ORDINARYDIFFERENTIALEQUATIONS
         FOR ENGINEERS
         —THE LECTURE NOTES FOR MATH-
         263 (2011)
                 ORDINARYDIFFERENTIALEQUATIONS
                 FOR ENGINEERS
                 JIAN-JUN XU
                 Department of Mathematics and Statistics, McGill University
                 Kluwer Academic Publishers
                 Boston/Dordrecht/London
                                  Contents
                                  1.  INTRODUCTION                                                               1
                                      1     Definitions and Basic Concepts                                        1
                                            1.1     Ordinary Differential Equation (ODE)                          1
                                            1.2     Solution                                                     1
                                            1.3     Order n of the DE                                            2
                                            1.4     Linear Equation:                                             2
                                            1.5     Homogeneous Linear Equation:                                 3
                                            1.6     Partial Differential Equation (PDE)                           3
                                            1.7     General Solution of a Linear Differential Equation            3
                                            1.8     ASystem of ODE’s                                             4
                                      2     The Approaches of Finding Solutions of ODE                           5
                                            2.1     Analytical Approaches                                        5
                                            2.2      Numerical Approaches                                        5
                                  2.  FIRST ORDER DIFFERENTIAL EQUATIONS                                         7
                                      1     Linear Equation                                                      7
                                            1.1     Linear homogeneous equation                                  8
                                            1.2     Linear inhomogeneous equation                                8
                                      2     Nonlinear Equations (I)                                             11
                                            2.1     Separable Equations.                                        11
                                            2.2     Logistic Equation                                           14
                                            2.3     Fundamental Existence and Uniqueness Theorem                16
                                            2.4     Bernoulli Equation:                                         17
                                            2.5     Homogeneous Equation:                                       18
                                      3     NonlinearEquations(II)—ExactEquationandIntegrating
                                            Factor                                                              20
                                            3.1     Exact Equations.                                            20
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