Advanced Mathematics for Engineering and Science
This is a mathematical text suitable for students of engineering and science who are at the third year undergraduate level or beyond. It is a book of applicable mathematics. It avoids the approach of listing only the techniques, followed by a few examples, without explaining why the techniques work. Thus, it provides not only the know-how but also the know-why. Equally, the text has not been written as a book of pure mathematics with a list of theorems followed by their proofs. The authors' aim is to help students develop an understanding of mathematics and its applications. They have refrained from using clichés like “it is obvious” and “it can be shown”, which may be true only to a mature mathematician. On the whole, the authors have been generous in writing down all the steps in solving the example problems.The book comprises ten chapters. Each chapter contains several solved problems clarifying the introduced concepts. Some of the examples are taken from the recent literature and serve to illustrate the applications in various fields of engineering and science. At the end of each chapter, there are assignment problems with two levels of difficulty. A list of references is provided at the end of the book.This book is the product of a close collaboration between two mathematicians and an engineer. The engineer has been helpful in pinpointing the problems which engineering students encounter in books written by mathematicians.
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analytic Answer approximate arbitrary constants assume boundary conditions boundary value problem calculate Cartesian coordinate system Chapter choose coefficients Combining Equations complex numbers compute consider contour convergence cosh covariant curve deduce defined denote determine domain elements evaluate Example fluid formula Fourier function f given by Equation Green's function implies independent variables initial conditions integral interval iteration Laplace transform Laplace's equation Legendre linear matrix method metric tensor non-zero Note obtain ordinary differential equations origin orthogonal partial differential equation plane polar coordinate system polynomial radius region respectively right side satisfies Equation separation of variables shown in Figure side of Equation Similarly singular point sinh solution of Equation solving Equation Substituting Equations surface Taylor series temperature theorem unit circle velocity w-plane write written yields zero