: Phil Earnhardt
Posted 7 months ago

all good, thanks for taking the time with the explanation

POSTED BY: Tom Pearce

Hello,

I notice on Exercise 1 in the notebook Lesson 8 Exercises.nb the first entry is 1/(x-1) instead of 1/(t-1)

Regards, John Burgers

POSTED BY: John Burgers

Thanks John—fixed on our side.

POSTED BY: Arben Kalziqi
Posted 7 months ago

Arben, As I suggested in the Q & A, I would like to see an osculating sphere added to the 3D graph under the Unit Binormal Vector section. Does the osculating sphere contain the osculating circle? Do they have the same radius?

POSTED BY: Gerald Oberg

Hi Gerald—could I get confirmation on whether the osculating sphere is just the sphere with the same radius as the osculating circle? Documentation on this seems a little sparse/mixed. (If it isn't, do you have a particular reference which jives with your understanding of it?)

POSTED BY: Arben Kalziqi
Posted 7 months ago

Online References: (1) https://mathworld.wolfram.com/OsculatingSphere.html (2) Osculating Spheres of Space Curves - Brown University → https://www.math.brown.edu/tbanchof/balt/ma106/lab4.html?dtext46.html

DG Textbook References: (3) E. Kreyszig, “Differential Geometry”, Dover (1991) pp. 54-55; (4) R.S. Millman, G.D. Parker, "Elements of differential geometry", Prentice-Hall (1979) pp. 39; (5) D.J. Struik, "Lectures on classical differential geometry", Dover (1988) pp. 25

Video: (6) Osculating Plane, Circle, and Sphere for a Space Curve → https://www.youtube.com/watch?v=08C4U8x8F04

POSTED BY: Gerald Oberg

Excellent, thank you. I'll have a look at this and hopefully have some code for you on Monday.

POSTED BY: Arben Kalziqi
Posted 7 months ago

One of my wife’s favorite shrubs is a spiral cypress or boxwood topiary. I found pictures of a couple and used them to estimate curves that would approximate their shapes. I think a curve something like this would make a more satisfying animation of an osculating sphere moving along its curve than would a helix where the osculating sphere would not change size. enter image description here

POSTED BY: Gerald Oberg

Thanks for this example, Gerald—it was a fun little exercise. It ain't the prettiest thing, but here it is—feel free to ask me if you have any questions about how anything works or why I did any particular thing in any particular way.

You may have to download the notebook to see the actual visualizaiton; it's a little heavy to run on an embedded cloud notebook, I suspect.

POSTED BY: Arben Kalziqi
Posted 7 months ago

Arben, It is Fabulous! Thank you so much for your efforts on this!

POSTED BY: Gerald Oberg

You're welcome! I'm glad you like it. If you modify the plot range a little bit, you could do this for any space curve you have in mind. Maybe I'll modify it to just accept an argument specifying the plot range so that other folks can play with this.

POSTED BY: Arben Kalziqi

This isn't a problem, I just thought it was hilarious. Before I evaluated the code in one of the lesson notebooks, this was the error:

enter image description here

It would be funny if "graphicsStuff" actually became a thing!

POSTED BY: Lori Johnson

Coming in Wolfram Language v14.0: graphicsStuff!

(This should be fixed in the currently-uploaded version.)

POSTED BY: Arben Kalziqi
Posted 7 months ago

Coming in Wolfram Language v14.0: graphicsStuff!

Are you testing us? That would have to be big-g GraphicsStuff. :)

POSTED BY: Phil Earnhardt

He's just kidding with me!

POSTED BY: Lori Johnson

Cool, thanks, Arben! [star eyes emoji]

(this message board does not like emojis)

POSTED BY: Lori Johnson

I am looking for the recording from today's (9/13) class but it's not in my in-basket. Has it been released?

Carl

POSTED BY: Carl Hahn

Hi Carl—it should be there now. Not sure why it was late; there can be a little variability with BigMarker on occasion.

POSTED BY: Arben Kalziqi

Hi Arben,

Happy to be taking part in another study group!

ISSUES:

a. I'm running 13.3.0. on OS X. When the magnification is increased from 50% to 75% or 100%, this error is generated: enter image description here The magnification does actually increase and the notebook functions fine, it's just annoying.

b. Are the "Solution" cells meant to be set to "open" in the exercise files? This happens with the updated files and I did refresh the files page before re-downloading the files.

There were some errors that were fixed in the update, so that was nice!

Any help would be appreciated.

Lori

POSTED BY: Lori Johnson

Hi Lori—I actually have been getting your first problem myself and had assumed that it was just something in my installation as I have a custom magnification set! Interesting; I'll look into this. And yes, the solution cells for the exercises are meant to be open. You are of course free to try them yourself first.

A little secret useful thing is that if you hold—on a Mac, at least—Option while clicking a cell bracket, it'll select all cells of that type. So you can hold opt, click the cell bracket for any Solution cell, then right click the cell and click "close all subgroups". It will then collapse all of the Solution cells.

POSTED BY: Arben Kalziqi

Hi Arben!

Thanks for the reply! You didn't have to be late to the study group replying to my comment!

Keep this in mind: open solution cells deny us the satisfaction of testing our recall for some, and for others, practicing new skills. Learning can't be an enjoyable challenge if the answers are so easily accessible. There's a reason the answers in textbooks are in the back.

Your "secret" 'select multiple things' tip should be helpful to one or two people!

Will submit any more issues later.

POSTED BY: Lori Johnson

Thanks for your feedback, Lori. I'll talk to the team about perhaps uploading and deploying these notebooks with the Solutions cells collapsed by default.

POSTED BY: Arben Kalziqi

Copious thanks! That you considered this perspective makes this educator beyond happy for all the future nerds who enjoy stretching their brains [triple happy face+nerd emojis]

POSTED BY: Lori Johnson

Indeed :). I believe the exercise notebooks which will be deployed to the full course framework will have this change made when the course goes live.

POSTED BY: Arben Kalziqi

In Lesson 5 Exercises, Exercise 3, Point C should be be {5,2} to complete the parallelogram. Doesn't affect the rest of the calculations since it is not used in the calculations.

POSTED BY: Thomas Rike

Thanks Thomas; this is fixed in the latest version of the exercises.

POSTED BY: Arben Kalziqi
Posted 7 months ago

Hello! I currently use Mathematica 12. The .nb files open in 12 but they are not looking good/useful. Any way to fix this aside from upgrading straight away?

POSTED BY: Michael Macon

Hi Michael. Could you give me an example of what you're seeing? I think that most things should work well enough in 12, but I don't have a copy installed currently.

POSTED BY: Arben Kalziqi
Posted 7 months ago

The text is vertical. See the pic. enter image description here

POSTED BY: Michael Macon

Holy moly! I'll ask internally about this.

POSTED BY: Arben Kalziqi

Michael, I might have to direct you to our tech support, but I'm curious whether this happens with the other notebooks as well. You say "files"; does that mean that the other lessons so far have all opened like this? Do the later notebooks do the same?

Hopefully we can work this out!

POSTED BY: Arben Kalziqi
Posted 7 months ago

Thanks for the follow-up. I tested out a bunch of the lessons and they all open that way---the words are vertical. I wonder if there's a simple setting I can adjust to view them as intended....

By the way, I tried on both Windows 10 and MacOs 11.7.8 (two different computers) and had the same result.

POSTED BY: Michael Macon

Two installations on different OSes is very strange indeed. I've had someone check in 12.3 on Windows 11 and it worked for them, at least. Could you try changing the magnification and letting me know what happens? Simple idea, I know, but I'm curious.

POSTED BY: Arben Kalziqi
Posted 7 months ago

Yes--I thought about the magnification too. Changing that did not make a difference.

POSTED BY: Michael Macon

I tried opening the files in Mathematica 11.2 and 10.0 on my PC and in both cases I just got an empty window. Correct file title, but nothing to see. I am working off my MAC with a current version of 13.3 and that opens fine.

POSTED BY: Carl Hahn

Thanks Carl. I believe we've found the issue and will be pushing out an update.

POSTED BY: Arben Kalziqi

Carl, if you download the latest versions of the notebooks on Amoeba, do you still have this issue?

POSTED BY: Arben Kalziqi
Posted 7 months ago

Hi, Michael. I'm running Mathematica 12.2, and I'm having no problem using the notebooks of this course. I've never having any issue downloading/running notebooks from Wolfram Research. I suspect your problem is not related to the version of Mathematica you're running.

I do get "Why the bleep" warnings -- a warning that I'm running an earlier version of Mathematica that the notebooks were saved in. I just ignore that error and use the notebook:

enter image description here

POSTED BY: Phil Earnhardt

As Hahn said, I, too, have some volunteer commitments at the same time, and I will rely on the recordings when I miss the live classes.

POSTED BY: Charles Glover

No problem, Charles. I think as a fellow physicist, you'll find a lot to appreciate here.

POSTED BY: Arben Kalziqi

Hi everybody,

We're hoping to get the permissions issue with our file-sharing service worked out by the end of the day today. I won't bore you with the details, but suffice it to say that we've had to go pretty high up in the IT chain on this one.

In the meantime, you can find all of the Lesson and Exercise notebooks at this new link.

See you tomorrow!

EDIT: We've fixed the issue and now the original link should have all of the Lesson and Exercise notebooks—including Aurelius' catch on an early exercise—should be available via the original link. I've thus updated the link above back to the original link.

POSTED BY: Arben Kalziqi

Trivial, but there is a typo in Lesson 3, Exercise 3:

vec1 = {4, 4 - 1};

should be

vec1 = {4, 4, -1};

which requires one change further down:

Graphics[{Red, Arrow[{{0, 0}, vec1}], Blue, 
  Arrow[{{0, 0}, unitVec1}]}]

should be:

Graphics3D[{Red, Arrow[{{0, 0, 0}, vec1}], Blue, 
  Arrow[{{0, 0, 0}, unitVec1}]}]

Thanks Aurelius! I've fixed this in my local copy and replaced it in our (perhaps temporary) updated materials link which I'll post in this thread.

POSTED BY: Arben Kalziqi
Posted 7 months ago

Re: the discussion of handedness in Monday's presentation, the handedness of physical objects is one of my favorite science topics. Physics/engineering students are aware of the use of the right-hand rule to visualize moving charged particles, current in a wire, and the associated magnetic fields. Handedness also plays a huge role in chemistry. Flipping the handedness of every molecule and structure in the human body would have a huge impact on the function of the human. Roger Zelazny speculates about such a flipping in a delightful little novel Doorways in the Sand. The quick read may be at a local library, or it could even be found online as a PDF.

CJD in the 1980s was related to wrong-handed molecules altering the structure of proteins in the brain; the Red Cross used to have screening questions about "Mad Cow Disease". Fortunately, this disease appears to have disappeared.

Turnbuckles have left-handed threading on one end of the bolt and right-handed threading on the other end. There must be distinct nuts with the two threadings to secure the tension. Polymath and tensegrity-maker Gerald de Jong has created a Turnbuckle Tensegrity: he figured out how to 3DP struts and nuts with both threadings. Gerald mentioned this model on social media, but he hasn't published anything about it on his website yet. Almost all turnbucles used in the world (e.g., screen door diagonal lines, container ship lashings, etc.) are at tension. Gerald's tensegrity-struts are in compression. Only those who pay excessive attention to turnbuckles would notice this structural pun.

The most famous left-hand screw is MIT's Big Screw award a penny-a-vote contest awarded to an instructor who did some "bad" thing to his/her/their students in the spring term. It is a massive screw with left-hand threading. The story of this winner is here):
enter image description here

Math Professor AP Mattuck apparently won the award twice; I know nothing about the circumstances. Perhaps he was teaching multivariable calculus one of those times...

POSTED BY: Phil Earnhardt

Phil—I'd heard about CJD in this context but the rest of this was news to me! Very amusing and interesting :).

POSTED BY: Arben Kalziqi

I am looking fwd to this class. I've previewed some of the Notebooks and they are awesome. Both for the Calculus and the beautiful examples of Mathematica code. As Gleison said, I too have work commitments at the same time, but I will be catching the recordings when I miss the live classes.

POSTED BY: Carl Hahn

I'm glad that you think so, Carl! I think the addition of the exercises will round things out and help you to start making beautiful visualizations like you see in the course on your own. (Though of course, basically every visualization in both the lessons and exercises has its code included in the notebook, and that alone is very useful!)

POSTED BY: Arben Kalziqi
Posted 7 months ago

Hi Arben, Thank you for making this introduction to multi-variable classes. I will try my best to attend all classes, but due to work commitments, I am not certain it will always be possible. I hope this is not a problem. I am looking forward to diving deep into the subject matter and making the most of the learning opportunities provided. My best regards, Gleison

POSTED BY: Gleison Silva

It's no problem at all! You will receive recordings of each day's lectures and will—later in the study group—have early access to the course framework, i.e. videos + lesson notebooks + quizzes + exercises.

POSTED BY: Arben Kalziqi

Hi everybody! This study group starts this coming Monday, so I wanted to bump this post as a reminder. See you soon!

POSTED BY: Arben Kalziqi
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