Partial Differential Equations and Applications: A Bridge for Students and Researchers in Applied Fields

Partial Differential Equations and Applications: A Bridge for Students and Researchers in Applied Fields, offers a unique approach to this key subject by connecting mathematical principles to the latest research advances in select topics. Beginning with very elementary PDEs, such as classical heat equations, wave equations and Laplace equations, the book focuses on concrete examples. It gives students basic skills and techniques to find explicit solutions for partial differential equations. As it progresses, the book covers more advanced topics such as the maximum principle and applications, Green's representation, Schauder theory, finite time blowup and sock waves. By exploring these topics, students gain necessary tools to deal with research topics in their own fields, whether proceeding in math or engineering areas. Class-tested over multiple years with advanced undergraduate and graduate courses Features many concrete examples and chapter exercise Appropriate for advanced undergraduate and graduate courses geared to math and engineering students Requires a minimal background in in advanced calculus and differential equations INDICE: 1. Introduction to Partial Differential Equations 2. Function Spaces and Fredholm Alternative 3. Eigenvalue Problems and Eigenfunction Expansion 4. Heat Equations 5. Wave Equations 6. Laplace Equations 7. Green's Representation for Laplace Equations 8. Green's Representation for Heat Equations 9. Systems of the First-Order Partial Differential Equations 10. Systems of Reaction-Diffusion Equations Appendix: Basics of Differential Equations 

• ISBN: 978-0-443-18705-6
• Editorial: Academic Press
• Encuadernacion: Rústica
• Páginas: 352
• Fecha Publicación: 12/07/2023
• Nº Volúmenes: 1
• Idioma: Inglés