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Calculus --- Calculus - Textbooks

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More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway into higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. William Dunham lucidly presents the definitions, theorems, and proofs. "Students of literature read Shakespeare; students of music listen to Bach," he writes. But this tradition of studying the major works of the "masters" is, if not wholly absent, certainly uncommon in mathematics. This book seeks to redress that situation. Like a great museum, The Calculus Gallery is filled with masterpieces, among which are Bernoulli's early attack upon the harmonic series (1689), Euler's brilliant approximation of pi (1779), Cauchy's classic proof of the fundamental theorem of calculus (1823), Weierstrass's mind-boggling counterexample (1872), and Baire's original "category theorem" (1899). Collectively, these selections document the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching--a story of genius triumphing over some of the toughest, most subtle problems imaginable. Anyone who has studied and enjoyed calculus will discover in these pages the sheer excitement each mathematician must have felt when pushing into the unknown. In touring The Calculus Gallery, we can see how it all came to be.

Calculus --- History. --- Calcul infinitésimal --- History --- Histoire --- Calculus - History.

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Each step higher in math studies is crucial to doing well at the next level. Pre-Calc is the gateway to higher level mathematics of which the best degrees and careers are built upon. The core essentials in 6 laminated pages can be used along with your text and lectures, as a review before testing, or as a memory companion that keeps key answers always at your fingertips. The most answers for your money in what students have said is "a must have" study tool.Suggested uses:o Quick Reference - instead of digging into the textbook to find a core answer you need while studying, use the guide to reinforce quickly and repeatedlyo Memory - refreshing your memory repeatedly is a foundation of studying, have the core answers handy so you can focus on understanding the conceptso Test Prep - no student should be cramming, but if you are, there is no better tool for that final review

Precalculus --- Mathematics --- Study and teaching --- CALCULUS --- MATHEMATICS

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Differential calculus. --- Sobolev spaces. --- Calcul différentiel --- Sobolev, Espaces de --- Differential calculus --- Sobolev spaces --- Calcul différentiel

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This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.

Calculus --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Functional analysis. --- Operator theory. --- Functional Analysis. --- Operator Theory. --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations