Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.
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.
Dealing chiefly with functions of a single real variable, this text by a distinguished educator introduces limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. 1963 edition.
This book introduces a methodology for solving the seismic inverse problem using purely numerical solutions built on 3D wave equations and which is free of the approximations or simplifications that are common in classical seismic inversion methodologies and therefore applicable to arbitrary 3D geological media and seismic source models. Source codes provided allow readers to experiment with the calculations demonstrated and also explore their own applications.
Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition.
Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition.
Considered the best book in the field, this completely self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus in on the tableau point of view. Topics include trees, tableau method for propositional logic, Gentzen systems, more. Includes 144 illustrations.
Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.
This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.