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PREFACE vii 1 Introduction 1 2 First-Order Differential Equations 24 3 Second-Order Linear Differential Equations 101 4 Higher-Order Linear Differential Equations 167 5 Series Solutions of Second-Order Linear Equations 187 6 The Laplace Transform 239 7 Systems of First-Order Linear Equations 279 8 Numerical Methods 352 9 Nonlinear Differential Equations and Stability 386 10 Partial Differential Equations and Fourier Series 461 11 Boundary Value Problems and Sturm-Liouville Theory 527 ANSWERS TO PROBLEMS 571 INDEX 602 |