# Vector Calculus with Linear Algebra and Applications Math 390, Spring 2011

## Course Materials

Syllabus [pdf]
Results from Survey on Study Habits
Why Vector Calculus rather than Multivariable Calculus? [html]

Schedule, Lecture Notes, and Homework

## LaTeX Information

Tex User's Group
LaTeX Software
An Introduction to Latex (Harvard Math Dept)
LaTeX on Wikipedia
The Not So Short Introduction to LATEX2e
LaTeX Commands Crib Sheet
LaTeX source of Homework 1 Problem Set
LaTeX source of Homework 2 Problem Set
LaTeX source of a lectures notes on Inverse Function Theorem

## Background Material From Multivariable Calculus and Linear Algebra

I will assume that students understand the theory and can do problems on the following topics from Math 251. Below, for each Chapter of [BL] Blaxandall and Liebeck we will cover in our course, I list the sections of [S] Stewart's "Calculus (Early Transcendentals)", and the corresponding sections of [SM] Smith and Minton's "Calculus", you need to have under your belt. Those sections tagged with R will be redone (fairly quickly) in our course.

For Chapter 2 of [BL]:
Stewart [S]: 12.1, 12.2, 12.3 (omit direction cosines), 12.4 (omit torque), 12.5 (R) (just parametrization of line and equation for plane), 12.6 (R), 13.1, 13.2 (derivatives only), 13.3 (arclength only).
Smith and Minton [SM]: 10.1, 10.2, 10.3, 10.4, 10.5 (R) (just parametrization of line and equation for plane), 10.6 (R), 11.1, 11.2 (derivatives and arclength only).

For Chapter 3 of [BL]:
[S]: 14.1, 14.2 (R), 14.3, 14.4 (R), 14.6 (R).
[SM]: 12.1, (R), 12.3, 12.4 (R), 12.6 (R).

For Chapters 5 and 6 of [BL]:
[S]: 16.1 (R), 16.2, 16.3 (FTC only) (R)
[SM]: 14.1 (R), 14.2, 14.3 (FTC only) (R)

For Chapter 7 of [BL]:
[S]: 15.1-15.3, 15.9 (R), 16.4 (R)
[SM]: 13.1, 13.2, 13.8 (R), 14.4 (R)

For Chapter 10 of [BL]:
[S]: 15.6 (R)
[SM]: 13.5 (R)

Suggested problems from Smith and Minton from the last time I took the course. I strongly recommend you do at least some of them.

OR: Suggested problems from Stewart from the last time I took the course. I strongly recommend you do at least some of them.

I will also assume familiarity with the following sections of David Lay's "Linear Algebra and its applications" (3rd edition update). This includes selected material from Math 221. Much of this material will be redone at a somewhat higher level from a geometric point of view in the first few lectures of the course.

1.2, 1.4, 1.5, 1.7-1.9, 2.1-2.3, 4.1-4.6.

Suggested problems from Lay from the last time I took the course.

## Exam I Info

Exam I will cover all material up to and including 2.10 (except for the Overview). In particular it covers the material discussed in the Linear Algebra review, though not the vector calculus review problems in Hwk 1.

Note that as I do in my Math 430 exams, some questions will require you to state definitions, theorems, give simple examples and counterexamples. Others will involve calculations and still others will require you to prove results. Any proofs will be similar to ones discussed in class or on hwk.

Exam I Solutions [pdf]