Book Preface
This book contains forty lessons called Programmes. Each Programme has been written in such a way as to make learning more effective and more interesting. It is like having a personal tutor because you proceed at your own rate of learning and any difficulties you may have are cleared before you have the chance to practise incorrect ideas or techniques.
You will find that each Programme is divided into numbered sections called frames. When you start a Programme, begin at Frame 1. Read each frame carefully and carry out any instructions or exercise that you are asked to do. In almost every frame, you are required to make a response of some kind, testing your understanding of the information in the frame, and you can immediately compare your answer with the correct answer given in the next frame. To obtain the greatest benefit, you are strongly advised to cover up the following frame until you have made your response. When a series of dots occurs, you are expected to supply the missing word, phrase, number or mathematical expression. At every stage you will be guided along the right path. There is no need to hurry: read the frames carefully and follow the directions exactly. In this way, you must learn.
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Each Programme opens with a list of Learning outcomes which specify exactly what you will learn by studying the contents of the Programme. The Programme ends with a matching checklist of Can Yon? questions that enables you to rate your success in having achieved the Learning outcomes. If you feel sufficiently confident then tackle the short Test exerche which follows. This is set directly on what you have learned in the Programme: the questions are straightforward and contain no tricks. To provide you with the necessary practice, a set of Further problems is also included: do as many of these problems as you can. Remember, that in mathematics, as in many other situations, practice makes perfect – or more nearly so.
Of the forty Programmes, the first twelve are at Foundation level. Some of these will undoubtedly contain material with which you are already familiar. However, read the Programme’s Learning outcomes and if you feel confident about them try the Quiz that immediately follows – you will soon find out if you need a refresher course. Indeed, even if you feel you have done some of the topics before, it would still be worthwhile to work steadily through the Programme: it will serve as useful revision and fill any gaps in your knowledge that you may have.
When you have come to the end of a Foundation level Programme and have rated your success in achieving the Learning outcomes using the Can You? checklist, go back to the beginning of the Programme and try the Quiz before you complete the Programme with the Test exercise and the Further problems. This way you will get even more practice.
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How to Read and Open File Type for PC ?Book Preface
Purpose and Structure of the Book
This book provides a comprehensive, thorough, and up-to-date treatment of engineering mathematics. It is intended to introduce students of engineering, physics, mathematics, computer science, and related fields to those areas of applied mathematics that are most relevant for solving practical problems. A course in elementary calculus is the sole prerequisite. (However, a concise refresher of basic calculus for the student is included on the inside cover and in Appendix 3.)
The subject matter is arranged into seven parts as follows:
A. Ordinary Differential Equations (ODEs) in Chapters 1–6
B. Linear Algebra. Vector Calculus. See Chapters 7–10
C. Fourier Analysis. Partial Differential Equations (PDEs). See Chapters 11 and 12
D. Complex Analysis in Chapters 13–18
E. Numeric Analysis in Chapters 19–21
F. Optimization, Graphs in Chapters 22 and 23
G. Probability, Statistics in Chapters 24 and 25.
These are followed by five appendices: 1. References, 2. Answers to Odd-Numbered Problems, 3. Auxiliary Materials (see also inside covers of book), 4. Additional Proofs, 5. Table of Functions. This is shown in a block diagram on the next page.
The parts of the book are kept independent. In addition, individual chapters are kept as independent as possible. (If so needed, any prerequisites—to the level of individual sections of prior chapters—are clearly stated at the opening of each chapter.) We give the instructor maximum flexibility in selecting the material and tailoring it to his or her need. The book has helped to pave the way for the present development of engineering mathematics. This new edition will prepare the student for the current tasks and the future by a modern approach to the areas listed above. We provide the material and learning tools for the students to get a good foundation of engineering mathematics that will help them in their careers and in further studies.
General Features of the Book Include:
• Simplicity of examples to make the book teachable—why choose complicated examples when simple ones are as instructive or even better?
• Independence of parts and blocks of chapters to provide flexibility in tailoring courses to specific needs.
• Self-contained presentation, except for a few clearly marked places where a proof would exceed the level of the book and a reference is given instead.
• Gradual increase in difficulty of material with no jumps or gaps to ensure an enjoyable teaching and learning experience.
• Modern standard notation to help students with other courses, modern books, and journals in mathematics, engineering, statistics, physics, computer science, and others.
Furthermore, we designed the book to be a single, self-contained, authoritative, and convenient source for studying and teaching applied mathematics, eliminating the need for time-consuming searches on the Internet or time-consuming trips to the library to get a particular reference book.
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| Download here | Read Now Ads | November 3, 2015 |
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