This book is designed for an introductory course in numerical methods for students of engineering and science at universities and colleges of advanced education. It is an outgrowth of a course of lectures and tutorials (problem solving sessions) which the author has given for a number of years at the University of New South Wales and elsewhere. The course is normally taught at the rate of 1i hours per week throughout an academic year (28 weeks). It has occasionally been given at double this rate over half the year, but it was found that students had insufficient time to absorb the material and experiment with the methods. The material presented here is rather more than has been taught in anyone year, although all of it has been taught at some time. The book is concerned with the application of numerical methods to the solution of equations - algebraic, transcendental and differential - which will be encountered by students during their training and their careers. The theoretical foundation for the methods is not rigorously covered. Engineers and applied scientists (but not, of course, mathematicians) are more con cerned with using methods than with proving that they can be used. However, they 'must be satisfied that the methods are fit to be used, and it is hoped that students will perform sufficient numerical experiments to con vince themselves of this without the need for more than the minimum of theory which is presented here.
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This book is designed for an introductory course in numerical methods for students of engineering and science at universities and colleges of advanced education. It is an outgrowth of a course of lectures and tutorials (problem solving sessions) which the author has given for a number of years at the University of New South Wales and elsewhere. The course is normally taught at the rate of 1i hours per week throughout an academic year (28 weeks). It has occasionally been given at double this rate over half the year, but it was found that students had insufficient time to absorb the material and experiment with the methods. The material presented here is rather more than has been taught in anyone year, although all of it has been taught at some time. The book is concerned with the application of numerical methods to the solution of equations - algebraic, transcendental and differential - which will be encountered by students during their training and their careers. The theoretical foundation for the methods is not rigorously covered. Engineers and applied scientists (but not, of course, mathematicians) are more con cerned with using methods than with proving that they can be used. However, they 'must be satisfied that the methods are fit to be used, and it is hoped that students will perform sufficient numerical experiments to con vince themselves of this without the need for more than the minimum of theory which is presented here.
Treating numerical methods as a tool for use by the engineer or applied scientist, this introductory text is concerned with the application of such methods to the solution of algebraic, transcendental and differential equations. With a minimum of mathematical theory needed for understanding, the book concentrates on the methods likely to be needed by students in training and later in their careers. The emphasis, as far as differential equations are concerned, is towards finite difference methods, since they form the basis of most introductory courses on numerical techniques. However, an introduction to integral methods is also given. For the same reason, the depth of coverage given to ordinary differential equations is rather greater than that to partial differential equations (especially hyperbolic equations). Nevertheless, the material included on PDEs would be suitable for leading on to more advanced courses, such as one in computational fluid dynamics. Worked examples and problems are provided. Many of the methods can be used with a simple electronic calculator, others involve so much computation that a programmable device is required, and some will need a digital computer. This text is intended for undergraduate engineers and applied scientists. It will service a standard introductory course of approximately 40 hours duration, and equip students to tackle more advanced courses on specialized topics. Worked examples and problems are provided. Many of the methods can be used with a simple electronic calculator, others involve so much computation that a programme is required, and some will need a digital computer. This book should be of interest to undergraduate engineers and applied scientists.
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