A treatise on advanced calculus : including those parts of the theory of functions of real and complex variables which form the logical basis of the infinitesimal analysis and its applications to geometry and physics / Philip Franklin

The book begins with the fundamental notions of real numbers, limits, continuity and convergence. The author then develops the logarithmic, exponential and trigonometric functions from their functional equations. Differential and integral calculus is developed from the beginning, but from an advanced standpoint. A chapter on the elementary functions of a complex variable precedes the first chapter on integration. Besides the usual topics common to most books on advanced calculus, several other less commonly included subjects are treated, such as the measure and content of sets, Stieltjes integrals, equi-continuity, the theory of functions of several complex variables, existence theorems for differential equations, Fourier integrals and Laplace transforms, Bernoulli polynomials and the Euler-Maclaurin sum formula, etc. Some topics, such as Bessel's functions, appear only among the varied exercises at the ends of the chapters. (MathSciNet)

Bibliogr. p. 585-586