Math 318 Fall, 2013
Review session for the Final: Dec 16 Monday 5:30-7:30 at UMRATH 140
Office hours for the Final: Dec 9 Monday 4:00 - 5:30, Dec 16 Monday 2:00 - 4:00, or by appointment
Final Exam: Dec 18 Wednesday 1:00-3:00 at Wilson 214
Here is a Practice Final.
Here is the course grades.
Lectures: MWF 1:10-2 Wilson 214
Instructor: Songhao Li Office: 207A Cupples I
Phone: (314)935-4208 email: sli@math.wustl.edu
Office Hour: M 2:30-4, F 11-12
Grader: Yiqian Fang
Course Webpage: http://www.math.wustl.edu/~sli/math318_fall2013/course.html
Textbook: Multivariable Mathematics by Theodore Shifrin
Suggested: Calculus on Manifolds by Michael Spivak (This text could be useful if you have taken Math 310.)
After
a brief review of linear algebra of Euclidean space, we study calculus
of several variables with some rigour. Topics may include:
-- Limits and continuity;
-- Derivatives and extrema;
-- Integrations;
-- Introduction to manifolds.
COURSE GRADE:
Homework 20%
Test 1 (Oct 7) 20%
Test 2 (Nov 11) 20%
Final (Dec 18) 40%
Tests will be in class and of 45 minutes in length.
Homeworks:
While collaboration is permitted, and in fact, encouraged, one should write up his/her own solution.
In other words, the exchange of ideas is permitted, but sharing the submitted version is not.
Please note that the grader and I will take notice of striking similarity in writing and take approriate action.
Assignments are due at the beginning of the class.
It is okay if you are late by a few minutes, but no late assignments will be accepted unless you have a valid reason.
If you cannot make it to a class when an assignment is due, you may arrange for a friend to submit it for you.
There
will be about 8 assignments, to be posted here. Hand-written solutions
are provided for your convenience. They have not been proof-read and
may contain minor errors.
Week 1
Aug 28: vectors in R^n Homework 1
Aug 30: dot product and subspaces of R^n
Week 2
Sept 2: Labour Day - No Class
Sept 4: linear transformation and matrix multiplication
Sept 6: vector-valued function of several variables and topology of R^n
Week 3
Sept 9: topology of R^n continued Homework 2
Sept 11: topology of R^n continued
Sept 13: function limit
Week 4
Sept 16: function continuity
Sept 18: function continuity continued Solution 1
Sept 20: directional direvative
Week 5
Sept 23: direvative Solution 2
Sept 25: direvative continued Homework 3
Sept 27: direvative continued
Week 6
Sept 30: direvative coninued
Oct 2: differentiation rules
Oct 4: review Solution 3
Week 7
Oct 7: Test 1 Test 1 with solution
Oct 9: differentiation rules continued (chain rule) Homework 4
Oct 11: differentiation rules continued (appliations of chain rule)
Week 8
Oct 14: Test 1 reviewed
Oct 16: gradient
Oct 18: Fall Break - No Class
Week 9
Oct 21: gradient continued Solution 4 Homework 5
Oct 23: curves - arclength
Oct 25: curves - curvature
Week 10
Oct 28: higher order partial derivatives
Oct 30: higher order partial derivatives Solution 5 Homework 6
Nov 1: Compactness and Maximum Value Theorem
Note: We will not cover Chapter 4 in class. Instead, we will pick up linear algebra results as needed.
Week 11
Nov 4: Maximum/Minimum Pratice Test 2
Nov 6: Second derivative test - examples
Nov 8: Review Solution 6
Week 12
Nov 11: Test 2 Test 2 with solution
Nov 13: Second derivative test - proof Homework 7 (updated, removed 5.2.3)
Nov 15: Second derivative test - examples and counter examples Term grades
Note:
Differing from Shifrin, we use the signs of the eigenvalues of a
symmetric matrix to determine if the corresponding quadratic form is
positive definite, negative definite or indefinite.
Week 13
Nov 18: Lagrangian multipliers - proof
Nov 20: Lagrangian multipliers - examples
Nov 22: Contraction mapping principle - examples Solution 7
Week 14
Nov 25: Contraction mapping principle - proof Homework 8
Nov 27: Happy Thanksgiving - No Class
Nov 29: Happy Thanksgiving - No Class
Week 15
Dec 2: Inverse function theorem
Dec 4: Inverse function theorem - proof
Dec 6: Implicit function theorem Homework 9 (Not to be handed-in) Solution 8 Solution 9