Description
A First Course in Differential Equations with Modeling Applications Edition 11 by Dennis G. Zill EBOOK PDF Instant Download
Table of Contents
Contents
Preface
Chapter 1: Introduction to Differential Equations
1.1 Denitions and Terminology
1.2 Initial-Value Problems
1.3 Differential Equations as Mathematical Models
Chapter 1 In Review
Chapter 2: First-Order Differential Equations
2.1 Solution Curves Without a Solution
2.1.1 Direction Fields
2.1.2 Autonomous First-Order DEs
2.2 Separable Equations
2.3 Linear Equations
2.4 Exact Equations
2.5 Solutions by Substitutions
2.6 A Numerical Method
Chapter 2 In Review
Chapter 3: Modeling with First-Order Differential Equations
3.1 Linear Models
3.2 Nonlinear Models
3.3 Modeling with Systems of First-Order DEs
Chapter 3 In Review
Chapter 4: Higher-Order Differential Equations
4.1 Preliminary Theory—Linear Equations
4.1.1 Initial-Value and Boundary-Value Problems
4.1.2 Homogeneous Equations
4.1.3 Nonhomogeneous Equations
4.2 Reduction of Order
4.3 Homogeneous Linear Equations with Constant Coefcients
4.4 Undetermined Coefcients—Superposition Approach
4.5 Undetermined Coefcients—Annihilator Approach
4.6 Variation of Parameters
4.7 Cauchy-Euler Equations
4.8 Green’s Functions
4.8.1 Initial-Value Problems
4.8.2 Boundary-Value Problems
4.9 Solving Systems of Linear DEs byElimination
4.10 Nonlinear Differential Equations
Chapter 4 In Review
Chapter 5: Modeling with Higher-Order Differential Equations
5.1 Linear Models: Initial-Value Problems
5.1.1 Spring/Mass Systems: Free Undamped Motion
5.1.2 Spring/Mass Systems: Free Damped Motion
5.1.3 Spring/Mass Systems: Driven Motion
5.1.4 Series Circuit Analogue
5.2 Linear Models: Boundary-Value Problems
5.3 Nonlinear Models
Chapter 5 In Review
Chapter 6: Series Solutions of Linear Equations
6.1 Review of Power Series
6.2 Solutions About Ordinary Points
6.3 Solutions About Singular Points
6.4 Special Functions
Chapter 6 In Review
Chapter 7: The Laplace Transform
7.1 Denition of the Laplace Transform
7.2 Inverse Transforms and Transforms ofDerivatives
7.2.1 Inverse Transforms
7.2.2 Transforms of Derivatives
7.3 Operational Properties I
7.3.1 Translation on the S-Axis
7.3.2 Translation on the t-Axis
7.4 Operational Properties II
7.4.1 Derivatives of a Transform
7.4.2 Transforms of Integrals
7.4.3 Transform of a Periodic Function
7.5 The Dirac Delta Function
7.6 Systems of Linear Differential Equations
Chapter 7 In Review
Chapter 8: Systems of Linear First-Order Differential Equations
8.1 Preliminary Theory—Linear Systems
8.2 Homogeneous Linear Systems
8.2.1 Distinct Real Eigenvalues
8.2.2 Repeated Eigenvalues
8.2.3 Complex Eigenvalues
8.3 Nonhomogeneous Linear Systems
8.3.1 Undetermined Coefcients
8.3.2 Variation of Parameters
8.4 Matrix Exponential
Chapter 8 In Review
Chapter 9: Numerical Solutions of Ordinary Differential Equations
9.1 Euler Methods and Error Analysis
9.2 Runge-Kutta Methods
9.3 Multistep Methods
9.4 Higher-Order Equations and Systems
9.5 Second-Order Boundary-Value Problems
Chapter 9 In Review
Appendices
Appendix A: Integral-Defined Functions
Appendix B: Matrices
Appendix C: Laplace Transforms
Answers for Selected Odd-Numbered Problems
Index
