Handbook of Differential Equations 3rd Edition by Daniel Zwillinger ISBN 9781483220963 1483220966

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Product details:
ISBN 10: 1483220966
ISBN 13: 9781483220963
Author: Daniel Zwillinger

Handbook of Differential Equations 3rd Edition Table of contents:

Part I: Introduction to Differential Equations

1. Overview of Differential Equations

   • Types of Differential Equations
   • Basic Concepts and Terminology
   • Initial and Boundary Conditions
   • Existence and Uniqueness of Solutions

2. First-Order Ordinary Differential Equations

   • Separable Equations
   • Linear Equations
   • Exact Equations
   • Integrating Factors
   • Applications and Modeling

Part II: Higher-Order Ordinary Differential Equations

3. Second-Order Linear Differential Equations

   • Homogeneous Equations
   • Non-Homogeneous Equations
   • The Method of Undetermined Coefficients
   • Variation of Parameters
   • The Laplace Transform

4. Higher-Order Linear Equations

   • General Solutions
   • Linear Independence and Wronskian
   • Series Solutions
   • Sturm-Liouville Problems

5. Nonlinear Ordinary Differential Equations

   • Phase Plane Analysis
   • Stability Theory
   • Qualitative Methods
   • Bifurcation Theory

Part III: Systems of Differential Equations

6. Linear Systems of Differential Equations

   • Matrix Methods
   • Eigenvalue Problems
   • Diagonalization and Jordan Forms
   • Solutions of Linear Systems

7. Nonlinear Systems and Chaos

   • Stability of Nonlinear Systems
   • Linearization and Fixed Points
   • The Lorenz System and Chaos Theory
   • Lyapunov’s Direct Method

Part IV: Partial Differential Equations

8. Basic Theory of Partial Differential Equations

   • Classification of PDEs
   • Solutions and General Methods
   • Boundary and Initial Conditions
   • Characteristics Method

9. Wave and Heat Equations

   • Solution Methods for Wave Equation
   • Solution Methods for Heat Equation
   • Separation of Variables
   • Fourier Series and Transformations

10. Laplace and Poisson Equations

    • Solution Techniques for Elliptic Equations
    • Green’s Functions
    • Potential Theory

Part V: Special Functions and Integral Transforms

11. Series Solutions and Special Functions

    • Power Series Solutions
    • Legendre Polynomials
    • Bessel Functions
    • Hermite and Laguerre Polynomials

12. Integral Transforms and Their Applications

    • The Laplace Transform
    • The Fourier Transform
    • The Z-Transform
    • Applications in Engineering and Physics

Part VI: Numerical Methods for Differential Equations

13. Numerical Methods for Ordinary Differential Equations

    • Euler’s Method
    • Runge-Kutta Methods
    • Stability and Error Analysis
    • Adaptive Methods

14. Numerical Methods for Partial Differential Equations

    • Finite Difference Method
    • Finite Element Method
    • Boundary Element Method
    • Numerical Solutions for Elliptic and Parabolic PDEs

Part VII: Applications and Advanced Topics

15. Applications in Physics and Engineering

    • Mechanics and Dynamics of Systems
    • Electromagnetic Waves
    • Heat Transfer and Fluid Dynamics
    • Population Dynamics and Epidemics

16. Advanced Topics in Differential Equations

    • Asymptotic Methods
    • Perturbation Theory
    • Variational Methods
    • Nonlinear Dynamics and Chaos

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