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# Elementary Differential Equations and Boundary Value Problems

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

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