# Methods of Applied Mathematics for Engineers and Scientists

Cambridge University Press, Jun 28, 2013 - Technology & Engineering
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 emphasises 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 co-ordinates. 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. MATLABŪ implementations of the methods and concepts are fully integrated.

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on the first look ,I can say ,it will be very useful for the student as well as teacher community as a reference

### Contents

 Solution of Multiple Equations 54 Matrix Analysis 99 VECTORS AND TENSORS 147 Vector Integral Theorems 204 ORDINARY DIFFERENTIAL EQUATIONS 233 Additional Details and Fortiﬁcation for Chapter 6 700 235 Numerical Solution of Initial and Boundary Value Problems 273 Additional Details and Fortiﬁcation for Chapter 7 715 303
 Additional Details and Fortiﬁcation for Chapter 10 771 379 Linear Partial Differential Equations 405 Integral Transform Methods 450 L3 Dirichlet Conditions and the Fourier Integral Theorem 819 456 Finite Difference Methods 483 Method of Finite Elements 523 Additional Details and Fortiﬁcation for Chapter 14 867 541 A Additional Details and Fortiﬁcation for Chapter 1 561

 Series Solutions of Linear Ordinary Differential Equations 347 Additional Details and Fortiﬁcation for Chapter 9 745 354 PARTIAL DIFFERENTIAL EQUATIONS 377