A Treatise on Advanced Calculus

"This book is a valuable contribution to the field of advanced calculus. It definitely bridges the gap between formal elementary work and the exacting rigor of modern analysis … it would be difficult to find better exposition at this level." ― American Mathematical Monthly This classic book offers a comprehensive logical treatment of the theory of calculus and related topics. Suitable for advanced undergraduates and graduate students in mathematics, it provides students with a substantial base for graduate work in physics by concentrating on theory rather than on techniques and applications. Topics include real numbers; limits of functions; exponential, logarithmic, and trigonometric functions; differentiation; complex numbers; integration; integrable functions; extensions and applications of integration; infinite series and infinite products; partial differentiation; multiple integration; sequences of functions; functions of complex variables; Fourier series and integrals; differential functions; and the Gamma function and other definite integrals. More than 600 problems amplify the text.