Includes bibliographical references and index.

The 17th-century calculus of Newton and Leibniz was built on shaky foundations, and it wasn't until the 18th and 19th centuries that mathematicians -- especially Bolzano, Cauchy, and Weierstrass -- began to establish a rigorous basis for the subject. The resulting discipline is now known to mathematicians as analysis. This book, aimed at readers with some grounding in mathematics, describes the nascent evolution of mathematical analysis, its development as a subject in its own right, and its wide-ranging applications in mathematics and science, modelling reality from acoustics to fluid dynamics, from biological systems to quantum theory.