Title:
A first course in differential equations with modeling applications
Personal Author:
Edition:
9th ed.
Publication Information:
Belmont, CA : Brooks Cole, 2009
Physical Description:
xiii, 362 p. : col. ill. ; 28 cm.
ISBN:
9780495108245
Subject Term:
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010205069 | QA372 Z54 2009 | Open Access Book | Book | Searching... |
Searching... | 30000010117726 | QA372 Z54 2009 | Open Access Book | Book | Searching... |
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Summary
Summary
A First Course in Differential Equations with Modeling Applications, 9th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.
Table of Contents
| 1 Introduction to Differential Equations |
| Definitions and Terminology |
| Initial-Value Problems |
| Differential Equations as Mathematical Models |
| Chapter 1 in Review |
| 2 First-Order Differential Equations |
| Solution Curves Without a Solution |
| Separable Variables |
| Linear Equations |
| Exact Equations and Integrating Factors |
| Solutions by Substitutions |
| A Numerical Method |
| Chapter 2 in Review |
| 3 Modeling with First-Order Differential Equations |
| Linear Models |
| Nonlinear Models |
| Modeling with Systems of First-Order Differential Equations |
| Chapter 3 in Review |
| 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 Differential Equations by Elimination |
| Nonlinear Differential Equations |
| Chapter 4 in Review |
| 5 Modeling with Higher-Order Differential Equations |
| Linear Models: Initial-Value Problems |
| Linear Models: Boundary-Value Problems |
| Nonlinear Models |
| Chapter 5 in Review |
| 6 Series Solutions of Linear Equations |
| Solutions About Ordinary Points |
| Solutions About Singular Points |
| Special Functions |
| Chapter 6 in Review |
| 7 Laplace Transform |
| Definition of the Laplace Transform |
| Inverse Transform and Transforms of Derivatives |
| Operational Properties I |
| Operational Properties II |
| Dirac Delta Function |
| Systems of Linear Differential Equations |
| Chapter 7 in Review |
| 8 Systems of Linear First-Order Differential Equations |
| Preliminary Theory |
| Homogeneous Linear Systems |
| Nonhomogeneous Linear Systems |
| Matrix Exponential |
| Chapter 8 in 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 |
| Chapter 9 in Review |
| Appendix I Gamma Function |
| Appendix II Matrices |
| Appendix III Laplace Transforms |
| Answers for Selected Odd-Numbered Problems |
