An Analytical Calculus: Volume 4
For School and University

Dr Maxwell guides the student through the early stages of analysis, while keeping the exposition as clear and uncomplicated as possible.

E. A. Maxwell (Author)

9780521090414, Cambridge University Press

Paperback / softback, published 20 November 2008

304 pages
21.6 x 14 x 1.7 cm, 0.39 kg

This is the final volume of a series covering all stages of development of the Calculus, from the last year at school to degree standard. The books are written for students of science and engineering as well as for specialist mathematicians, and are designed to bridge the gap between the works used in schools and more advanced studies, with their emphasis on rigour. Dr Maxwell guides the student through the early stages of analysis, while keeping the exposition as clear and uncomplicated as possible. The aim is to instil a knowledge of general method rather than to study the particular functions in detail; in this way the student is led on naturally to apply what they have learnt to move advanced mathematical contexts. Dr Maxwell is, as usual, lucid in his presentation, explaining difficulties in greater detail than is customary in an advanced textbook, and guarding against the pitfalls that await the beginner.

Preface
Introduction
Part I: Ordinary differential equations
19. Equations of the form y'=f(x. y)
20. Linear differential equations: general properties
21. The linear differential equation with constant coefficients
22. The linear differential equation with constant coefficients: alternative method
Part II: The definition of functions by infinite series and integrals
23. The convergence of series
24. The definition of functions by series
25. Power series
26. The definition of functions by integrals
27. The solution of differential equations in terms of infinite series
28. Fourier series
Part III: Laplace's equation and related equations
29. The transformation of Laplace's equation
30. 'Laplace' equations
31. Spherical harmonics
Answers to examples
Index.

Subject Areas: Probability & statistics [PBT]