**Instructor:** Daniel W. van Wyk

**Course on Canvas:** https://canvas.dartmouth.edu/courses/50253/ ⇗

## Syllabus

Lecture Date Textbook sections Description Week 1 Wednesday, January 5 Sec. 1.1 Ordered sets, fields, rational and irrational numbers Friday, January 7 Sec. 1.2 Absolute value, triangle inequality, and arithmetic and geometric means Week 2 Monday, January 10 Sec. 1.3 Bounded sets, intervals, supremum and infimum Wednesday, January 12 Sec. 1.3 (cont.) Completeness axiom and Archimedean property Friday, January 14 Sec. 1.4 Countable and uncountable sets, Week 3 Monday, January 17 Martin Luther King Jr. Day No lecture Wednesday, January 19 2.1 Convergent sequences: epsilon-delta definition Thursday, January 18 (x-hour) 2.1 and 2.2 Convergent Monotone sequences Friday, January 21 2.2 Cauchy sequences Week 4 Monday, January 24 2.3 Subsequences Wednesday, January 26 3.1 Limit of a function Friday, January 28 3.2 Continuity Week 5 Monday, January 31 3.3 Intermediate and Extreme values Wednesday, February 2 3.3, 3.4 Intermediate and Extreme values, Uniform continuity Thursday, February 3 (x-hour) 3.4 Uniform continuity Friday, February 4 4.1 Derivatives and their properties Week 6 Monday, February 7 Wednesday, February 9 4.2 Mean Value Theorem Friday, February 11 5.1 Riemann Integral Week 7 Monday, February 14 5.2 Conditions for Riemann integrability Wednesday, February 16 5.3 The Fundamental Theorem of Calculus Thursday, February 17 (x-hour) 6.1 Convergence of infinite series Friday, February 18 6.2 Comparison test Week 8 Monday, February 21 6.3 Absolute convergence Wednesday, February 23 7.1 Sequences and series of functions, pointwise convergence Friday, February 25 7.1 Sequences and series of functions, pointwise convergence (continued) Week 9 Monday, February 28 7.2 Uniform convergence Wednesday, March 2 7.3 Uniform Convergence and inherited properties Friday, March 4 7.4 Power series Week 10 Monday, March 7 7.5 Taylor's Formula