Mert Gurbuzbalaban, WWH 429
E-mail: firstname.lastname@example.org where alpha=mert and beta=cims
Office Hours: 6-7pm, Mondays or by appointment
Insuk Seo, WWH 1004
E-mail: email@example.com where gamma=insuk and beta=cims
Class: Mondays 7:10-9pm, WWH 201, Courant Institute of Mathematics Sciences
This is a rigorous-style graduate-level analysis course meant to introduce Master's students to differentiation and integration for vector-valued functions of one and several variables. Covered topics include curves, surfaces, manifolds, inverse and implicit function theorems, integration on manifolds, Stokes’ theorem, applications. There will also be additional material related to convex analysis and optimization.
Jan 27: Convex sets (Ch 1) and overview of Ch 1.
Feb 3: Non-euclidean norms and overview of Ch 2. Minkowski functional.
Feb 10: Directional derivatives, differentiation (Ch 3.1 - 3.3).
Feb 17: President's Day
Feb 24: Functions of class C^q, relative extrema.
Mar 3: Ch 3.6 - 4.1. Convex functions and linear transformations
Mar 10: Ch 4.1 - 4.5. Affine transformations. Inverse function theorem.
Mar 17: Spring break
Mar 24: Midterm
Mar 31: Ch 4.5 - 4.8. Inverse/Implicit Function Theorem, Lagrange multipliers.
Apr 7: Manifolds (skipped intersection of manifolds), Ch 6.1 - 6.4.
Apr 14: Ch 7.1 - 7.2.
Apr 21: Ch 7.3 -
Apr 28: Selected topics from Ch 8 and 5
May 5: Selected topics from Ch 8 and 5
May 12: Final exam
Note: For HW submissions after the deadline, please reach out to our grader Insuk directly. Late HWs will be assessed a late penalty of 10% per day. Solutions posted here are selected from submitted homeworks and might contain some typos/minor errors.