Co T.B. Methods of Applied Mathematics for Engineers and Scientists

Cambridge, New York, Melbourne, Madrid, Cape Town,Singapore, S˜ao Paulo, Delhi, Mexico City: Cambridge University Press, 2013. 897 p. — ISBN: 978-1-107-00412-2 (hardback).Based on course notes from over twenty years of teaching engineering and physical sciences at Michigan Technological University, Tomas Co's engineering mathematics textbook is rich with examples, applications, and exercises. Professor Co uses analytical approaches to solve smaller problems to provide mathematical insight and understanding, and numerical methods for large and complex problems. The book emphasizes applying matrices with strong attention to matrix structure and computational issues such as sparsity and efficiency. Chapters on vector calculus and integral theorems are used to build coordinate-free physical models with special emphasis on orthogonal coordinates. Chapters on ODEs and PDEs cover both analytical and numerical approaches. Topics on analytical solutions include similarity transform methods, direct formulas for series solutions, bifurcation analysis, Lagrange-Charpit formulas, shocks/rarefaction and others. Topics on numerical methods include stability analysis, DAEs, high-order finite-difference formulas, Delaunay meshes, and others. MatLAB implementations of the methods and concepts are fully integrated.