$\newcommand{\R}{\mathbb R }$ $\newcommand{\bfa}{\mathbf a}$ $\newcommand{\bfb}{\mathbf b}$ $\newcommand{\bfu}{\mathbf u}$ $\newcommand{\bfx}{\mathbf x}$ $\newcommand{\bfy}{\mathbf y}$ $\newcommand{\ep}{\varepsilon}$
Fall Term
For the Fall Term, weeks begin on Thursdays and end on Wednesdays.
Week 1 (September 6-12). Preliminary material:
Week 2 (September 13-19).
Week 3 (September 20-26).
Week 4 (September 27-October 3).
Week 5 (October 4-10).
Week 6 (October 11-17). More on differentiation:
Week 7 (October 18-24).
Week 8 ((October 25-31).
Week 9 (November 1-14).
Week 10 (November 15-21). Extreme Value Problems: Online Notes, Section 2.8.
Week 11 (November 22- 26) The Implicit Function Theorem:
Week 12 (November 29 - December 5). The Implicit Funcrion Theorem, continued, and the Inverse Function Theorem: Online Notes, Section 3.2
Spring Term. Dates in the later part of the term are tentative.
Week 13 (January 7-11). Last remarks on the Implicit and Inverse Function Theorems, and review of integration of functions of a single variable. Reference: Online Notes, Section 4.1
Week 14 (January 14-18). More on the basics of integration, for functions of 1 and more variables. Reference: Online Notes, Section 4.2
Week 15 (January 21-25).
The basics of integration for functions of several variables
(continued), and Iterated Integrals. Reference:
Online Notes, Section 4.3
Week 16 (January 28 - February 1). Changes of variables for multiple integrals. Reference: Online Notes, Section 4.4
Week 17 (February 4-8). Additional topics related to integration, including improper integrals and differentiating under the integral sign. Reference: Online Notes, Section 4.5
Week 18 (February 11-15). line integrals. Reference: Online notes, Section 5.1 See also Section 5.1 of Folland's Advanced Calculus
Week 19 (February 25 - March 1). Green's Theorem, surface area, and surface integrals Online notes, Section 5.2, to appear See also Sections 5.2 and 5.3 of Folland's Advanced Calculus.
Week 20 (March 4-8). surface area, and surface integrals (cont'd) div, grad and curl, and the Divergence Theorem. Online Notes, to appear See also Sections 5.4 and 5.5 of Folland's Advanced Calculus.
Week 21 (March 11-15). Stokes Theorem
Week 22 (March 18-22). related topics and applications
Week 23 (March 25-29). Introduction to Fourier series, time permitting; make-up for cancelled lectures.
Week 24 (April 1-5). a little more about Fourier series, time permitting.
Fall Term
* Sept. 24-28: Tutorial 1, no quiz,
Homework 1.1, due September 28.
* Oct. 1-5: Tutorial 2, Quiz 1.
* Oct. 8-12: no tutorial, no quiz.
Homework 1.2, due October 12.
* Oct. 15-19: Tutorial 3, Quiz 2.
Term Test 1, October 19.
* Oct. 22-26: Tutorial 4, no quiz.
* Oct 29 - Nov. 2: Tutorial 5, Quiz 3.
* Nov. 12-16: Tutorial 6, no quiz.
Homework 1.3, due November 16.
* Nov. 19-23: Tutorial 7, Quiz 4.
Term Test 2, November 23.
* Nov. 26-30: Tutorial 8, no quiz.
Homework 1.4, due December 5.
Spring Term (tentative).