**PDF Free Download | Elementary Differential Equations and Boundary Value Problems 10th Edition by William E. Boyce and Richard C. DiPrima**

## Contents of Elementary Differential Equations and Boundary Value Problems

**Chapter 1. Introduction**- Some Basic Mathematical Models; Direction Fields
- Solutions of Some Differential Equations
- Classification of Differential Equations
- Historical Remarks
**Chapter 2. First Order Differential Equations**- Linear Equations; Method of Integrating Factors
- Separable Equations
- Modeling with First Order Equations
- Differences Between Linear and Nonlinear Equations
- Autonomous Equations and Population Dynamics
- Exact Equations and Integrating Factors
- Numerical Approximations: Euler’s Method
- The Existence and Uniqueness Theorem
- First Order Difference Equations
**Chapter 3. Second Order Linear Equations**- Homogeneous Equations with Constant Coefficients
- Solutions of Linear Homogeneous Equations; the Wronskian
- Complex Roots of the Characteristic Equation
- Repeated Roots; Reduction of Order
- Nonhomogeneous Equations; Method of Undetermined Coefficients
- Variation of Parameters
- Mechanical and Electrical Vibrations
- Forced Vibrations
**Chapter 4. Higher Order Linear Equations**- General Theory of nth Order Linear Equations
- Homogeneous Equations with Constant Coefficients
- The Method of Undetermined Coefficients
- The Method of Variation of Parameters
**Chapter 5. Series Solutions of Second Order Linear Equations**- Review of Power Series
- Series Solutions Near an Ordinary Point, Part I
- Series Solutions Near an Ordinary Point, Part II
- Euler Equations; Regular Singular Points
- Series Solutions Near a Regular Singular Point, Part I
- Series Solutions Near a Regular Singular Point, Part II
- Bessel’s Equation
**Chapter 6. The Laplace Transform**- Definition of the Laplace Transform
- Solution of Initial Value Problems
- Step Functions
- Differential Equations with Discontinuous Forcing Functions
- Impulse Functions
- The Convolution Integral
**Chapter 7. Systems of First Order Linear Equations**- Introduction
- Review of Matrices
- Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues,
- Eigenvectors
- Basic Theory of Systems of First Order Linear Equations
- Homogeneous Linear Systems with Constant Coefficients
- Complex Eigenvalues
- Fundamental Matrices
- Repeated Eigenvalues
- Nonhomogeneous Linear Systems
**Chapter 8. Numerical Methods**- The Euler or Tangent Line Method
- Improvements on the Euler Method
- The Runge–Kutta Method
- Multistep Methods
- Systems of First Order Equations
- More on Errors; Stability
**Chapter 9. Nonlinear Differential Equations and Stability**- The Phase Plane: Linear Systems
- Autonomous Systems and Stability
- Locally Linear Systems
- Competing Species
- Predator–Prey Equations
- Liapunov’s Second Method
- Periodic Solutions and Limit Cycles
- Chaos and Strange Attractors: The Lorenz Equations
**Chapter 10. Partial Differential Equations and Fourier Series**- Two-Point Boundary Value Problems
- Fourier Series
- The Fourier Convergence Theorem
- Even and Odd Functions
- Separation of Variables; Heat Conduction in a Rod
- Other Heat Conduction Problems
- The Wave Equation: Vibrations of an Elastic String
- Laplace’s Equation
- Appendix A Derivation of the Heat Conduction Equation
- Appendix B Derivation of the Wave Equation
**Chapter 11. Boundary Value Problems and Sturm–Liouville Theory**- The Occurrence of Two-Point Boundary Value Problems
- Sturm–Liouville Boundary Value Problems
- Nonhomogeneous Boundary Value Problems
- Singular Sturm–Liouville Problems
- Further Remarks on the Method of Separation of Variables: A Bessel
- Series Expansion
- Series of Orthogonal Functions: Mean Convergence