Mathematical methods of science and engineering

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.