Calculus With Theory: Lecture Notes

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Integers and exponents Square roots, and the existence of irrational numbers The Riemann condition Properties of integrals Integrability of bounded piecewise-monotonic functions Continuity of the square root function Rational exponents – an application of the intermediate-value theorem The small span theorem and the extreme-value theorem Theorem and proof Exercises on derivatives The fundamental theorems of calculus The trigonometric functions The exponential and logarithm functions Integration Taylor’s formula L’Hopital’s rule for 0/0 Notes on error estimates The basic theorems on power series A family of non-analytic functions Fourier Series

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18.014 Calculus with Theory Fall 2010

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