Fall 2016
General Information
Syllabus
Lectures
Homework
Exams
Lectures
8/29/16. 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.