Instructor: | Marcel Oliver |
Email: | m.oliver@jacobs-university.de |
Phone: | 200-3212 |
Office hours: | Mo 11:30, We 10:00 in Research I, 107 |
Lectures: | Mo 9:45 and Tu 14:15 in East Hall 4 |
Tutorial: | Th 19:30 in East Hall 4 |
Homework: | 20% |
Midterm Exam: | 30% |
Final Exam: | 50% |
04/02/2019: | Applications of the integral I: Taylor's formula; indefinite integrals; Uniform convergence revisited: exchange of integration and differentiation (see, e.g., this handout, Theorem 5.5) |
05/02/2019: | Applications of the integral II: Laplace's method and Stirling's formula (see O.A. Ivanov, Easy as \(pi\)? An introduction to higher mathematics, Springer, 1999, Section 2.5) |
11/02/2019: | Laplace's method (finish); Uniform convergence of series, Cauchy's criterion (Rudin, 7.7-7.10); uniform limits of continuous functions are continuous (Rudin, 7.11-7.12) |
12/02/2019: | Point-set topology in metric spaces I: open and closed sets (Rudin, 2.15-2.24) |
18/02/2019: | Point-set topology in metric spaces II: compact sets (Rudin, 2.31-2.40) |
19/02/2019: | Point-set topology in metric spaces II: more about compactness (Rudin, 2.41, 4.16 with alternative proof); continuous pre-images of open sets are open (Rudin, 4.8) |
25/02/2019: | Monotonically convergent sequences of functions on a compact set are uniformly convergent (Rudin, 7.13); convergence, integration, and differentiation revisited. |
26/02/2019: | Equicontinuity and the Arzela-Ascoli theorem |
04/03/2019: | Stone-Weierstrass theorem |
05/03/2019: | Power series, radius of convergence |
11/03/2019: | Curves in \(R^n\) |
12/03/2019: | Midterm Review |
18/03/2019: | Midterm Exam |
19/03/2019: | Linear transformations, norm of a linear transformation, invertibility |
25/03/2019: | Total derivative |
26/03/2019: | Directional derivative, partial derivatives |
01/04/2019: | Chain rule |
02/04/2019: | Taylor's formula in \(R^n\) |
08/04/2019: | Contraction mapping theorem |
09/04/2019: | Inverse function theorem |
23/04/2019: | Implicit function theorem I |
29/04/2019: | Implicit function theorem II |
30/04/2019: | Riemann integral in \(R^n\) I: definition and elementary properties |
06/05/2019: | Riemann integral in \(R^n\) II: iterated integrals and Fubini's theorem |
07/05/2019: | Riemann integral in \(R^n\) III: change of variables and polar coordinates |
13/05/2019: | Riemann integral in \(R^n\) IV: the divergence theorem with elementary applications |
14/05/2019: | Review for final exam |
TBA: | Final Exam |