Walter Rudin 3종 세트: PMA, RCA, FA
Principles of Mathematical Analysis(PMA)는 해석학 교재로 가장 많이 쓰이는 책 중 하나이다. 해석학 교재 하면 대부분의 사람이 PMA를 추천한다Chapter 9~11는 보지 않는 것이 정신건강에 좋다. 물론 Rudin의 책답게 영 좋지 않은 서술이 되어 있다. 출판사는 McGraw Hill, Inc.이다. 참고로 아마존 평점은 4.2 out of 5 stars로, 높은 편이다.[1]
목차
이하 Appendix(부록)와 Exercises(예제)는 생략한다.
Chapter 1. The Real and Complex Number Systems
- Introduction
- Ordered Sets
- Fields
- The Real Field
- The Extended Real Number System
- The Complex Field
- Euclidean Spaces
Chapter 2. Basic Topology
- Finite, Countable, and Uncountable Sets
- Metric Spaces
- Compact Sets
- Perfect Sets
- Connected Sets
Chapter 3. Numerical Sequences and Series
- Convergent Sequences
- Subsequences
- Cauchy Sequences
- Upper and Lower Limits
- Some Special Sequences
- Series
- Series of Nonnegative Terms
- The Number e
- The Root and Ratio Tests
- Power Series
- Summation by Parts
- Absolute Convergence
- Addition and Multiplication of Series
- Rearrangements
Chapter 4. Continuity
- Limit of Functions
- Continuous Functions
- Continuity and Compactness
- Continuity and Connectedness
- Discontinuities
- Monotonic Functions
- Infinite Limits and Limits at Infinity
Chapter 5. Differentiation
- The Derivative of a Real Function
- Mean Value Theorems
- The Continuity of Derivatives
- L'Hospital's Rule
- Derivatives of Higher Order
- Taylor's Theorem
- Differentiation of Vector-valued Functions
Chapter 6. The Riemann-Stieltjes Integral
- Definition and Existence of the Integral
- Properties of the Integral
- Integration and Differentiation
- Integration of Vector-valued Functions
- Rectifiable Curves
Chapter 7. Sequences and Series of Functions
Chapter 8. Some Special Functions
Chapter 9. Functions of Several Variables
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