Zill Dennis G. A First Course in Differential Equations with Modeling Applications

11th edition. — Boston: Cengage Learning , 2017. — 492 p. — ISBN: 9781305965720.Straightforward and easy to read, A First Course in Differential Equations with Modeling Applications, 11th Edition, gives you a thorough overview of the topics typically taught in a first course in differential equations. Your study of differential equations and its applications will be supported by a bounty of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and MindTap Math - an available option which includes an online version of the book, lecture videos, a pre-course assessment, and more.Introduction to Differential Equations
Defnitions and Terminology
Initial-Value Problems
Differential Equations as Mathematical Models
In Review
First-Order Differential Equations
Direction Fields
Autonomous First-Order DEs
Separable Equations
Linear Equations
Exact Equations
Solutions by Substitutions
A Numerical Method
In Review
Modeling with First-Order Differential Equations
Linear Models
Nonlinear Models
Modeling with Systems of First-Order DEs
In Review
Higher-Order Differential Equations
Initial-Value and Boundary-Value Problems
Homogeneous Equations
Nonhomogeneous Equations
Reduction of Order
Homogeneous Linear Equations with Constant
Coeffcients
Undetermined Coeffcients—Superposition Approach
Undetermined Coeffcients—Annihilator Approach
Variation of Parameters
Cauchy-Euler Equations
Initial-Value Problems
Boundary-Value Problems
Solving Systems of Linear DEs by Elimination
Nonlinear Differential Equations
In Review
Modeling with Higher-Order Differential Equations
Spring/Mass Systems Free Undamped Motion
Spring/Mass Systems Free Damped Motion
Spring/Mass Systems Driven Motion
Series Circuit Analogue
Linear Models Boundary-Value Problems
Nonlinear Models
In Review
Series Solutions of Linear Equations
Review of Power Series
Solutions About Ordinary Points
Solutions About Singular Points
Special Functions
In Review
The Laplace Transform
Definition of the Laplace Transform
Inverse Transforms
Transforms of Derivatives
Operational Properties I
Translation on the S-Axis
Translation on the t-Axis
Derivatives of a Transform
Transforms of Integrals
Transform of a Periodic Function
The Dirac Delta Function
Systems of Linear Differential Equations
In Review
Systems of Linear First-Order Differential Equations
Preliminary Theory—Linear Systems
Homogeneous Linear Systems
Distinct Real Eigenvalues
Repeated Eigenvalues
Complex Eigenvalues
Undetermined Coefficients
Variation of Parameters
Matrix Exponential
In Review
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
In Review
Appendices
Appendix A Integral-Defined Functions
Appendix B Matrices
Appendix C Laplace Transforms
Answers for Selected Odd-Numbered Problems