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More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway to 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. Now with a new preface by the author, this book documents 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, subtlest problems imaginable. In touring The Calculus Gallery, we can see how it all came to be.

Calculus --- History. --- Absolute value. --- Addition. --- Algebraic number. --- Antiderivative. --- Arc length. --- Augustin-Louis Cauchy. --- Baire category theorem. --- Bernhard Riemann. --- Binomial theorem. --- Bounded function. --- Calculation. --- Central limit theorem. --- Characterization (mathematics). --- Coefficient. --- Complex analysis. --- Continuous function (set theory). --- Continuous function. --- Contradiction. --- Convergent series. --- Corollary. --- Countable set. --- Counterexample. --- Dense set. --- Derivative. --- Diagram (category theory). --- Dichotomy. --- Differentiable function. --- Differential calculus. --- Differential equation. --- Division by zero. --- Equation. --- Existential quantification. --- Fluxion. --- Fourier series. --- Fundamental theorem. --- Geometric progression. --- Geometric series. --- Geometry. --- Georg Cantor. --- Gottfried Wilhelm Leibniz. --- Harmonic series (mathematics). --- Henri Lebesgue. --- Infimum and supremum. --- Infinitesimal. --- Infinity. --- Integer. --- Integration by parts. --- Intermediate value theorem. --- Interval (mathematics). --- Joseph Fourier. --- Karl Weierstrass. --- L'Hôpital's rule. --- Lebesgue integration. --- Lebesgue measure. --- Length. --- Leonhard Euler. --- Limit of a sequence. --- Logarithm. --- Mathematical analysis. --- Mathematician. --- Mathematics. --- Mean value theorem. --- Measurable function. --- Natural number. --- Notation. --- Nowhere continuous function. --- Number theory. --- Pointwise. --- Polynomial. --- Power rule. --- Princeton University Press. --- Q.E.D. --- Quadratic. --- Quantity. --- Rational number. --- Real analysis. --- Real number. --- Rectangle. --- Riemann integral. --- Root test. --- Scientific notation. --- Series (mathematics). --- Set theory. --- Sign (mathematics). --- Stone–Weierstrass theorem. --- Subset. --- Subtangent. --- Summation. --- Tangent. --- Textbook. --- Theorem. --- Theory. --- Transcendental number. --- Trigonometric functions. --- Uniform continuity. --- Uniform convergence. --- Unit interval. --- Upper and lower bounds. --- Vito Volterra. --- Westmont College.