Physical scientists and engineers need mathematical tools in their everyday work. This book, Mathematical Methods of Science and Engineering: Aided with MATLAB, presents mathematics in a form appropriate for undergraduate science and engineering courses in a friendly and lucid way. Modeling any physical system, either in science or engineering, needs a thorough and strong understanding of differential equations. Ordinary differential equations and a special class of them (Bessel, Legendre, Laguerre, Tchebyshev, and Jacobi equations) and partial and nonlinear differential equations with applications to physical problems are central topics in this book. The theory of a complex variable with applications to the evaluation of improper integrals and the solution of potential problems are developed from an elementary to a reasonably advanced level. The complex variable theory prepares the background for the study of integral transformsthe Fourier, Laplace, Hankel, and Mellin transformswith applications to electric circuits, transmission lines, ODE, PDE, and mechanical systems. The least squares approximation of an arbitrary function in terms of the Fourier series, Bessel, Legendre, Laguerre, and Tchebyshev polynomials is laid on a strong mathematical foundation. The vector algebra, vector calculus, and linear algebra with matrices and determinants are given adequate importance. Due to uncertainty in physical system models, weather forecasting, and financial markets, probability and statistics are important topics in mathematics education and are developed with a broad coverage. Numerical methods for interpolation, roots of equations, integrations, ordinary and partial differential equations, and evaluation of eigenvalues and eigenvectors are treated in sufficient depth with MATLAB-based algorithms. Improper integrals, special functions, integral equations, and calculus of variations are also outlined as they are important topics in science and engineering.
Salient Features
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Each topic is developed step-by-step from the basics to an advanced level.
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Topics introduced are supported by examples drawn from the physical and engineering sciences.
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A wealth of worked-out examples and progressively more challenging exercises are incorporated.
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Definitions and theorems are followed by numerical examples to elucidate the concepts contained therein.
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MATLAB is used to reinforce concepts and solve problems that require extensive computation. MATLAB scripts are also provided in many chapters of to encourage the readers to develop their own codes for various algorithms discussed in the book. This will allow the readers to understand, appreciate, and interpret the significance of the solutions of many problems of physical and engineering sciences.
About the Author:
Kanti B. Datta Ph.D., D.Sc., FNAE, served the Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, for 19 years (1982-2001) where he remained professor from 1985 to 2001. Earlier, his other major tenure for 17 years (1965-1982) had been in the Department of Applied Physics, University of Calcutta. As a Visiting Research Fellow, Professor Datta visited the Department of Applied Mathematics, Comenius University, Bratislava, Slovakia (1975-1976) and the Department of Mathematics and Computing Sciences, Eindhoven University of Technology, Holland (1979-1980). During 19801982, he served the Institute of Control Engineering, National Chiao Tung University, Hsinchu, Taiwan, as a Visiting Expert. Professor Datta was a Visiting Professor in the Department of Mathematics, Northern Illinois University (2001-2002) and an Affiliate Professor in System Science and Mathematics, Washington University in St. Louis (20022004).
Although an electrical engineer by profession, his research in the theory of control systems, where mathematics is the principal tool for analysis, motivated Professor Datta to record his experience in Applied Mathematics in a book titled Mathematical Methods of Science and Engineering: Aided with MATLAB.
