.

0 (hodnocen0 x )

BK

New York : Springer, 1999

xiv,233 s.

ISBN 0-387-98698-7 (váz.)

Undergraduate texts in mathematics

Obsahuje 68 ilustrací, předmluvu, dodatky, tabulky, rejstřík

Bibliografie: s. 207-208

Transformace integrální - teorie - aplikace - učebnice vysokošk.

000054956

Contents // Preface ix // 1 Basic Principles 1 // 1.1 The Laplace Transform... 1 // 1.2 Convergence... 6 // 1.3 Continuity Requirements... 8 // 1.4 Exponential Order... 12 // 1.5 The Class £... 13 // 1.6 Basic Properties of the Laplace Transform... 16 // 1.7 Inverse of the Laplace Transform... 23 // 1.8 Translation Theorems... 27 // 1.9 Differentiation and Integration of the // Laplace Transform... 31 // 1.10 Partial Fractions... 35 // 2 Applications and Properties 41 // 2.1 Gamma Function ... 41 // 2.2 Periodic Functions... 47 // 2.3 Derivatives... 53 // 2.4 Ordinary Differential Equations... 59 // 2.5 Dirac Operator... 74 // • • • // xm // xiv Contents // 2.6 Asymptotic Values . . ... 88 // 2.7 Convolution... 91 // 2.8 Steady-State Solutions... 103 // 2.9 Difference Equations... 108 // 3 Complex Variable Theory 115 // 3.1 Complex Numbers... 115 // 3.2 Functions... 120 // 3.3 Integration... 128 // 3.4 Power Series... 136 // 3.5 Integrals of the Type 147 // 4 Complex Inversion Formula 151 // 5 Partial Differential Equations 175 // Appendix 193 // References 207 // Tables 209 // Laplace Transform Operations ... 209 // Table of Laplace Transforms... 210 // Answers to Exercises 219 // Index // 231