Description
This text is geared toward students who have an undergraduate degree or extensive coursework in engineering or the physical sciences and who wish to develop their understanding of the essential topics of applied mathematics. The methods covered in the chapters form the core of analysis in engineering and the physical sciences. Readers will learn the solutions, techniques, and approaches that they will use as academic researchers or industrial R&D specialists. For example, they will be able to understand the fundamentals behind the various scientific software packages that are used to solve technical problems (such as the equations describing the solid mechanics of complex structures or the fluid mechanics of short-term weather prediction and long-term climate change), which is crucial to working with such codes successfully. Detailed and numerous worked problems help to ensure a clear and well-paced introduction to applied mathematics. Computational challenge problems at the end of each chapter provide students with the opportunity for hands-on learning and help to ensure mastery of the concepts. Adaptable to one- and two-semester courses.
Table of Contents
Part I. Linear Algebra: 1. Linear algebra and finite dimensional vector spaces; 2. Linear transformations; 3. Application to systems of equations; 4. The spectrum of eigenvalues; Part II. Complex Variables: 5. Basic concepts: 6. Analytic functions of a complex variable; 7. The Cauchy integral theorems; 8. Series expansions and contour integration; Part III. Partial Differential Equations: 9. Linear partial differential equations; 10. Linear ordinary differential equations; 11. Green's functions for ordinary differential equations; 12. Poisson's equation and Green's functions; 13. Combined Green's function and eigenfunction methods; Bibliography; Index.
