This volume aims to bridge between elementary textbooks on calculus and established books on advanced analysis. It provides elucidation of the reversible process of differentiation and integration through two featured principles: the chain rule and its inverse - the change of variable - as well as the Leibniz rule and its inverse - the integration by parts. The chain rule or differentiation of composite functions is ubiquitous since almost all (a.a.) functions are composite functions of (elementary) functions and with the change of variable method as its reverse process. The Leibniz rule or differentiation of the product of two functions is essential since it makes differentiation nonlinear and with the method of integration by parts as its reverse process.

Readers will find numerous worked-out examples and exercises in this volume. Detailed solutions are provided for most of the common exercises so that readers remain enthusiastically motivated in solving and understanding the concepts better.

The intention of this volume is to lead the reader into the rich fields of advanced analysis and to obtain a much better view of useful mathematics.

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Charlotte y Peter Fiell son dos autoridades en historia, teor�a y cr�tica del dise�o y han escrito m�s de sesenta libros sobre la materia, muchos de los cuales se han convertido en �xitos de ventas. Tambi�n han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Dise�o del siglo XX, El dise�o industrial de la A a la Z, Scandinavian Design y Dise�o del siglo XXI.

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