**Contents of Differential Equations Book**

**Chapter 1. Basic Concepts**

Differential Equations Notation

Solutions

Initial-Value and Boundary-Value Problems

**Chapter 2. An Introduction to Modeling and Qualitative Methods Mathematical Models**

The “Modeling Cycle”

Qualitative Methods

**Chapter 3. Classifications of First-Order Differential Equations**

Standard Form and Differential Form

Linear Equations

Bernoulli Equations

Homogeneous Equations

Separable Equations

Exact Equations

**Chapter 4. Separable First-Order Differential Equations General Solution**

Solutions to the Initial-Value Problem

Reduction of Homogeneous Equations

**Chapter 5. Exact First-Order Differential Equations**

Defining Properties Method of Solution

Integrating Factors

**Chapter 6. Linear First-Order Differential Equations Method of Solution**

Reduction of Bernoulli Equations

**Chapter 7. Applications of First-Order Differential Equations**

Growth and Decay Problems

Temperature Problems

Falling Body Problems Dilution Problems

Electrical Circuits Orthogonal Trajectories

**Chapter 8. Linear Differential Equations: Theory of Solutions**

Linear Differential Equations

Linearly Independent Solutions

The Wronskian Nonhomogeneous Equations

**Chapter 9. Second-Order Linear Homogeneous Differential Equations with Constant Coefficients**

Introductory Remark

The Characteristic Equation

The General Solution

**Chapter 10. nth-Order Linear Homogeneous Differential Equations with Constant Coefficients**

The Characteristic Equation

The General Solution

**Chapter 11. The Method of Undetermined Coefficients**

Simple Form of the Method Generalizations Modifications

Limitations of the Method

**Chapter 12. Variation of Parameters**

The Method

Scope of the Method

**Chapter 13. Initial-Value Problems for Linear Differential Equations**

**Chapter 14. Applications of Second-Order Linear Differential Equations**

Spring Problems

Electrical Circuit Problems

Buoyancy Problems

Classifying Solutions

**Chapter 15. Matrices Matrices and Vectors Matrix Addition**

Scalar and Matrix Multiplication

Powers of a Square Matrix

Differentiation and Integration of Matrices

The Characteristic Equation

**Chapter 16. eAt 140 Definition**

Computation of eAt

**Chapter 17. Reduction of Linear Differential Equations to a System of First-Order Equations**

An Example

Reduction of an nth Order Equation

Reduction of a System

**Chapter 18. Graphical and Numerical Methods for Solving First-Order Differential Equations**

Qualitative Methods Direction Fields

Euler’s Method

Stability

**Chapter 19. Further Numerical Methods for Solving First-Order Differential Equations General Remarks Modified Euler’s Method**

Runge–Kutta Method

Adams–Bashford–Moulton Method Milne’s Method

Starting Values Order of a Numerical Method

**Chapter 20. Numerical Methods for Solving Second-Order Differential Equations Via Systems**

Second-Order Differential Equations

Euler’s Method

Runge–Kutta Method

Adams–Bashford–Moulton Method

**Chapter 21. The Laplace Transform**

Definition

Properties of Laplace Transforms

Functions of Other Independent Variables

**Chapter 22. Inverse Laplace Transforms Definition Manipulating Denominators**

Manipulating Numerators

**Chapter 23. Convolutions and the Unit Step Function**

Convolutions Unit Step Function

Translations

**Chapter 24. Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms**

Laplace Transforms of Derivatives

Solutions of Differential Equations

**Chapter 25. Solutions of Linear Systems by Laplace**

Transforms

The Method

**Chapter 26. Solutions of Linear Differential Equations with Constant Coefficients by Matrix Methods**

Solution of the Initial-Value Problem

Solution with No Initial Conditions

**Chapter 27. Power Series Solutions of Linear Differential**

Equations with Variable Coefficients

Second-Order Equations

Analytic Functions and Ordinary Points

Solutions Around the Origin of Homogeneous Equations

**Download Differential Equations Book 4th Edition by Richard Bronson & Gabriel B. Costa in free pdf format.**