MATE 4052 Advanced Calculus
- Time and place
- LWV 8:30--9:20, SH-004.
- Topics
- Normed vector space. Banach space, convergent series, spaces of
linear and multinear operators.
- Differentiation. Properties of the derivative, derivative of
mappings into products of Banach spaces.
- Mean value theorem and applications.
- Local inversion theorem and implicit function theorem.
Time permitting:
- Higher order differentiation, Taylor expansions, approximation to
finite order, calculus of extrema.
- Application to differential equations.
- References
- R. Coleman, "Calculus on Normed Vector Spaces", Universitext,
Springer (primary reference).
- T. Apostol, "Mathematical Analysis", 2nd edition, Addison-Wesley,
1974.
- H. Cartan, "Differential Calculus", Hermann, 1971.
- W. Rudin, "Principles of Mathematical Analysis", 3rd edition,
McGraw-Hill, 1976.
- Evaluation
- Based on homework, exams.
- Homework updated May 11.
Last modified: Thu May 12 03:11:12 AST 2016