Foundations of Mathematical Analysis - Comprehensive Modern Analysis Textbook
This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. Upper-level undergraduate students with a background in calculus will benefit from its teachings, along with beginning graduate students seeking a firm grounding in modern analysis.
Self-Contained Curriculum Structure
A self-contained text, it presents the necessary background on the limit concept, and the first seven chapters could constitute a one-semester introduction to limits. Subsequent chapters discuss differential calculus of the real line, the Riemann-Stieltjes integral, sequences and series of functions, transcendental functions, inner product spaces and Fourier series, normed linear spaces and the Riesz representation theorem, and the Lebesgue integral.
Extensive Exercise Collection
Supplementary materials include an appendix on vector spaces and more than 750 exercises of varying degrees of difficulty. Hints and solutions to selected exercises, indicated by an asterisk, appear at the back of the book. This extensive problem set allows students to test their understanding and develop problem-solving skills across all major topics in modern analysis.
Topics Covered
- Limit concepts and foundational theory
- Differential calculus of the real line
- Riemann-Stieltjes integral
- Sequences and series of functions
- Transcendental functions
- Inner product spaces and Fourier series
- Normed linear spaces and Riesz representation theorem
- Lebesgue integral
- Vector spaces (appendix)
Ideal for Advanced Mathematics Students
Designed for upper-level undergraduate students with calculus background and beginning graduate students, this text provides the rigorous foundation needed for advanced work in mathematical analysis, functional analysis, and related fields. The Dover Publications edition offers exceptional value for students and self-learners building expertise in modern analysis.
