Diffrential equations and linear algebra / by Jerry Farlow, James E. Hall, Jean Marie McDill and Beverly H. West

By: Farlow, JerryContributor(s): Hall, James E | Mcdill, Jean Marie | West, Beverly HMaterial type: TextTextPublication details: New Jersey. : Prentic Hall ; 2002Description: xxiv, 641 p. : ill. ; 24 cmISBN: 0130862509 (hbk)Other title: Diffrential equation & linear algebraSubject(s): Differential equationsDDC classification: 515.35 LOC classification: 515.35 | FAR-D 2002 902
Contents:
1. First-Order Differential Equations. Dynamical Systems: Modeling. Solutions and Direction Fields. Separation of Variables: Quantitative Analysis. Euler's Method: Numerical Analysis. Picard's Theorem: Theoretical Analysis. 2. Linearity and Nonlinearity. Linear Equations: The Nature of Their Solutions. Solving the First-Order Linear Differential Equation. Growth and Decay Phenomena. Linear Models: Mixing and Cooling. Nonlinear Models, Logistic Equation. Systems of DEs: A First Look. 3. Linear Algebra. Matrices: Sums and Products. Systems of Linear Equations. The Inverse of a Matrix. Determinants and Cramer's Rule. Vector Spaces and Subspaces. Basis and Dimension. 4. Second-Order Linear Differential Equations. The Harmonic Oscillator. Real Characteristic Roots. Complex Characteristic Roots. Undetermined Coefficients. Forced Oscillations. Conservation and Conversion. 5. Linear Transformations. Linear Transformations. Properties of Linear Transformations. Eigenvalues and Eigenvectors. Coordinates and Diagonalization. 6. Linear Systems of Differential Equations. Theory of Linear DE Systems. Linear Systems with Real Eigenvalues. Linear Systems with Nonreal Eigenvalues. Decoupling a Linear DE System. Stability and Linear Classification. 7. Nonlinear Systems of Differential Equations. Nonlinear Systems. Linearization. Numerical Solutions. Chaos, Strange Attractors, and Period Doubling. 8. Forced Equations and Systems. Linear Nonhomogeneous Problems. Variation of Parameters. Laplace Transform I. Laplace Transform II. Forced Oscillations. 9. Discrete Dynamical Systems. Iterative Equations. Linear Iterative Systems. Nonlinear Iterative Equations: Chaos Again. 10. Control Theory. Feedback Controls. Introduction to Optimal Control. Pontryagin Maximum Principle. Appendix: Complex Numbers and Complex-Valued Functions. Appendix: Linear Transformations. Appendix: Partial Fractions. Appendix: Spreadsheets for Systems. Bibliography. Answers to Selected Problems. Index.
Summary: This text encourages students to think both quantitatively and qualitatively when approaching differential equations. Before finding the analytical solution of a differential equation, the text presents the qualitative aspects of the problem to help students use linear algebra.
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Index included

1. First-Order Differential Equations. Dynamical Systems: Modeling. Solutions and Direction Fields. Separation of Variables: Quantitative Analysis. Euler's Method: Numerical Analysis. Picard's Theorem: Theoretical Analysis. 2. Linearity and Nonlinearity. Linear Equations: The Nature of Their Solutions. Solving the First-Order Linear Differential Equation. Growth and Decay Phenomena. Linear Models: Mixing and Cooling. Nonlinear Models, Logistic Equation. Systems of DEs: A First Look. 3. Linear Algebra. Matrices: Sums and Products. Systems of Linear Equations. The Inverse of a Matrix. Determinants and Cramer's Rule. Vector Spaces and Subspaces. Basis and Dimension. 4. Second-Order Linear Differential Equations. The Harmonic Oscillator. Real Characteristic Roots. Complex Characteristic Roots. Undetermined Coefficients. Forced Oscillations. Conservation and Conversion. 5. Linear Transformations. Linear Transformations. Properties of Linear Transformations. Eigenvalues and Eigenvectors. Coordinates and Diagonalization. 6. Linear Systems of Differential Equations. Theory of Linear DE Systems. Linear Systems with Real Eigenvalues. Linear Systems with Nonreal Eigenvalues. Decoupling a Linear DE System. Stability and Linear Classification. 7. Nonlinear Systems of Differential Equations. Nonlinear Systems. Linearization. Numerical Solutions. Chaos, Strange Attractors, and Period Doubling. 8. Forced Equations and Systems. Linear Nonhomogeneous Problems. Variation of Parameters. Laplace Transform I. Laplace Transform II. Forced Oscillations. 9. Discrete Dynamical Systems. Iterative Equations. Linear Iterative Systems. Nonlinear Iterative Equations: Chaos Again. 10. Control Theory. Feedback Controls. Introduction to Optimal Control. Pontryagin Maximum Principle. Appendix: Complex Numbers and Complex-Valued Functions. Appendix: Linear Transformations. Appendix: Partial Fractions. Appendix: Spreadsheets for Systems. Bibliography. Answers to Selected Problems. Index.

This text encourages students to think both quantitatively and qualitatively when approaching differential equations. Before finding the analytical solution of a differential equation, the text presents the qualitative aspects of the problem to help students use linear algebra.

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