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Useful Mathematical Tools

# Useful Mathematical Tools - Leibnitz’s Rule Integration...

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Useful Mathematical Tools Spring 2009 Summation Notation Product Notation Factorial Indicator Function – Let Ω be a space with elements ω. Let A be a subset of Ω. Then the indicator function of A is given by Properties of the indicator function i) ii) iii) Special Case of Indicator Function Arithmetic Series Geometric Series Finite Sum Infinite Sum

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Binomial Theorem Expansions of i) ii) Fundamental Theorem of Calculus Suppose that f is a continuous function on the interval [a, b], then
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Unformatted text preview: Leibnitz’s Rule Integration by Parts Suppose that f, g are continuously differentiable function on the interval [a, b], then Monotone Functions A monotone function is one which is always increasing or decreasing. A sufficient condition to check for monotonicity is 1. If for all x, then is monotone increasing 2. If for all x, then is monotone decreasing Gamma Function Facts about the gamma function 1. 2. 3....
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Useful Mathematical Tools - Leibnitz’s Rule Integration...

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