Differential Equations with Boundary-Value Problems / Edition 5by Dennis G. Zill, Michael R. Cullen
Pub. Date: 10/28/2000
Publisher: Cengage Learning
This new Fifth Edition of Zill and Cullen's best-selling book provides a thorough treatment of boundary-value problems and partial differential equations. This edition maintains all the features and qualities that have made Differential Equations with Boundary-Value Problems popular and successful over the years. Written in a straightforward, readable, helpful, not-too-theoretical manner, this new edition keeps the reader firmly in mind and strikes a perfect balance between the teaching of traditional content and the incorporation of evolving technology.
Table of ContentsPREFACE. ACKNOWLEDGEMENTS. 1. INTRODUCTION TO DIFFERENTIAL EQUATIONS. Definition and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Review. 2. FIRST-ORDER DIFFERENTIAL EQUATIONS. Solutions Curves Without the Solution. Separable Variables. Linear Equations. Exact Equations. Solutions by Substitutions. A Numerical Solution. Review. 3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS. Linear Equations. Nonlinear Equations. Systems of Linear and Nonlinear Differential Equations. Review. Project Module: Harvesting of Renewable Natural Resources, by Gilbert N. Lewis. 4. HIGHER-ORDER DIFFERENTIAL EQUATIONS. Preliminary Theory: Linear Equations. Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients: Superposition Approach. Undetermined Coefficients: Annihilator Approach. Variation of Parameters. Cauchy-Euler Equation. Solving Systems of Linear Equations by Elimination. Nonlinear Equations. Review. 5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS. Linear Equations: Initial-Value Problems. Linear Equations: Boundary-Value Problems. Nonlinear Equations. Review. Project Module: The Collapse of the Tacoma Narrows Suspension Bridge, by Gilbert N. Lewis. 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Solutions About Ordinary Points. Solutions About Singular Points. Two Special Equations. Review. 7. THE LAPLACE TRANSFORM. Definition of the Laplace Transform. Inverse Transform and Transforms of a Derivatives. Translation Theorems. Additional Operational Properties. Dirac Delta Function. Systems of Linear Equations. Review. 8. SYSTEMS OF LINEAR FIRST-ORDER DIFFERNTIAL EQUATIONS. Preliminary Theory.Homogeneous Linear Systems with Constant Coefficients. Variation of Parameters. Matrix Exponential. Review. Project Module: Earthquake Shaking of Multistory Buildings, by Gilbert N. Lewis. 9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS. Euler Methods and Error Analysis. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Review. 10. PLANE AUTONOMOUS SYSTEMS AND STABILITY. Autonomous Systems, Critical Points, and Periodic Solutions. Stability of Linear Systems. Linearization and Local Stability. Modeling Using Autonomous Systems. Review. 11. ORTHOGONAL FUNCTIONS AND FOURIER SERIES. Orthogonal Functions. Fourier Series. Fourier Cosine and Sine Series. Sturm-Liouville Problem. Bessel and Legendre Series. Review. 12. PARTIAL DIFFERENTIAL EQUATIONS AND BOUNDARY-VALUE PROBLEMS IN RECTANGULAR COORDINATES. Separable Partial Differential Equations. Classical Equations and Boundary-Value Problems. Heat Equation. Wave Equation. Laplace's Equation. Nonhomogeneous Equations and Boundary Conditions. Orthogonal Series Expansions. Boundary-Value Problems Involving Fourier Series in Two Variables. Review. 13. BOUNDARY-VALUE PROBLEMS IN OTHER COORDINATE SYSTEMS. Problems Involving Laplace's Equation in Polar Coordinates. Problems in Polar and Cylindrical Coordinates: Bessel Functions. Problems in Spherical Coordinates: Legendre Polynomials. Review. 14. INTEGRAL TRANSFORM METHOD. Error Function. Applications of the Laplace Transform. Fourier Integral. Fourier Transforms. Review. 15. NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS. Elliptic Equations. Parabolic Equations. Hyperbolic Equations. Review. APPENDIX I: GAMMA FUNCTION. APPENDIX II: INTRODUCTION TO MATRICES. APPENDIX III: LAPLACE TRANSFORMS. SELECTED ANSWERS TO ODD-NUMBERED PROBLEMS. INDEX.
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