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Clear and engaging introduction for graduate students in engineering and the physical sciences to essential topics of applied mathematics.
List 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.
About the author
Thomas J. Pence has taught at Michigan State University since 1986. His research in theoretical solid mechanics involves broad aspects of material modeling and structural stability, especially for soft highly deformable materials. A current focus is on the topic of nonlinear elastic and porous media as it relates to biological tissue growth and remodeling. Dr. Pence is active on the editorial boards of The Journal of Elasticity, The International Journal of Solids and Structures, and The Journal of Mechanics of Materials and Structures. He currently serves on the US National Committee for Theoretical and Applied Mechanics and was the organizer of the 2014 US National Congress on Theoretical and Applied Mechanics.Indrek S. Wichman has taught at Michigan State University for thirty-three years, during which time he has won two teaching awards and developed or co-developed five courses, including the Engineering Analysis course on which this book is based. His research in combustion is largely theoretical but also has numerical and experimental components. One of the experiments was conducted on the International Space Station (ISS) in 2014; another is scheduled for 2021. An American Scientist cover article co-authored by Dr Wichman discussed his microgravity combustion research for NASA. His research has encompassed combustion, diffusion flames and flame/surface interaction as well as ignition, quenching and material flammability studies.
Summary
A clear and engaging textbook for graduate-level or advanced undergraduate students in engineering or the physical sciences seeking to develop their understanding of the essential topics of applied mathematics. Also suitable for researchers who want to learn more of the theoretical underpinnings of modern applied science.
