MATH 413
Advanced Calculus
Fall Semester 2003
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Tue & Thr 1:00 - 2:20
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| PLACE: |
ES 142
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| INSTRUCTOR: |
Karin Reinhold, ES 128A, phone 442-4641
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| Office hours: 2:25-3:00 Tues Thrs
or by appt., or by e-mail.
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TEXT: |
Advanced Calculusd, by Folland, Prentice hall.
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PRE-REQUISITE: |
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COURSE OBJECTIVE:
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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