## MATH 62CM: Modern Mathematics: Continuous Methods

A proof-based introduction to manifolds and the general Stokes' theorem. This includes a treatment of multilinear algebra, further study of submanifolds of Euclidean space (with many examples), differential forms and their geometric interpretations, integration of differential forms, Stokes' theorem, and some applications to topology. Prerequisites:
Math 61CM and 63CM.

Terms: Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Cant, D. (PI)
;
Chodosh, O. (PI)

## MATH 63CM: Modern Mathematics: Continuous Methods

A proof-based course on ordinary differential equations and other applications of derivatives. Topics include the inverse and implicit function theorems, implicitly-defined submanifolds of Euclidean space, linear systems of differential equations and necessary tools from linear algebra, stability and asymptotic properties of solutions to linear systems, existence and uniqueness theorems for nonlinear differential equations, behavior of solutions near an equilibrium point, and Sturm-Liouville theory. Prerequisite:
Math 61CM.

Terms: Win
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Ryzhik, L. (PI)
;
Yang, K. (TA)

Filter Results: