'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 transforms?the Fourier, Laplace, Hankel, and Mellin transforms?with 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.
' Each topic is developed step-by-step from the basics to an advanced level. Topics introduced are supported by examples drawn from the physical and engineering sciences. A wealth of worked-out examples and progressively more challenging exercises are incorporated. Definitions and theorems are followed by numerical examples to elucidate the concepts contained therein.
' Chapter 1 Ordinary Differential Equations Chapter 2 Ordinary Differential Equations of Higher Order Chapter 3 Complex Numbers Chapter 4 Functions of a Complex Variable Chapter 5 Derivatives in a Complex Domain Chapter 6 Complex Integration Chapter 7 Infinite Series in a Complex Variable Chapter 8 Calculus of Residues Chapter 9 Introduction to Vectors Chapter 10 Vector Differential Calculus Chapter 11 Vector Integral Calculus Chapter 13 Linear Transformations, Matrices, and Determinants Chapter 15 Fourier Series Chapter 17 Laplace Transform Chapter 19 Theory of Probability Chapter 21 Least Squares Approximation Chapter 23 Series Solutions of Differential Equations Chapter 25 Legendre Differential Equation Chapter 27 Modeling with Partial Differential Equations Chapter 29 Multivalued Functions of a Complex Variable Chapter 31 Nonlinear Differential Equations Chapter 33 Calculus of Variations Chapter 35 Numerical Methods for Differential Equations Chapter 12 Matrix and Vector Space Chapter 14 Eigenvalues, Eigenvectors, and Jordan Forms Chapter 16 Fourier Transform Chapter 18 Applications of Laplace Transform Chapter 20 Mathematical Statistics Chapter 22 Improper Integrals and Special Functions Chapter 24 Bessel Differential Equation Chapter 26 Laguerre and Hermite Differential Equations Chapter 28 Hyperbolic, Parabolic, and Elliptic PDEs Chapter 30 Complex Variables and Potential Theory Chapter 32 Integral Equations Chapter 34 Numerical Computations: Basics Chapter 36 Numerical Linear Algebra Appendix A: Fluid Dynamics Appendix B: Heat Conduction Index
'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 1980-1982, 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 (2002-2004).
