Math 522 - Advanced Calculus
- Prerequisites: Math 521.
- Frequency: Spring (II)
- Student Body: Math majors, Physics and Engineering majors and graduate students in related areas
- Credits: 3. (N-A)
- Recent Texts:
- Course Coordinator: Patrick Ahern.
- Background and Goals: The sequence Math 521-522 has the objective of conveying an understanding of the structure of analysis in itself as well as its role as a tool for other disciplines. This sequence is highly recommended for any math major and it is essential for students preparing for graduate studies in mathematics; also it should be taken by students in physics and engineering who intend to do graduate work in their areas.
- Alternatives: N/A
- Subsequent Courses: Math 623
Content coverage:
- Functions on n-space.
- Differentiability, chain rule, Taylor's formula.
- Maps from R^m into R^n.
- The derivative as a linear map.
- Inverse mapping theorem.
- Implicit functions.
- Shrinking Lemma (contraction).
- Multiple integration.
- Elementary multiple integration and iterated integrals (review).
- Change of variable.
- (k-dimensional) Area.
- Differential forms (essentially in R^n).
- Poincare's Lemma.
- Stokes' Theorem.
- Grad, curl, and div.
- Laplacian.
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