MATH 326 Syllabus
- Prerequisites: 324, 308
- Text: Advanced Calculus,3rd edition , by Taylor
and Mann.
- Questions:
Please contact Brooke Miller (C-36F, 3-6830)
if you have questions or suggestions concerning the syllabus.
Note: The level of rigor of 326 is higher than that of 324, but
is not at the
level of the somewhat axiomatic treatment in 327-8. Arguments are made
to
justify such theorems as the implicit function theorem, but students
are
not expected to make small proofs to work problems.
Syllabus for 26-29 Lectures
Note: Sections refer to the textbook.
The number of lectures allotted to the various topics are meant as
guidelines,
only.
- 1. Elementary Topology:
-
- §5.1, §5.2, §5.3 (3 lectures)
- 2. Elements of Partial Differentiation:
-
- §6.1-§6.5 (4-5 lectures): (Partial derivatives,
implicit functions, geometrical significance of partial derivatives,
maxima
and minima, differentials, composite functions and chain rule)
- §6.6-§6.8 (3 lectures): (Derivatives of implicit functions,
extremal problems with constraints, Lagrange multipliers)
- 3. General Theorems on Partial Differentiation
-
- §7.1-§7.5 (5 lectures): (Includes material on equality of
mixed partials and Taylor's
Theorem in several variables)
- 4. Implicit Function Theorem
-
- 5. Inverse Function Theorem and Transformations
-
- 6. Change of Variables Formula
-
- Review Green's theorem and Divergence theorem (1 lecture)
- §15.32, §15.62 (2 lectures)
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