Analysis I
Vladimir Ivanov
Syllabus of the course
Lectures 1 notes – Limit superior and limit inferior, Problem Set 1
Lectures 2 notes – Real Exponentiation, Part 3, Problem Set 2
Lectures 3 notes – Series, Absolute Convergence
Lectures 4 notes – Non-negative series, Cauchy Criterion
Lectures 5 notes – Root Test and Ratio Test
Lectures 6 notes – Subsets of the real line
Lectures 7 notes – The limit of a function at a point, part 1
Lectures 8 notes – The limit of a function at a point, part 2
Lectures 9 notes – Continuous functions
Lectures 10 notes – The Maximum Principle
Lectures 11 notes – The Intermediate Value Theorem
Lectures 12 notes – Compact Subsets of the Real Line
Lectures 13 notes – Sequences in R^m, Open and Closed Subsets of R^m
Lectures 14 notes – Multivariable Continuous Functions
Lectures 15 notes – Homeomorphisms. Connectedness.
Recommended textbooks
Real Analysis
- T.Tao, Analysis I
- V.Zorich, Mathematical Analysis I
- W.Rudin, Principles of Mathematical Analysis
- S.Abbott, Understanding Analysis