Math 317: Calculus IV

This fall-winter semester I will be the lecturer for Math 317-101.

Lectures are Monday, Wednesday, and Friday from 10am to 11am in Buchanan A203. Office hours are on Monday from 11am to noon in LSK 303c, and Thursday from 4pm to 5pm in LSK 303b.

The textbook is `Multivariable Calculus, 7th edition' by J. Stewart (the 5th or 6th editions are also fine).

This is the course outline.

Homework assignments:

Assignment 1: from Section 13.1: exercises 4, 10, 12, 16, 30, 40, 48. Solutions: page 1, page 2, page 3.

Assignment 2: from Section 13.2: exercises 6, 8, 16, 20, 48. From Section 13.3: 2, 16. Solutions: page 1, page 2, page 3, page 4.

Assignment 3: from Section 13.3: exercises 18, 22, 24, 32, 50. From Section 13.4: 4, 8(a).

Trivia

Wolfram Alpha agrees that the osculating circle of \(y=\ln x\) at \(x=1\) has radius \(2\sqrt{2}\) and center \((3,-2)\).

Using computers to visualize and solve problems

Computers are an (almost) indispensable tool for the type of 3-dimensional mathematics that we are studying, because computers are much better at drawing surfaces, curves, and vector fields than most humans are. For this reason I encourage you to try and use some computer programs while studying the material and while making the homework. One huge caveat here is of course that you cannot rely on computers to do everything for you, because you will not be allowed to bring a computer to the midterms or final (not even a graphical calculator). But even so, a computer will help you visualize the material, and that will make it easier to understand.

The first tool that I would recommend is Wolfram Alpha. This is a website that can process queries about (among other things) mathematical problems, and that can solve them using symbolic manipulations (i.e., it understands that \(\cos^2 t + \sin^2 t = 1\)). Be careful, because Wolfram Alpha is a bit finicky, and a single misplaced parenthesis or poorly defined variable can make it impossible to use. (But the same holds to a higher degree for other math apps as well.)

The downside to Wolfram Alpha is its limited scope (you can't, for instance, rotate 3D graphs to get a better look). For those of you who want more options, I recommend a serious math application. My favorite is Mathematica, but Matlab and Maple are also good. The problem with these three apps is that they cost a lot of money (although students can get a license at a discount). A good free alternative is Scilab, which is very similar to Matlab.
Here are some examples of code that produces graphs in Scilab: a surface, a helix, the intersection between a cylinder and a cubic surface, a toroidal spiral, and a cubic curve.

Boilerplate

The grading scheme will be: Grade = 50% Final + 20% Midterm 1 + 20% Midterm 2 + 10% Homework.

There will be 10 homework assignments, due on Wednesdays (except in midterm exam weeks).

Homework is due at 10am on Wednesday, before class begins.
No late homework will be accepted.

Your two lowest homework scores will be dropped. No further concession
will be made, for any (including medical) reason.

If you miss one of the midterm exams for medical reasons, you need to inform me as soon as possible,
and provide a doctor's note specifically stating that you were medically unfit to write the missed
exam on that day. Doing so will ensure that I will replace the missing mark with your final mark when
calculating your final grade. No make-up exams will be given.