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Author:   Stephen A. Wirkus (Arizona State University, Phoenix, USA) ,  Randall J. Swift (California State Polytechnic University, Pomona, USA)
Publisher:   Taylor & Francis Ltd
Imprint:   Chapman & Hall/CRC
Dimensions:   Width: 15.60cm , Height: 4.00cm , Length: 23.40cm
Weight:   1.089kg
ISBN:  

9781584884767

ISBN 10:   1584884762
Pages:   688
Publication Date:   23 October 2006
Audience:   College/higher education ,  Tertiary & Higher Education
Replaced By:   9781466509085
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   In Print  
Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock.

Table of Contents

TRADITIONAL FIRST ORDER DIFFERENTIAL EQUATIONS Some Basic Terminology Separable Differential Equations Some Physical Problems arising as Separable Equations Exact Equations Linear Equations GEOMETRICAL & NUMERICAL METHODS FOR FIRST ORDER EQUATIONS Direction Fields - the Geometry of Differential Equations Existence and Uniqueness for First Order Equations First Order Autonomous Equations - Geometrical Insight Population Modeling: An Application of Autonomous Equations Numerical Approximation with the Euler Method Numerical Approximation with the Runge-Kutta Method An Introduction to Autonomous Second Order Equations ELEMENTS OF HIGHER ORDER LINEAR EQUATIONS Some Terminology Essential Topics from Linear Algebra Reduction of Order - The Case n=2 Operator Notation Numerical Considerations for nth Order Equations TECHNIQUES OF HIGHER ORDER LINEAR EQUATIONS Homogeneous Equations with Constant Coefficients A Mass on a Spring Cauchy-Euler (Equidimensional) Equation Nonhomogeneous Equations The Method of Undetermined Coefficients via Tables The Method of Undetermined Coefficients via the Annihilator Method Variation of Parameters FUNDAMENTALS OF SYSTEMS OF DIFFERENTIAL EQUATIONS Systems of Two Equations - Motivational Examples Useful Terminology Linear Transformations and the Fundamental Subspaces Eigenvalues and Eigenvectors Matrix Exponentials TECHNIQUES OF SYSTEMS OF DIFFERENTIAL EQUATIONS A General Method, Part I: Solving Systems with Real, Distinct Eigenvalues A General Method, Part II: Solving Systems with Repeated Real or Complex Eigenvalues Solving Linear Homogeneous and Nonhomogeneous Systems of Equations Nonlinear Equations and Phase Plane Analysis Epidemiological Models LAPLACE TRANSFORMS Fundamentals of the Laplace Transform Properties of the Laplace Transforms Step Functions, Translated Functions, and Periodic Functions The Inverse Laplace Transform Laplace Transform Solution of Linear Differential Equations Solving Linear Systems using Laplace Transforms The Convolution SERIES METHODS Power Series Representations of Functions The Power Series Method Ordinary and Singular Points The Method of Frobenius Bessel Functions Appendix A: An Introduction to MATLAB, Maple, and Mathematica Appendix B: Graphing Factored Polynomials Appendix C: Selected Topics from Linear Algebra Appendix D: Answers to Selected Exercises All chapters have additional problems and each chapter has its own project(s).

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