Instructor Manual Applied Partial Differential Equations and Fourier Series and Boundary Value Problems 4th Edition by Richard Haberman ISBN 0130652431 9780130652430

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Product details:
ISBN 10: 0130652431
ISBN 13: 9780130652430
Author: Richard Haberman

Instructor Manual Applied Partial Differential Equations and Fourier Series and Boundary Value Problems 4th Edition Table of contents:

Part I: Introduction to Partial Differential Equations

1. Introduction to Partial Differential Equations (PDEs)

   • Overview of Partial Differential Equations
   • Types of PDEs and Their Classifications
   • Boundary Conditions and Initial Conditions

2. Fundamental Solutions and Mathematical Modeling

   • Formulating Physical Problems Using PDEs
   • Examples from Heat, Wave, and Laplace Equations

3. Linear and Nonlinear PDEs

   • Linear PDEs and Superposition Principle
   • Nonlinear PDEs and Their Behavior

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Part II: Solution Techniques for PDEs

4. Separation of Variables

   • Solving PDEs by Separation of Variables
   • Application to Heat, Wave, and Laplace Equations

5. Fourier Series and Fourier Transforms

   • Fourier Series: Basic Concepts and Convergence
   • Fourier Transforms for Solving PDEs

6. Laplace Transforms

   • Using Laplace Transforms in Solving PDEs
   • Example Problems with Step-by-Step Solutions

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Part III: Boundary Value Problems

7. Boundary Value Problems for the Heat Equation

   • Solving the Heat Equation with Various Boundary Conditions
   • Steady-State and Transient Solutions

8. Wave Equation and Vibrating Strings

   • Solution of the Wave Equation
   • Standing and Traveling Waves

9. Laplace’s Equation and Potential Theory

   • Boundary Conditions for Laplace’s Equation
   • Solutions in Rectangular, Cylindrical, and Spherical Coordinates

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Part IV: Advanced Topics in PDEs

10. Green’s Functions and Superposition

    • Introduction to Green’s Function Method
    • Applications to Inhomogeneous Boundary Value Problems

11. Nonlinear PDEs and Shock Waves

    • Techniques for Solving Nonlinear PDEs
    • Formation and Propagation of Shock Waves

12. Numerical Methods for PDEs

    • Finite Difference and Finite Element Methods
    • Stability and Convergence of Numerical Solutions

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Part V: Special Topics and Applications

13. Heat Conduction and Diffusion Problems

    • Solving Time-Dependent Heat Equation
    • Modeling Heat Transfer in Different Geometries

14. Fluid Mechanics and the Navier-Stokes Equation

    • Introduction to the Navier-Stokes Equation
    • Fluid Flow and Boundary Layer Problems

15. Electromagnetic Wave Propagation

    • Electromagnetic Waves and Maxwell’s Equations
    • Solutions to Wave Equation in Different Media

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