The Theory of Functions of Real Variables

Author: Lawrence M Graves
Publisher: Courier Corporation
ISBN: 0486158136
Format: PDF
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This balanced introduction covers all fundamentals, from the real number system and point sets to set theory and metric spaces. Useful references to the literature conclude each chapter. 1956 edition.

Complex Variables

Author: Stephen D. Fisher
Publisher: Courier Corporation
ISBN: 0486406792
Format: PDF
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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.

Elements of the Theory of Functions

Author: Konrad Knopp
Publisher: Courier Dover Publications
ISBN: 0486165604
Format: PDF, Kindle
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Well-known book provides a clear, concise review of complex numbers and their geometric representation; linear functions and circular transformations; sets, sequences, and power series; analytic functions and conformal mapping; and elementary functions. 1952 edition.

Integration Measure and Probability

Author: H. R. Pitt
Publisher: Courier Corporation
ISBN: 0486488152
Format: PDF, Kindle
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Introductory treatment develops the theory of integration in a general context, making it applicable to other branches of analysis. More specialized topics include convergence theorems and random sequences and functions. 1963 edition.

Complex Variables for Scientists and Engineers

Author: John D. Paliouras
Publisher: Courier Corporation
ISBN: 0486493474
Format: PDF, ePub, Mobi
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Outstanding undergraduate text provides a thorough understanding of fundamentals and creates the basis for higher-level courses. Numerous examples and extensive exercise sections of varying difficulty, plus answers to selected exercises. 1990 edition.

Theory of Approximation of Functions of a Real Variable

Author: Aleksandr Filippovich Timan
Publisher: Courier Corporation
ISBN: 9780486678306
Format: PDF, ePub
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Excellent graduate-level monograph investigates relationship between various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Based on classical approximation theorem of Weierstrass, P. L. Chebyshev’s concept of the best approximation, converse theorem of S. N. Bernstein on existence of a function with a given sequence of best approximations. Each chapter includes problems and theorems supplementing main text. 1963 edition. Bibliography.

Complex Variables and the Laplace Transform for Engineers

Author: Wilbur R. LePage
Publisher: Courier Corporation
ISBN: 0486136442
Format: PDF
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Acclaimed text on engineering math for graduate students covers theory of complex variables, Cauchy-Riemann equations, Fourier and Laplace transform theory, Z-transform, and much more. Many excellent problems.

The Functions of Mathematical Physics

Author: Harry Hochstadt
Publisher: Courier Corporation
ISBN: 0486652149
Format: PDF, Docs
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A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics. In the 18th and 19th centuries, the theorists who devoted themselves to this field — pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel — were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating membrane, some, such as those related to the theory of discontinuous groups, still remain of purely mathematical interest. Chapters One and Two examine orthogonal polynomials, with sections on such topics as the recurrence formula, the Christoffel-Darboux formula, the Weierstrass approximation theorem, and the application of Hermite polynomials to quantum mechanics. Chapter Three is devoted to the principal properties of the gamma function, including asymptotic expansions and Mellin-Barnes integrals. Chapter Four covers hypergeometric functions, including a review of linear differential equations with regular singular points, and a general method for finding integral representations. Chapters Five and Six are concerned with the Legendre functions and their use in the solutions of Laplace's equation in spherical coordinates, as well as problems in an n-dimension setting. Chapter Seven deals with confluent hypergeometric functions, and Chapter Eight examines, at length, the most important of these — the Bessel functions. Chapter Nine covers Hill's equations, including the expansion theorems.

Complex Variables

Author: Francis J. Flanigan
Publisher: Courier Corporation
ISBN: 0486613887
Format: PDF, ePub, Mobi
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Contents include calculus in the plane; harmonic functions in the plane; analytic functions and power series; singular points and Laurent series; and much more. Numerous problems and solutions. 1972 edition.