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George Brinton Thomas Jr. (January 11, 1914 – October 31, 2006) was an American mathematician and professor of mathematics at MIT. Internationally, he is best known for being the author of the widely used calculus textbook Calculus and Analytic Geometry, known today as Thomas' Textbook.
In integral calculus we would want to write a fractional algebraic expression as the sum of its partial fractions in order to take the integral of each simple fraction separately. Once the original denominator, D 0 , has been factored we set up a fraction for each factor in the denominator .
His books are standard textbooks in universities in many countries. One of his best-known textbooks is Calculus: Early Transcendentals (1995), [1] a set of textbooks which is accompanied by a website for students. Stewart was also a violinist and a former member of the Hamilton Philharmonic Orchestra. [2]
Fundamental theorem of calculus; Integration by parts; Inverse chain rule method; Integration by substitution. Tangent half-angle substitution; Differentiation under the integral sign; Trigonometric substitution; Partial fractions in integration. Quadratic integral; Proof that 22/7 exceeds π; Trapezium rule; Integral of the secant function ...
for the infinite series. Note that if the function () is increasing, then the function () is decreasing and the above theorem applies.. Many textbooks require the function to be positive, [1] [2] [3] but this condition is not really necessary, since when is negative and decreasing both = and () diverge.
James Stewart, Daniel Clegg, Saleem Watson (2016) Single Variable Calculus: Early Transcendentals (Instructor's Edition) 9E, Cengage ISBN 978-0-357-02228-9; E. T. Whittaker & G. N. Watson (1963) A Course in Modern Analysis, 4th edition, §2.3, Cambridge University Press ISBN 0-521-58807-3
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It would be a few decades later that Newton and Leibniz independently developed infinitesimal calculus, which grew, with the stimulus of applied work that continued through the 18th century, into analysis topics such as the calculus of variations, ordinary and partial differential equations, Fourier analysis, and generating functions.
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