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This Seventh Edition maintains the all the winning qualities that have made A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS a best-seller over the years. Written in a straightforward, helpful, not-too-theoretical manner Zill's approach keeps students with differing levels firmly in mind. The new edition strikes a perfect balance between the teaching of traditional content and the incorporation of evolving technology.
Preface. Acknowledgments. 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. Solution by Substitutions. A Numerical Solution. Review. 3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS. Linear Equations. Nonlinear Equations. Systems of Linear and Nonlinear Equations. Review. 4. HIGHER-ORDER DIFFERENTIAL EQUATIONS. Preliminary Theory. 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. 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Solutions About Ordinary Points. Solutions About Singular Points. Two Special Equations. Review. 7. LAPLACE TRANSFORM. Definition of the Laplace Transform. Inverse Transform and Transform of a Derivative. Translation Theorems. Additional Operational Properties. Dirac Delta Function. Systems of Linear Equations. Review. 8. SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS. Preliminary Theory. Homogeneous Linear Systems with Constant Coefficients. Variation of Parameters. Matrix Exponential. Review. 9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS. Euler Methods. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Review. Appendix I: Gamma Function. Appendix II: Introduction to Matrices. Appendix III: Table of Laplace Transforms. Selected Answers to Odd-Numbered Problems.
Posted June 24, 2001