Gibson George A. Advanced Calculus

London: Macmillan & Co. Ltd., 1966. — 510 p.A sequel tо an elementary treatise on the calculus.
The first edition of Professor Gibson’s Elementary Treatise on the Calculus was published in 1901. Pressure of work made it impossible for him to proceed, till after his resignation in 1927, with the preparation of a projected treatise dealing with more advanced aspects of the subject. The book was completed by the summer of 1929, and was passing through the press at the time of his death on 1st April, 1930.
The first eight chapters are devoted mainly to the Differential Calculus, and the remaining seven to Riemann’s theory of integration. The treatise begins with Dedekind’s theory of irrational numbers ; then follow discussions of bounded sets, sequences, limits, and differentiation of functions of one variable and of functions of several variables. Chapter V deals with existence theorems for implicit functions and with the theory of Jacobians. Three further chapters contain accounts of infinite series, complex functions of a real variable, Lagrange’s expansion, MAXIMA and minima, infinite products, and Gamma Function