Integration of Functions
The first edition of Hardy's Integration of Functions of a Single Variable was published in 1905, with this 1916 second edition being reprinted up until 1966. Now this digital reprint of the second edition will allow the twenty-first-century reader a fresh exploration of the text. Hardy's chapters provide a comprehensive review of elementary functions and their integration, the integration of algebraic functions and Laplace's principle, and the integration of transcendental functions. The text is also saturated with explanatory notes and usable examples centred around the elementary problem of indefinite integration and its solutions. Appendices contain useful bibliographic references and a workable demonstration of Abel's proof, rewritten specifically for the second edition. This innovative tract will continue to be of interest to all mathematicians specialising in the theory of integration and its historical development.
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2Bx+C calculated class of functions coefficients are polynomials coefficients rational common factor complete constant multiple cosh curves of deficiency curves whose deficiency deficiency is unity defined definite integrals determine differential coefficient double points dx f elementary algebra elementary function elementary transcendental eliminate elliptic functions elliptic integrals example explicit algebraical functions exponentials expressible in terms expression in finite f dx finite number finite terms follows G. H. HARDY given Goursat's Hence infinity integral calculus integral dx integrals of algebraical integration of rational irreducible irreducible polynomial Jydx Lemma Liouville log log means of elementary number of double number of terms obtain an equation partial fractions particular plane curves problem proof proved pseudo-elliptic quadratic rational function rational or algebraical reduced roots of Q solution substitution suppose symmetric polynomial terms of elementary theorem theory of equations transcendental functions transcendents transformation unicursal curve values vanish identically variable