The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. Indeed, not everyone agreed with the Jesuits. In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules.
With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts.
Because the separate real and imaginary parts of any analytic function must satisfy Laplace’s equation, complex analysis is widely applicable to two-dimensional problems in physics.Pulsing with drama and excitement, Infinitesimal celebrates the spirit of discovery, innovation, and intellectual achievement-and it will forever change the way you look at a simple line. It is useful in many branches of mathematics, including number theory and applied mathematics as well as in physics, including hydrodynamics, thermodynamics, and electrical engineering.Ĭomplex analysis is particularly concerned with the analytic functions of complex variables (or, more generally, meromorphic functions).
Book DescriptionĬomplex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It has been used for undergraduate complex analysis course at Georgia Tech and at a few other places.
Infinitesimals book pdf#
Complex Analysis by George Cain can be downloaded in pdf format free of charge. This is free a textbook for an introductory course in complex analysis.
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