Essential Mathematics for Engineers and Scientists

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.

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.

'In our modern world, mathematics has proven to be essential for all of engineering and sciences. With the right balance between rigorous treatments, informal discussions, beautiful applications, and a myriad of informative examples, this book is not only essential but also truly enjoyable.' Alain Goriely, Oxford University 'The book presents fundamental topics from linear algebra, complex analysis and partial differential equations which make up the core of the scientific software packages used to solve real-word problems. The straightforward and clear style focused on applications of mathematics makes the book accessible to engineers and scientists. Numerous examples are presented in detail, and a good selection of exercises is given at the end of each chapter. Humor and insightful comments stimulate learning and the development of critical thinking skills. The book will make an excellent resource for an upper undergraduate or graduate-level course in mathematical topics for engineers and scientists.' Corina Drapaca, Pennsylvania State University 'A comprehensive and engaging book that discusses most of the basic mathematical techniques relevant to engineering and the physical sciences. The authors go well beyond what is typical in this genre by providing comprehensive coverage of advanced topics such as vector spaces, the Fredholm alternative and tensor algebra, and extensive exposure to complex variable methods including branch cuts, Laplace transform inversion and the Plemelj formulae. Further advanced subjects include the notion of the adjoint of a linear differential operator. All this in addition to very thorough coverage of the more standard solution techniques for linear ordinary and partial differential equations, eigenfunction methods and Green's functions. Every topic is skillfully illustrated by examples that reinforce and illustrate the many theoretical concepts one finds in this book.' David Steigmann, University of California, Berkeley 'This book is written for engineers and scientists as well as undergraduates with engineering and physical sciences. It covers a range of fundamental mathematics including Linear Algebra, Complex Variables, and Partial Differential Equations. The book features a lot of examples to explain concepts, theorems, and application math skills. It can also be used by graduate students as a reference book to advance in their engineering studies and practice.' Shensheng Tang, St Cloud State University