MAT 141: Fall 2016 | |

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## Lectures8/29/16. Lecture 1: Sets, natural numbers, induction, sums.8/31/16. Lecture 2: Integers, rationals, reals. 9/7/16. Lecture 3: Constructing the reals, cardinality questions. 9/12/16. Lecture 4: Cardinality questions, the complex numbers, inequalities. 9/14/16. Lecture 5: Area axioms, definition of the integral. 9/19/16. Lecture 6: Applications of integrals. 9/21/16. Lecture 7: Limits and continuity. 10/3/16. Lecture 8: Sperner’s lemma and the Brouwer Fixed Point Theorem. 10/5/16. Lecture 9: Differentiation and it’s properties. 10/10/16. Lecture 10: The mean value theorem and extrema, Jensen’s inequality. 10/12/16. Lecture 11: The Fundamental Theorem of Calculus and integration methods. 10/17/16. Lecture 12: The Fundamental Theorem of Algebra and properties of polynomials. 10/19/16. Lecture 13: Taylor polynomials and indeterminants. 10/24/16. Lecture 14: More limits, the Weierstrass approximation theorem, the Gaussian. 10/26/16. Lecture 15: Stirling’s approximation and Newton’s method. 11/7/16. Lecture 16: Introduction to Ordinary Differential Equations. 11/9/16. Lecture 17: Equilibrium behavior of moving particles. 11/14/16. Lecture 18: Sequences and infinite series. 11/16/16. Lecture 19: Convergence of infinite series. 11/21/16. Lecture 20: Sequences and series of functions. 11/28/16. Lecture 21: Power series and applications. 11/30/16. Lecture 22: Generating functions, Fourier series. 12/5/16. Lecture 23: Fourier series and convolution. 12/7/16. Lecture 24: Equidistribution modulo 1 and related problems. Content of some slides closely follows Apostol. |

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