Differential Equations Demystified by S. Krantz

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Differential Equations Demystified by S. Krantz

PDF Free Download | Differential Equations Demystified A Self Teaching Guide by Steven G. Krantz

Contents of Differential Equations PDF

  • CHAPTER 1. What Is a Differential Equation?
  • Introductory Remarks
  • The Nature of Solutions
  • Separable Equations
  • First-Order Linear Equations
  • Exact Equations
  • Orthogonal Trajectories and Families
  • of Curves
  • Homogeneous Equations
  • Integrating Factors
  • Reduction of Order
  • The Hanging Chain and Pursuit Curves
  • Electrical Circuits
  • Exercises
  • CHAPTER 2. Second-Order Equations
  • Second-Order Linear Equations with
  • Constant Coefficients
  • The Method of Undetermined
  • Coefficients
  • The Method of Variation of Parameters
  • For more information about this title, click here
  • The Use of a Known Solution to
  • Find Another
  • Vibrations and Oscillations
  • Newton’s Law of Gravitation and
  • Kepler’s Laws
  • Higher-Order Linear Equations,
  • Coupled Harmonic Oscillators
  • Exercises
  • CHAPTER 3. Power Series Solutions and Special Functions
  • Introduction and Review of
  • Power Series
  • Series Solutions of First-Order
  • Differential Equations
  • Second-Order Linear Equations:
  • Ordinary Points
  • Exercises
  • CHAPTER 4. Fourier Series: Basic Concepts
  • Fourier Coefficients
  • Some Remarks About Convergence
  • Even and Odd Functions: Cosine and
  • Sine Series
  • Fourier Series on Arbitrary Intervals
  • Orthogonal Functions
  • Exercises
  • CHAPTER 5. Partial Differential Equations and Boundary Value Problems
  • Introduction and Historical Remarks
  • Eigenvalues, Eigenfunctions, and
  • the Vibrating String
  • The Heat Equation: Fourier’s
  • Point of View
  • The Dirichlet Problem for a Disc
  • Sturm–Liouville Problems
  • Exercises
  • CHAPTER 6. Laplace Transforms
  • Introduction
  • Applications to Differential
  • Equations
  • Derivatives and Integrals of
  • Laplace Transforms
  • Convolutions
  • The Unit Step and Impulse
  • Functions
  • Exercises
  • CHAPTER 7. Numerical Methods
  • Introductory Remarks
  • The Method of Euler
  • The Error Term
  • An Improved Euler Method
  • The Runge–Kutta Method
  • Exercises
  • CHAPTER 8. Systems of First-Order Equations
  • Introductory Remarks
  • Linear Systems
  • Homogeneous Linear Systems with
  • Constant Coefficients
  • Nonlinear Systems: Volterra’s
  • Predator–Prey Equations
  • Exercises

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