
Differential Equations: A Systems Approach, 1/e
Jack L. Goldberg, University of Michigan Published July, 1997 by Prentice Hall Engineering/Science/Mathematics
 
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Introduction. The Cartesian and Exponential Forms. Roots of Polynomial Equations and Numbers. Matrix Notation and Terminology. The Solution of Simultaneous Equations. The Algebra of Matrices. Matrix Multiplication. The Inverse of a Matrix. The Computation of Agif/super_k.gif1. Determinants. Linear Independence. 1. FirstOrder Differential Equations. Preliminaries. Definitions. The FirstOrder Linear Equation. Applications of FirstOrder Linear Equations. Nonlinear Equations of First Order. 2. Linear Systems. Introduction. Eigenvalues and Eigenvectors. FirstOrder Systems. Solution and Fundamental Solution Matrices. Some Fundamental Theorems. Solutions of Nonhomogeneous Systems. Nonhomogeneous InitialValue Problems. Fundamental Solution Matrices. 3. SecondOrder Linear Equations. Introduction. Sectionally Continuous Functions. Linear Differential Operators. Linear Independence and the Wronskian. The Nonhomogeneous Equation. Constant Coefficient Equations. SpringMass Systems in Free Motion. The Electric Circuit. Undetermined Coefficients. The SpringMass System: Forced Motion. The CauchyEuler Equation. Variation of Parameters. 4. Higher Order Equations. Introduction. The Homogeneous Equation. The Nonhomogeneous Equation. Companion Systems. Homogeneous Companion Systems. Variation of Parameters. 5. The Laplace Transform. Introduction. Preliminaries. General Properties of the Laplace Transform. Sectionally Continuous Functions. Laplace Transforms of Periodic Functions. The Inverse Laplace Transform. Partial Fractions. The Convolution Theorem. The Solution of InitialValue Problems. The Laplace Transform of Systems. Tables of Transforms. 6. Series Methods. Introduction. Analytic Functions. Taylor Series of Analytic Functions. Power Series Solutions. Legendre's Equations. Three Important Examples. Bessel's Equation. The Wronskian Method. The Frobenius Method. 7. Numerical Methods. Introduction. Direction Fields. Notational Conventions. The Euler Method. Heun's Method. Taylor Series Methods. RungeKutta Methods. Multivariable Methods. Higher Order Equations. 8. BoundaryValue Problems. Introduction. Separation of Variables. Fourier Series Expansions. The Wave Equation. The OneDimensional Heat Equation. The Laplace Equation. A Potential about a Spherical Surface.
