具体描述
This logically self-contained introduction to analysis centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. From the reviews: "This material can be gone over quickly by the really well-prepared reader, for it is one of the book's pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it." --AMERICAN MATHEMATICAL SOCIETY
作者简介
Serge Lang (May 19, 1927 – September 12, 2005) was a French-born American mathematician. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was a member of the Bourbaki group.
Lang was born in Paris in 1927, and moved with his family to California as a teenager, where he graduated in 1943 from Beverly Hills High School. He subsequently graduated from the California Institute of Technology in 1946, and received a doctorate from Princeton University in 1951. He held faculty positions at the University of Chicago and Columbia University (from 1955, leaving in 1971 in a dispute). At the time of his death he was professor emeritus of mathematics at Yale University.
目录信息
Chapter 1: Real Numbers
Chapter 2: Limits and Continuous Functions
Chapter 3: Differentiation
Chapter 4: Elementary Functions
Chapter 5: The Elementary Real Integral
Chapter 6: Normed Vector Spaces
Chapter 7: Limits
Chapter 8: Compactness
Chapter 9: Series
Chapter 10: The Integral in One Variable
Appendix: The Lebesgue Integral
Chapter 11: Approximation with Convolutions
Chapter 12: Fourier Series
Chapter 13, Improper Integrals
Chapter 14: The Fourier Integral
Chapter 15: Calculus in Vector Spaces
Chapter 16: The Winding Number and Global Potential Functions
Chapter 17: Derivatives in Vector Spaces
Chapter 18: Inverse Mapping Theorem
Chapter 19: Ordinary Differential Equations
Chapter 20: Multiple Integration
Chapter 22: Differential Forms
Appendix
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