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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
|Introduction to Differential Equations|
|Definitions and Terminology|
|Differential Equations as Mathematical Models|
|Chapter 1 in Review|
|First-Order Differential Equations|
|Solution Curves Without a Solution|
|Exact Equations and Integrating Factors|
|Solutions by Substitutions|
|A Numerical Method|
|Chapter 2 in Review|
|Modeling with First-Order Differential Equations|
|Modeling with Systems of First-Order Differential Equations|
|Chapter 3 in Review|
|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|
|Solving Systems of Linear Differential Equations by Elimination|
|Nonlinear Differential Equations|
|Chapter 4 in Review|
|Modeling with Higher-Order Differential Equations|
|Linear Models: Initial-Value Problems|
|Linear Models: Boundary-Value Problems|
|Chapter 5 in Review|
|Series Solutions of Linear Equations|
|Solutions About Ordinary Points|
|Solutions About Singular Points|
|Chapter 6 in Review|
|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|
|Systems of Linear First-Order Differential Equations|
|Homogeneous Linear Systems|
|Nonhomogeneous Linear Systems|
|Chapter 8 in Review|
|Numerical Solutions of Ordinary Differential Equations|
|Higher-Order Equations and Systems|
|Second-Order Boundary-Value Problems|
|Chapter 9 in Review|
|Answers for Selected Odd-Numbered Problems|
|Table of Contents provided by Publisher. All Rights Reserved.|