| Date | Topics | Reading |
|---|
| Wed 1st Feb |
Introduction and overview: |
Rudin Ch 2 and 3 |
| Fri 3rd Feb |
Limits and continuity |
Rudin 4.1-4.13 |
| Mon 6th Feb |
Continuity and compactness |
Rudin 4.13-4.21 |
| Wed 8th Feb |
Continuity and connectedness (Intermediate Value Theorem) |
Rudin 4.12-4.34 |
| Fri 10th Fb |
Differentiability, examples |
Rudin 5.1-5.6 |
| Mon 13th Feb |
Examples, Rolle's Theorem, Mean Value Theorem |
Rudin 5.7-5.11 |
| Wed 15th Feb |
MVT, L'Hôpital's rule, devil's staircase |
Rudin 5.11-5.14 |
| Fri 17th Feb |
Taylor's Theorem and applications |
Rudin 5.14-5.19 |
| Mon 20th Feb |
No class (President's Day) |
None |
| Wed 22nd Feb |
Integration |
Rudin 6.1-6.7 |
| Fri 24th Feb |
Continuous and monotonic functions are integrable |
Rudin 6.8-6.11 |
| Mon 27th Feb |
Properties of integration |
Rudin 6.12-6.19 |
| Wed 1st March |
Fundamental Theorem of Calculus |
Rudin 6.20-6.27 |
| Friday 3rd March |
Pointwise and uniform convergence |
Rudin 7.1-7.12 |
| Mon 6th March |
Uniform convergence differentiation and integration |
Rudin 7.13-7.18 |
| Wed 8th March |
Power series |
Rudin 8.1-8.5 |
| Friday 10th March |
Equicontinuity/Ascoli-Arzela Theorem |
Rudin 7.19-7.25 |
| Mon 13th March |
Stone-Weierstrass Theorem |
Rundin 7.26-7.33 |
| Wed 15th March |
Introduction to multivariable functions, continuity |
Spivak Ch 1 |
| Fri 17th March |
Derivatives, Chain rule |
Spivak Ch2 p 15-22 |
| Mon 20th March |
Partial derivatives, Jacobian, Chain rule pt 2 |
Spivak p 25-31 |
| Wed 22nd March |
Inverse Function Theorem |
Spivak p 31-39 |
| Fri 24th March |
Implicit Function Theorem/Rank Theorem |
Spivak p 39-45 |
| Mon 27th March |
No Class - Spring break. |
. |
| Wed 29th March |
No Class - Spring break. |
. |
| Fri 31st March |
No Class - Spring break. |
. |
| Mon 3rd April |
IFT examples, max/minima, lagrange |
Class notes |
| Wed 5th April |
Integration, measure, content |
Spivak Ch3 p 46-52 |
| Fri 7th April |
Fubini Theorem |
Spivak p 52-58 |
| Mon 10th April |
Integration examples, partitions of unity |
Class notes |
| Wed 12th April |
Change of variables |
Spivak p 66-73 |
| Fri 14th April |
Tensors |
Class notes and Spivak Ch 4 p 75-77 |
| Mon 17th Apil |
Alternating Tensors |
Spivak Ch 4 p 78 - 83 |
| Wed 19th April |
Orientation, vector fields, differential forms |
Spivak p 83- 89 |
| Fri 21st April |
Pullbacks, differential, closed and exact forms. |
Spivak p 89 - 92 |
| Mon 24th April |
Poincare Lemma, n-chains. |
Spivak p 94 -100 |
| Wed 26th April |
Integrating forms |
Spivak p 100-104 |
| Fri 28th April |
Stokes's Theorem, consequences |
Class notes and Spivak |
| Mon 1st May |
Manifolds |
Spivak Ch5 |
| Wed 3rd May |
Fields, forms, orientation |
Spivak Ch5 |
| Fri 5th May |
Stokes's Theorem redux |
Spivak Ch 5 |