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

About the author Philip Franklin (1898 - 1965) was a prominent American mathematician who specialized in analysis. He taught at MIT from the 1920s until his retirement in 1964. "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. Preface I. Real Numbers II. Limits of Functions III. Exponential, Logarithmic, and Trigonometric Functions IV. Differentiation V. Complex Numbers VI. Integration VII. Integrable Functions VIII. Extensions and Applications of Integration IX. Infinite Series and Infinite Products X. Partial Differentiation XI. Multiple Integration XII. Sequences of Functions XIII. Functions of Complex Variables XIV. Fourier Series and Integrals XV. Differential Equations XVI. The Gamma Function and Other Definite Integrals Bibliography Index Tags: