Advanced Mathematics for Engineering and Science

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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.


Table of Contents:

Ch 1 Review of Calculus and Ordinary Differential Equations
Ch 2 Series Solutions and Special Functions
Ch 3 Complex Variables
Ch 4 Vector and Tensor Analysis
Ch 5 Partial Differential Equations I
Ch 6 Partial Differential Equations II
Ch 7 Numerical Methods
Ch 8 Numerical Solution of Partial Differential Equations
Ch 9 Calculus of Variations
Ch 10 Special Topics