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.