## 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

The final exam will count 30% of your overall grade.

**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.

The Grade and Makeup Information