Math 521 - Advanced Calculus
- Prerequisites: Math 340 or concurrent registration. Students are advised to take Math 421 or Math 341 before Math 521.
- Frequency: Fall (I), Spring (II), Summer (SS)
- Student Body: Math majors, Physics and Engineering majors and graduate students in related areas
- Credits: 3. (N-A)
- Recent Texts: S. Lang, Undergraduate Analysis, 2nd ed. (Springer-Verlag)
- 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: Students can consider Math 421 for a weaker version of Math 521
- Subsequent Courses: Math 522.
Content coverage:
- The real numbers, R and R^n
- Elements of set theory
- Some topological properties of R^n
- Sequences and series of real numbers
- Functions, limits, continuity
- Differentiation
- Integration
- Sequences and series of functions, uniform convergence, power series, the elementary functions
- Fourier series
- Curve length
- Metric spaces and advanced topics
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