Masse R. Laplace Transforms 2021 torrent

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The subject of this book is the Laplace transform which is a particular mathematical transform. The Laplace transform provides an extremely powerful method for solving linear differential equations involving initial conditions. It does this by converting differential equations into algebraic equations. Differentiation is thereby replaced with algebraic manipulations. Even many differential equations having impulsive or discontinuous forcing functions can be easily solved using Laplace transforms. These transforms therefore find application in the numerous diverse fields where differential equations are used to describe changes in an entity. The material in this book is organized and presented in a manner designed to make this a comprehensive reference work on Laplace transforms. Most of the sources for this book are given in the references at the end of the book.
Preface.
Definition of the Laplace Transform.
Properties of the Laplace Transform.
Laplace Transforms of Derivatives and Integrals.
Derivatives and Integrals of Laplace Transforms.
Laplace Transforms of Discontinuous and Periodic Functions.
Inverse Laplace Transforms.
Convolution.
Laplace Transforms of Series Expansions.
Solution of Linear Ordinary Differential Equations having Constant Coefficients.
Solution of Partial Differential Equations.
Complex Variables.
Inverse Laplace Transforms from Residue Integration.
Solution of Linear Ordinary Differential Equations having Variable Coefficients.
Evaluating Integrals Equations with the Laplace Transform.
Appendix A The Greek Alphabet.
Appendix B Integration by Parts.
Appendix C Partial Fractions
Appendix D Summary of Propositions.
Appendix E Laplace Transform Tables.
Appendix F Properties of Laplace Transforms.
Appendix G Power Series.
Appendix H Special Functions.
References