Thomas J. Pence, Indrek S. WichmanCambridge University Press, 5/21/2020EAN 9781108425445, ISBN10: 1108425445Hardcover, 754 pages, 25.1 x 19.6 x 4.1 cmLanguage: EnglishThis 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.Part I. Linear Algebra1. Linear algebra and finite dimensional vector spaces2. Linear transformations3. Application to systems of equations4. The spectrum of eigenvaluesPart II. Complex Variables5. Basic concepts6. Analytic functions of a complex variable7. The Cauchy integral theorems8. Series expansions and contour integrationPart III. Partial Differential Equations9. Linear partial differential equations10. Linear ordinary differential equations11. Green's functions for ordinary differential equations12. Poisson's equation and Green's functions13. Combined Green's function and eigenfunction methodsBibliographyIndex.
