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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
• 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
• 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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