MATH 413
Advanced Calculus

Fall Semester 2003

Exam 4: take home part

TIME OF MEETING: Tue & Thr  1:00 - 2:20
INSTRUCTOR: Karin Reinhold,  ES 128A,  phone 442-4641
Office hours:   2:25-3:00 Tues Thrs  or by appt.,  or by e-mail.
TEXT: Advanced Calculusd, by Folland, Prentice hall.


This is the first part of a year long course in Advanced Calculus.

Preliminars: some topology of euclidean spaces, sun=bsets, limits and continuity, sequences, completeness, compacteness, connectedness, uniform continuity.
Differential Calculus in R^n: Diferentiability, algebra of differentiable functions, differentiation of vector valued functions, the Chain Rule, the Mean Value Theorem. Higher order partial derivatives, Taylor's Theorem, critical points, extreme value problems. Vector valued functions.
Implicit Functions: The Implicit Function theorem, curves in the plane, surfaces and curves in space, transformations and coordinate systems, functional dependence.
Integration in higher dimentions, multiple integrals, Riemann sums. Evaluation via iterated integrals, change of variables, functions defined by integrals, improper integrals.

TEST SCHEDULE: (tentative)

Sept 23: Exam 1, chapter 1
Oct 23: Exam 2, chapter 2
Nov 13: Exam 3, chapter 3
Dec 9: Exam 4, chapter 4
Dec 15: Final Exam 10:30-12:30
The above schedule is ambitious, we'll adjust it as we advance thorugh the material of the course. The final grade will be based on homework assignments and the best three scores of your tests. A minimum average of 50% is required to pass the course, not more than one exam can be failed (below 30%), all 4 exams are required to pass the course, plus a final exam.
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