Advanced Mathematics for Engineering and Science

C. F. Chan Man, D. De Kee, P. N. Kaloni9812382917, 9789812382917, 9789812564832

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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Table of contents :
Cover Page……Page 1
Title Page……Page 4
ISBN 9812382917……Page 5
PREFACE……Page 6
2 Series Solutions and Special Functions……Page 8
3 Complex Variables……Page 9
5 Partial Differential Equations I……Page 10
7 Numerical Methods……Page 11
8 Numerical Solution of Partial Differential Equations……Page 12
10 Special Topics……Page 13
Subject Index……Page 14
1 REVIEW OF CALCULUS AND ORDINARY DIFFERENTIAL EQUATIONS……Page 16
2 SERIES SOLUTIONS AND SPECIAL FUNCTIONS……Page 104
3 COMPLEX VARIABLES……Page 206
4 VECTOR AND TENSOR ANALYSIS……Page 316
5 PARTIAL DIFFERENTIAL EQUATIONS I……Page 416
6 PARTIAL DIFFERENTIAL EQUATIONS II……Page 526
7 NUMERICAL METHODS……Page 584
8 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS……Page 696
9 CALCULUS OF VARIATIONS……Page 754
10 SPECIAL TOPICS……Page 824
REFERENCES……Page 876
APPENDICES……Page 882
AUTHOR INDEX……Page 890
A,B,C,D……Page 892
J,K,L……Page 893
M,N,O,P,Q,R,S……Page 894
T,U,V,W,Z……Page 895
STANDARD DERIVATIVES AND INTEGRALS……Page 896
Back Cover Page……Page 898