Math 131C: General Course Outline
131C. Topics in Analysis. (4) Lecture, three hours; discussion, one hour. Requisites: courses 131A, 131B or 131AH, 131BH. Covers multivariable calculus and applications to ordinary differential equations.
Math 131C studies primarily multivariable analysis: definition of differentiability in several variables, partial derivatives, chain rule, Taylor expansion in several variables, inverse and implicit function theorems, equality of mixed partials, multivariable integration, change of variables formula, differentiation under the integral sign, analysis on curves and surfaces. Further topics to be chosen, usually including basic applications to ordinary differential equations (existence and uniqueness theorems for solutions) and the Green, Gauss and Stoke theorems.
Conway, J., A First Course In Analysis, Cambridge University Press
Coddington, E., An Introduction to Ordinary Differential Equations, Dover Publications