David. Bleecker
Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text:
the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks
convergence of numerical solutions of PDEs and implementation on a computer
convergence of Laplace series on spheres
quantum mechanics of the hydrogen atom
solving PDEs on manifolds
The text requires some knowledge of calculus but none on differential equations or linear algebra.
1. Review and Introduction 2. First-Order PDEs 3. The Heat Equation 4. Fourier Series and Sturm-Liouville Theory 5. The Wave Equation 6. Laplace`s Equation 7. Fourier Transforms 8. Numerical Solutions: An Introduction 9. PDEs In Higher Dimensions
Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities.
