MATH 3150 — Section 1, Real Analysis
Text book: Elementary Analysis - The theory of calculus, Kenneth A. Ross, Springer Verlag, UTM, 2013.
Syllabus: pdf
Schedule of topics: pdf
Homework:
Midterm:
Lectures:
Lecture 1 [01/06/2025] pdf: Course overview, natural numbers and proofs by induction (Section 1)
Lecture 2 [01/09/2025] pdf: The rational numbers, the rational zeros theorem (Section 2)
Lecture 3 [01/13/2025] pdf: The real numbers (Section 1.3), Min, max, sup and inf (Section 4)
Lecture 4 [01/16/2025] pdf: The completness axiom, the Arquimedean property of R, density of Q in R, +/-infity (Sections 4 and 5)
Lecture 5 [01/23/2025] pdf: Sequences and limits (Sections 7 and 8)
Lecture 6 [01/27/2025] pdf: Sequence theorems (Section 9)
Lecture 7 [01/30/2025] pdf: Monotone sequences, lim inf and lim sup, Cauchy sequences (Sections 10, 11 and 12)
Lecture 8 [02/03/2025] pdf: More lim inf and lim sup (Section 12), subsequences (Section 11), series (Section 14)
Lecture 9 [02/06/2025] pdf: Convergence tests for series (Sections 14 and 15)
Lecture 10 [02/10/2025] pdf: More examples of convergence tests, continuous functions (Section 17)
Lecture 11 [02/13/2025] pdf: Properties of continuous functions (Section 18), Uniform continuity (Section 19)
Lecture 12 [02/20/2025] pdf: More on uniform continuity (Section 19)
Lecture 13 [02/24/2025] pdf: Power series (Section 23)