ABSTRACT
The first and second editions of “An Introduction to Partial Differential Equation with MATLAB®” gained popularity among instructors and students at various universities throughout the world. Plain mathematical language is used in a friendly manner to provide a basic introduction to partial differential equations focusing on Fourier series and integrals.
Suitable for a one- or two-semester introduction to PDEs and Fourier series, the book offers equations based on method of solution and provides both physical and mathematical motivation as much as possible.
This third edition changes the book structure by lifting the role of the computational part much closer to the revised analytical portion. The re-designed content will be extremely useful for students of mathematics, physics and engineering who would like to focus on the practical aspects of using the theory of PDEs for modeling and later while taking various courses in numerical analysis, computer science, PDE-based programming, and optimization.
Included in this new edition is a substantial amount of material on reviewing computational methods for solving ODEs (symbolically and numerically), visualizing solutions of PDEs, using MATLAB's symbolic programming toolbox, and applying various numerical schemes for computing with regard to numerical solutions in practical applications, along with suggestions for topics of course projects.
Students will use sample MATLAB and Python codes available online for their practical experiments and for completing computational lab assignments and course projects.
Chapter 1. Introduction. Chapter 2. The Big Three PDEs. Chapter 3. Using MATLAB for Solving Differential Equations and Visualizing Solutions. Chapter 4. Fourier Series. Chapter 5. Solving the Big Three PDEs on Finite Domains. Chapter 6. Review of Numerical Methods for Solving ODEs. Chapter 7. Solving PDEs Using Finite Difference Approximations. Chapter 8. Integral Transforms. Chapter 9. Using MATLAB's Symbolic Math Toolbox with Integral Transforms. Chapter 10. PDEs in Higher Dimensions. Chapter 11. Overview of Spectral, Finite Element, and Finite Volume Methods.
