Mathematical methods for physics and engineering. A comprehensive guide.

*(English)*Zbl 0884.00001
Cambridge: Cambridge University Press. xix, 1008 p. (1997).

This mathematical textbook mainly for students of science or engineering deals with the following topics (in this order): Elemantary calculus, complex numbers and hyperbolic functions, series and limits, partial differentiation, multiple integrals, linear algebra up to vector calculus, line, surface and volume integrals, Fourier series, Fourier and Laplace transforms, ordinary differential equations (including series solutions and eigenfunction methods), linear partial differential equations (of first and second order), analytic functions, tensors, calculus of variations, linear integral equations, group and representation theory, probability and statistics, numerical methods, and (as appendix) the gamma function. Each special topic is presented in three stages: a clear introduction, a theoretical explanation and detailed worked examples, in particular with physical background. Each chapter ends with numerous exercises followed by hints and solutions.

Though the authors pretend that they “have deliberately avoided strictly mathematical questions” (p. xvii), they could not avoid them all over. At very few passages they failed, so at the radius of convergence (p. 83), the definition of a limit (p. 92) and the statement that the Fourier series of a discontinuous function “does not produce a discontinuous function” (p. 332). On the other side, there are superfluous conditions as (iv) in the Dirichlet conditions (p. 327), and the linear independence of the particular integral in (13.7) (p. 397). The book ends with an index, but it does not contain a list of symbols explaining e.g. \(\approx\) (p. 3), \(\simeq\) (p. 96), \(\propto\) (p. 570) and \(\sim\) (p. 904). Actually, \(\approx\) is defined on p. 82, but used in another sense on p. 568. Finally, let us emphasize that Leibniz (p. 8) must not be written with tz.

Though the authors pretend that they “have deliberately avoided strictly mathematical questions” (p. xvii), they could not avoid them all over. At very few passages they failed, so at the radius of convergence (p. 83), the definition of a limit (p. 92) and the statement that the Fourier series of a discontinuous function “does not produce a discontinuous function” (p. 332). On the other side, there are superfluous conditions as (iv) in the Dirichlet conditions (p. 327), and the linear independence of the particular integral in (13.7) (p. 397). The book ends with an index, but it does not contain a list of symbols explaining e.g. \(\approx\) (p. 3), \(\simeq\) (p. 96), \(\propto\) (p. 570) and \(\sim\) (p. 904). Actually, \(\approx\) is defined on p. 82, but used in another sense on p. 568. Finally, let us emphasize that Leibniz (p. 8) must not be written with tz.

Reviewer: Lothar Berg (Rostock)

##### MSC:

00A06 | Mathematics for nonmathematicians (engineering, social sciences, etc.) |