Synopses & Reviews
Students of mathematics can learn from this classroom-tested volume about what modern analysis is and its applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. A self-contained textbook, it offers the background necessary for a firm grasp of the limit concept. (The first seven chapters could constitute a one-semester course on introduction to limits.) This is followed by a discussion of the limit of a function, a review of differential calculus, a detailed introduction to the theory of Riemann-Stieltjes integration, the study of sequences and series of functions, Fourier series, the Riesz representation theorem, and the Lebesgue integral. End-of-chapter exercises help reinforce the material, which is aimed at upper-level undergraduate students with a background in calculus, as well as to beginning graduate students who want a firm grounding in modern analysis.
Synopsis
Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises. 1981 edition. Includes 34 figures.
Synopsis
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. A self-contained text, it presents the necessary background on the limit concept. (The first seven chapters could constitute a one-semester course on 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. More than 750 exercises help reinforce the material. 1981 edition. 34 figures.