Calendar
Calendar
| Date | Topic | Section | Notes |
|---|---|---|---|
| Tuesday, January 12 | First day of class. Properties of continuous functions on intervals. | 3.3-3.4 | Jan 12 |
| Thursday, January 14 | Properties of continuous functions on intervals. Derivatives. | 4.1-2 | Jan 14 |
| Tuesday, January 19 | Mean Value Theorem. Intermediate Value property of derivatives. Inverse function theorem. | 4.2, TBB 7.9, Lebl 4.4 | Jan 19 |
| Thursday, January 21 | Inverse function theorem. Implicit function theorem (discussion, not proof). | 4.4, 8.5, TBB 12.6 | Jan 21 |
| Tuesday, January 26 | Riemann Integral. | 5.1-2 | Jan 26 |
| Thursday, January 28 | Riemann Integral: Properties. Integrability of continuous functions. | 5.2 | Jan 28 |
| Tuesday, February 2 | Integrability of piecewise continuous functions. Fundamental Theorem of Calculus. | 5.3 | Feb 2 |
| Thursday, February 4 | Riemann-Lebesgue theorem. Sets of measure zero. | TBB 8.6.3, TBB 6.8 | Feb 4 |
| Tuesday, February 9 | Oscillation of a function. Proof of Riemann-Lebesgue. | TBB 6.7 | Feb 9 |
| Thursday, February 11 | Conclusion of proof. Beyond Riemann integration. | Feb 11 | |
| Tuesday, February 16 | Conclusion of proof. Beyond Riemann integration. | Feb 16 | |
| Thursday, February 18 | Sequences and series of functions. Uniform convergence and continuity. | 6.1-2 | Feb 18 |
| Tuesday, February 23 | Uniform convergence: integrals and derivatives. | 6.2 | Feb 23 |
| Thursday, February 25 | Power series. | 2.6.5, 6.2 | Feb 25 |
| Tuesday, March 2 | Power and Taylor series. | TBB 10.5 | Mar 2 |
| Thursday, March 4 | Taylor and Fourier series. | TBB 10.8 | Mar 4 |
| Tuesday, March 9 | Taylor series | Mar 9 | |
| Thursday, March 11 | Trigonometric and Fourier series | Mar 11 | |
| Tuesday, March 16 | Picard’s theorem | 6.3 | Mar 16 |
| Thursday, March 18 | Picard’s theorem | Mar 18 | |
| Tuesday, March 23 | Metric spaces. | 7.1 | Mar 23 |
| Thursday, March 25 | Metric spaces of functions. Topology. | 7.1-2 | Mar 25 |
| Tuesday, March 30 | Completeness and compactness. Continuous functions. | 7.3-7.5 | Mar 30 |
| Thursday, April 1 | Compactness. Continuous functions. | Apr 1 | |
| Tuesday, April 6 | Compactness. Continuous functions. Contraction mappings. | Apr 6 | |
| Thursday, April 8 | Continuous functions. Contraction mappings. | Apr 8 | |
| Tuesday, April 13 | No meeting (Spring Break) | ||
| Thursday, April 15 | No meeting (Spring Break) | ||
| Tuesday, April 20 | Differentiation under the integral sign | K. Conrad blurb | Apr 20 |
| Thursday, April 22 | Differentiation under the integral sign | Apr 22 | |
| Tuesday, April 27 | Differentiation under integra, non-compact domains | Apr 27 | |
| Thursday, April 29 | Fundamental Theorem of Algebra. Final exam study | Apr 29 | |
| Final exam |
Section numbers are for Lebl, except if noted TBB for Thomson-Bruckner-Bruckner.