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Calculus Made Easy ignores the use of limits with its epsilon-delta definition, replacing it with a method of approximating (to arbitrary precision) directly to the correct answer in the infinitesimal spirit of Leibniz, now formally justified in modern nonstandard analysis and smooth infinitesimal analysis.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
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 ...
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
The following other wikis use this file: Usage on en.wikisource.org Wikisource:Community collaboration/Monthly Challenge/August 2022; Index:Calculus Made Easy.pdf
Levi, Mark (2009), "6.3 How Much Gold Is in a Wedding Ring?", The Mathematical Mechanic: Using Physical Reasoning to Solve Problems, Princeton University Press, pp. 102– 104, ISBN 978-0-691-14020-9. Levi argues that the volume depends only on the height of the hole based on the fact that the ring can be swept out by a half-disk with the ...
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