Mathematical Methods for Physics and Engineering: A Comprehensive Guide
The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.
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Complex numbers and hyperbolic functions
Series and limits
Matrices and vector spaces
general and particular solutions
separation of variables
Calculus of variations
Applications of complex variables
Line surface and volume integrals
Firstorder ordinary diﬀerential equations
Higherorder ordinary diﬀerential equations
Series solutions of ordinary diﬀerential equations
Eigenfunction methods for diﬀerential equations
Preface to the third edition page
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Página 45 - The derivative of the product of two functions is equal to the first function times the derivative of the second plus the second times the derivative of the first.
Página 47 - This can now be rearranged into the more convenient and memorisable form This can be expressed in words as the derivative of a quotient is equal to the bottom times the derivative of the top minus the top times the derivative of the bottom, all over the bottom squared.
Página xix - I know the kings of England, and I quote the fights historical, From Marathon to Waterloo, in order categorical ; I'm very well acquainted too with matters mathematical, I understand equations, both the simple and quadratical, About binomial theorem I'm teeming with a lot o' news, With many cheerful facts about the square of the hypotenuse. I'm very good at integral and differential calculus, I know the scientific names of beings animalculous, In short, in matters vegetable, animal and mineral, I...