Bøger i Dover Books on Mathematics serien

Classic graduate-level exposition covers theory and applications to ordinary and partial differential equations. Includes derivation of Laplace transforms of various functions, Laplace transform for a finite interval, and more. 1948 edition.

This text for advanced undergraduate and graduate students presents a rigorous approach that also emphasizes applications. Encompassing more than the usual amount of material on the problems of computation with series, the treatment offers many applications, including those related to the theory of special functions. Numerous problems appear throughout the book.The first chapter introduces the elementary theory of infinite series, followed by a relatively complete exposition of the basic properties of Taylor series and Fourier series. Additional subjects include series of functions and the applications of uniform convergence; double series, changes in the order of summation, and summability; power series and real analytic functions; and additional topics in Fourier series. The text concludes with an appendix containing material on set and sequence operations and continuous functions. Dover (2014) republication of the edition originally published by Holt, Rinehart & Winston, New York, 1962.See every Dover book in print atwww.doverpublications.com

This introduction to calculus is designed for beginning college undergraduates majoring in mathematics as well as undergraduates pursuing other areas of science and engineering for whom calculus will be a vital tool. The three-part treatment begins by exploring the core of the calculus, concentrating on three basic ideas: the definite integral, the derivative, and the fundamental theorem of calculus. Part Two takes up topics such as the maximum and minimum of a function, Taylor's series, partial derivatives, differentiation of vectors, and Green's theorem in the plane. Part Three, which contains no further mathematical development, applies the techniques developed earlier to significant problems in the natural, social, and physical sciences. Appendixes supplement the treatment, offering helpful information on the rudiments of analytic geometry, real numbers, and functions. Numerous examples and exercises appear throughout the text, and solutions to the problems are available as free downloads from the Dover website. Dover (2016) republication of the edition originally published by McGraw-Hill, New York, 1967.See every Dover book in print atwww.doverpublications.com

This volume offers a guided tour of modern mathematics' Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. 1989 edition. Includes 32 figures.

This text assumes no knowledge of mathematical logic. Beginning with a nonstandard construction of the real number system, it leads students thorough the basic topics of elementary real analysis, topological spaces, and Hilbert space. Includes nonstandard treatments of equicontinuity, nonmeasurable sets, and the existence of Haar measure. 1977 edition.

This text discusses the mathematical foundations of statistical inference for building 3-dimensional models from image and sensor data that contain noise -- a task involving autonomous robots guided by video cameras and sensors. The text employs a theoretical accuracy for the optimization procedure, which maximizes the reliability of estimations based on noise data. 1996 edition.

Proceeds from general to special, including chapters on vector analysis on manifolds and integration theory.

Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, transform methods. Hundreds of solved examples, exercises, applications. 1990 edition. Appendices.

Stimulating study of how abstract methods of pure mathematics can solve problems in applied math. Solving integral equations, finding Green's function, spectral representation of ordinary differential operators, more. Problems. Bibliography.