Methods of Applied Mathematics for Engineers and Scientists

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Cambridge University Press, Jun 28, 2013 - Technology & Engineering
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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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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

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About the author (2013)

Tomas Co is a professor of chemical engineering at Michigan Technological University. After completing his PhD in chemical engineering at the University of Massachusetts, Amherst he was a postdoctoral researcher at Lehigh University, a visiting researcher at Honeywell Corp., and a visiting professor at Korea University. He has been teaching applied mathematics to graduate and advanced undergraduate students at Michigan Tech for more than twenty years. His research areas include advanced process control including plant-wide control, nonlinear control and fuzzy logic. His journal publications span broad areas in such journals as IEEE Transactions in Automatic Control, Automatica, the AIChE Journal, Computers in Chemical Engineering, and Chemical Engineering Progress. He is a regular nominee for the Distinguished Teaching Awards at Michigan Tech and is a member of the Michigan Technological University Academy of Teaching Excellence.

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