Syllabus for Analysis 1 Qualifying Exam

The Analysis 1 exam covers essentially the material taught in MTH G101 (Analysis 1).

Topics

Metric spaces: topology of metric spaces, continuous maps, sequences and limits, compactness, connectedness, completeness, and the contraction lemma.
Calculus of one variable: basic properties of derivatives and integration.
Sequences and series of functions: uniform convergence, equicontinuous families of functions.
Functions of several variables: the differential of a map, the chain rule, inverse and implicit function theorems, integration of differential forms, Stokes' Theorem.
Existence and uniqueness of ODE, applications.

Introduction to Analysis, by Maxwell Rosenlicht, Dover, 1986.
Principles of Mathematical Analysis, 3rd Edition, by Walter Rudin, McGraw-Hill, 1976.

Started: Sept. 8, 2003. Last modified: Last modified: Sept. 8, 2003
Page created and maintained by: Alex Suciu
Comments to: alexsuciu@neu.edu