Transcription of ORDINARY DIFFERENTIAL EQUATIONS FOR ENGINEERS | …
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ORDINARY DIFFERENTIAL EQUATIONS . FOR ENGINEERS . THE LECTURE NOTES FOR MATH- 263 (2011). ORDINARY DIFFERENTIAL EQUATIONS . FOR ENGINEERS . JIAN-JUN XU. Department of Mathematics and Statistics, McGill University Kluwer Academic Publishers Boston/Dordrecht/London Contents 1. INTRODUCTION 1. 1 De nitions and Basic Concepts 1. ORDINARY Di erential Equation (ODE) 1. Solution 1. Order n of the DE 2. Linear Equation: 2. Homogeneous Linear Equation: 3. Partial Di erential Equation (PDE) 3. General Solution of a Linear Di erential Equation 3. A System of ODE's 4. 2 The Approaches of Finding Solutions of ODE 5. Analytical Approaches 5. Numerical Approaches 5. 2. FIRST ORDER DIFFERENTIAL EQUATIONS 7. 1 Linear Equation 7. Linear homogeneous equation 8. Linear inhomogeneous equation 8. 2 Nonlinear EQUATIONS (I) 11.
4. LAPLACE TRANSFORMS 75 1 Introduction 75 2 Laplace Transform 77 2.1 Definition 77 2.1.1 Piecewise Continuous Function 77 2.1.2 Laplace Transform 77 2.2 Existence of Laplace Transform 77 3 Basic Properties and Formulas of Laplace Transform 78 3.1 Linearity of Laplace Transform 78 3.2 Laplace Transforms for f(t) = eat 78
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