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A First Course Differential Equations with Modeling Applications (Ninth Edition) by Dinnis G. Zill

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A First Course Differential Equations with Modeling Applications (Ninth Edition) written by Dinnis G. Zill , Loyola Marymount University.

A First Course Differential Equations with Modeling Applications (Ninth Edition) written by Dinnis G. Zill cover the following topics of Differential Equations.

• 1. INTRODUCTION TO DIFFERENTIAL EQUATIONS
Preface
1.1 Definitions and Terminology
1.2 Initial-Value Problems
1.3 Differential Equations as Mathematical Models
CHAPTER 1 IN REVIEW

• 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 Variables
2.3 Linear Equations
2.4 Exact Equations
2.5 Solutions by Substitutions
2.6 A Numerical Method
CHAPTER 2 IN REVIEW

• 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

• 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 Coefficients
4.4 Undetermined Coefficients—Superposition Approach
4.5 Undetermined Coefficients—Annihilator Approach
4.6 Variation of Parameters
4.7 Cauchy-Euler Equation
4.8 Solving Systems of Linear DEs by Elimination
4.9 Nonlinear Differential Equations
CHAPTER 4 IN REVIEW

• 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

• 6. SERIES SOLUTIONS OF LINEAR EQUATIONS
6.1.1 Review of Power Series
6.1.2 Power Series Solutions
6.3 Special Functions
6.3.1 Bessel’s Equation
6.3.2 Legendre’s Equation CHAPTER 6 IN REVIEW

• 7. THE LAPLACE TRANSFORM
7.1 Definition of the Laplace Transform
7.2 Inverse Transforms and Transforms of Derivatives
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 287
7.5 The Dirac Delta Function
7.6 Systems of Linear Differential Equations
CHAPTER 7 IN REVIEW

• 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 Coefficients
8.3.2 Variation of Parameters
8.4 Matrix Exponential
CHAPTER 8 IN REVIEW

• 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
I Gamma Function APP-1
II Matrices APP-3
III Laplace Transforms APP-21

• Answers for Selected Odd-Numbered Problems ANS

• Index I

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