## Advanced Calculus, Fall 1999 - Spring 2000.

Instructor: Professor Wei-Cheng Wang,

Meeting: General III building, room 109, T1T2F1F2.

First Class: September 17, 1999

Grading: 30% Homework+quiz, 40% (20%+20%) midterm and 30% final exam.

Textbook: J. E. Marsden: Elementary Classical Analysis (1993)

Course description:

Announcement:

Check back from time to time for updated information:

Final:

Coverage: Sections 8.1-8.5, 9.1-9.5, 9.7.

Date: June 16, 8AM - 10AM

Major topics:

Chapter 8:

Measure zero sets: Deinition and examples (examples are important), relation with Rimann integrable functions.

Riemann integrals:

Integrable functions, Lebesque Theorem and sets with volume:

Improper integrals: Pay extra attention to the construction procedure.

Convergence of Improper integrals of elementary functions:

Typical questions are like the quiz on June 2nd.

Chapter 9:

Fubini's Theorem: Be careful about domain of integration when switching order of integrations.

Change of variable formula: try calculate the Jacobian and write down the intrgration formula for an arbitrary change of variable. Pay attention on the one to one condition, (there's a home work problem on this subject). Applications to cylindrical and spherical coordinates.

Interchanges of limits, integrations and derivatives: For example, a typical question would be: Give a sufficient condition such that the statement in Example 9.7.1 is true. Give a counter example when the condition is not satisfied.