Elementary Differential Equations

Description

Elementary Differential Equations presents the standard material in a first course on differential equations, including all standard methods which have been a part of the subject since the time of Newton and the Bernoulli brothers. The emphasis in this book is on theory and methods and differential equations as a part of analysis. Differential equations is worth studying, rather than merely some recipes to be used in physical science. The text gives substantial emphasis to methods which are generally presented first with theoretical considerations following. Essentially all proofs of the theorems used are included, making the book more useful as a reference. The book mentions the main computer algebra systems, yet the emphasis is placed on MATLAB and numerical methods which include graphing the solutions and obtaining tables of values. Featured applications are easily understood. Complete explanations of the mathematics and emphasis on methods for finding solutions are included. Content: Preface 1 Some Prerequisite Topics I First Order Scalar Differential Equations, Methods 2 The Idea Of A Differential Equation 3 Homogeneous Linear Equations 4 Nonhomogeneous Equations 5 Laplace Transform Methods III Series Methods For Scalar 6 Power Series 7 Power Series Methods IV First Order Linear Systems 8 First Order Systems Of Differential Equations, Theory 9 Methods For First Order Systems V Partial Differential Equations 10 Boundary Value Problems And Fourier Series 11 Some Famous Partial Differential Equations VI Non-linear Systems Of O.D.E. 12 Theory Of Ordinary Differential Equations 13 Equilibrium Points And Limit Cycles 14 The Center Manifold Appendix A: Calculus Review 381 Appendix B Series, Appendix C Review Of Linear Algebra Appendix D Theory Of Functions Of Many Variables Appendix E Spectral Theory Appendix F Linear Transformations Appendix G Implicit Function Theorem Appendix H The Jordan Curve Theorem Bibliography Index