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