MAT257 Analysis II, University of Toronto 2007-08

MATH 257 Analysis II 2007-2008

Almut Burchard, Instructor

Course schedule
How to reach me: Almut Burchard, 6186 Bahen Center, 6-4174.
almut @math ,
Lectures MWF 2:10-3pm, WB 130 / BA 2165 / WB 130.
Office hours MW 5-6pm and by appointment.
Teaching assistant: Michael Bailey, bailey @math .
Tutorial R 4-6pm, AP 120.
Text:   "Calculus on Manifolds", by M. Spivak. Perseus Books, ISBN 0-8053-9021-9, plus selected additional material.

Course content:
  1. Topology of R^n: Metrics and norms, compactness, continuous functions, extreme value theorem.
  2. Derivatives: inverse and implicit function theorems, Taylor expansion, maxima and minima, Lagrange multipliers.
  3. Integrals: Fubini's theorem, partitions of unity, change of variables.
  4. Differential forms. Poincaré lemma. Surface integrals. Vector fields; Gradient, divergence, and curl.
  5. Manifolds in R^n: integration on manifolds; Stokes' theorem for differential forms and its classical versions in R^2 and R^3.
Prerequisites: MAT157Y1, MAT240H1
Co-requisite: MAT247H1
  5% : Class participation
15% : 9 hand-in homework sets (drop two)
30% : 3 mid-term tests
50% : Final examination
Remarks. Our goal is to understand the entire book, fill in the details, and master the exercises by the end of the year. We will at times take a slightly more general point of view than the book (which focuses exclusively on R^n), and also expand on examples and applications.

Attendance in lectures and tutorials is expected. The weekly tutorial offers an opportunity to share insight, ask additional questions, look at more examples, and work on problems. You are encouraged to discuss lectures and homework problems with each other and with us, and you may consult other sources. However, you should write up your assignments yourself, in your own words, and be ready to defend them! Exams will be closed-book, closed notes.