Real analysis: course
This is a one-semester course in real analysis (aka advanced calculus). Certain facts about derivative, integral, the real number system, continuity and differentiability of functions of a single variable, integration of functions of a single variable, infinite series etc are proven. Goal: good familiarity with the foundations of Calculus, ability to work in the definition-theorem-proof format, some "mathematical maturity".
- Metric spaces
- Functions of several variables
- Extrema of functions of several variables
- Functions of several variables: exercises
- Parametric curves
- Independence of path
- Real analysis: test 1
- Real analysis: test 2
- Real analysis: final 1
- Real analysis: test 3
- Real analysis: test 4
- Real analysis: final 2
Text: A First Course in Real Analysis by Protter and Morrey (Chapters 2-5,9).
Alternative is a more geometric then analytical approach, see Vector calculus: course.