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Book Description
The objective of this book is to provide a mathematical text at the third year level and beyond, appropriate for students of engineering and sciences. It is a book of applicable mathematics. We have avoided the approach of listing only the techniques followed by a few examples, without explaining why the techniques work. Thus we have provided not only the know how but also the know why. Equally it is not written as a book of pure mathematics with a list of theorems followed by their proofs. Our emphasis is to help students develop an understanding of mathematics and its applications. We have refrained from using cliches like "it is obvious" and "it can be shown", which might be true only to a mature mathematician. In general, we have been generous in writing down all the steps in solving the example problems. Contrary to the opinion of the publisher of S. Hawking's book, A Short History of Time, we believe that, for students, every additional equation in the worked examples will double the readership.
Many engineering schools offer little mathematics beyond the second year level. This is not a desirable situation as junior and senior year courses have to be watered-down accordingly. For graduate work, many students are handicapped by a lack of preparation in mathematics. Practicing engineers reading the technical literature, are more likely to get stuck because of a lack of mathematical skills. Language is seldom a problem. Further self-study of mathematics is easier said than done. It demands not only a good book but also an enormous amount of self-discipline. The present book is an appropriate one for self-study. We hope to have provided enough motivation, however we cannot provide the discipline!
The advent of computers does not imply that engineers need less mathematics. On the contrary, it requires more maturity in mathematics. Mathematical modelling can be more sophisticated and the degree of realism can be improved by using computers. That is to say, engineers benefit greatly from more advanced mathematical training. As Von Karman said: "There is nothing more practical than a good theory". The black box approach to numerical simulation, in our opinion, should be avoided. Manipulating sophisticated software, written by others, may give the illusion of doing advanced work, but does not necessarily develop one's creativity in solving real problems. A careful analysis of the problem should precede any numerical simulation and this demands mathematical dexterity.
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