Math 318 Spring, 2015

Lectures: MWF 2:10pm-3:00pm Room 230 Cupples II

Instructor: Songhao Li **Office:** 207A Cupples I

**Phone:** (314)935-4208** email****:** sli@math.wustl.edu

**Office Hour: **MW 1pm-2pm or by appointment

**TA:** Jongwhan Park

**TA office hour:** MW 4:30pm-5:30pm Room 8 (basement) Cupples I

**Course Webpage:** http://www.math.wustl.edu/~sli/math318_spring2015/course.html

**Textbook:** *Multivariable Mathematics by* Theodore Shifrin

**Suggested:** *Calculus on Manifolds by* Michael Spivak

Note:
Spivak is a more advanced and more condensed textbook. It is useful if
you plan to pursue graduate studies in mathematics or math-related
subjects.

We will cover most, if not all, of the following topics:

-- Linear algebra of Euclidean space;

-- Limits and continuity;

-- Derivatives and extrema;

-- Inverse and implicit function theorems;

It is unlikely that we will have time to cover integration, but for your own sake, it will give a more complete picture if you read the chapters on integration.

For
most of you, even though the topics sound familiar, the course will
feel significantly different from the previous calculus courses you
have taken.

Everything will be defined and proved with rigour.

COURSE GRADE:

Homework 20%

Test 1 (Feb 11) 20%

Test 2 (Mar 18) 20%

Final (May 4) 40%

Tests will be in class and of 45 minutes in length.

Jan 16: functions on R^n

Jan 23: topology of R^n: closed sets

Jan 30: continuity

Feb 4: derivative

Feb 6: examples of derivative

Note: Assignment 4 is due on Feb 20!

Feb 11: test 1

Feb 13: continuous partial derivative implies differentiablity

Feb 20: chain rule

Feb 27: arclength

Mar 6: Kepler's 3rd law (cf. Exercise 3.5.15)

Mar 20: Higher order partial direvatives

Mar 25: Compact subset of R^n

Apr 1: Critical points and examples

Apr 8: Examples of 2nd derivative test

Apr 10: Lagrangian multiplier

Apr 17: Contraction mapping principle

Apr 24: Proof of inverse function theorem, implicit function theorem