Advanced Analytic Methods in Applied Mathematics, Science, and Engineering

Advanced Analytic Methods in Applied Mathematics, Science, and Engineering


Based on a physical mathematics course taught by the author for over ten years at the Massachusetts Institute of Technology (MIT), this book offers students an active learning experience. With its powerful yet easy-to-understand approach, it focuses on helping learners grasp the central mathematical themes rather than the peripheral details, reducing the time spent memorizing formulae.

The first five chapters bridge the initial gap which students often face, since core skills needed for graduate studies are sometimes inadequately covered in undergraduate education. Chapter 1 begins with a brief refresher on ordinary differential equations and an exposition on the topic of operator calculus. Chapter 2 presents a review of the essentials of complex analysis and various transforms. Chapters 3 through 5 move on to a discussion of partial differential equations.

The topics of the remaining five chapters train students to apply the basic mathematical skills they have acquired to solve advanced problems. Because many problems encountered in real-life applications or research often are not solvable in closed form, the author demonstrates how to obtain approximate analytical solutions. Specific topics include the WKB approximation, the asymptotic form of integrals with a large parameter, regular perturbation and singular perturbation. Important and original research is also incorporated. Numerous examples and interactive "Problems for the Reader" are generously interspersed throughout to help learners absorb concepts more effectively. Exercises in each chapter are carefully designed to strengthen students' ability to solve general problems. Throughout the learning process, the author also shares valuable problem-solving tools and tips acquired through more than 40 years of research and teaching.


LuBan Press
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I appreciate the way the different topics are explained and the level of detail that is given in the calculation. This is missing from many of the other books that I know, perhaps all of them.... This book has definite advantages over ... the main competitors.

— Michael Brenner, Division of Engineering and Applied Sciences, Harvard University