Elementary Differential Equations and Boundary Value Problems

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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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