Math 4310-002 Schedule
Week Date Section Topics
1 Aug 27 Course introduction, 1.1 Review of the rules of logic (from Math 3000 or 3200)
Aug 29 1.2 Infinite sets and countability
Aug 31 1.3, 1.4 The field axioms for rational numbers
2 Sep 3 HOLIDAY Labor Day
Sep 5 2.1 Cauchy sequences and definition of real numbers
Sep 7 2.2 Ordered field axioms for the real numbers
3 Sep 10 3.1.1 Supremum and infimum
Sep 12 3.1.2 Limits and limit points
Sep 14 3.2 Open and closed sets
4 Sep 17 3.3 Compact sets
Sep 19 4.1.1, 4.1.2 Basic definition of continuous function
Sep 21 4.1.3, 4.1.4 Alternative definition of continuous function
5 Sep 24 4.2.1 Intermediate value theorem
Sep 26 4.2.2 Continuous functions on compact sets
Sep 28 4.2.3 Monotone functions
6 Oct 1 REVIEW Review of Chapters 1-4
Oct 3 EXAM First midterm exam
Oct 5 5.1.1 Definition of the derivative
7 Oct 8 5.1.2 Continuous differentiability
Oct 10 5.2.1, 5.2.2 Properties of the derivative and the intermediate value theorem
Oct 12 5.2.2, 5.2.3 The mean value theorem and global properties of derivatives
8 Oct 15 5.3.1, 5.3.2 The product and chain rules
Oct 17 5.3.3 The inverse function theorem
Oct 19 5.4.1, 5.4.2, 5.4.3 Taylor's theorem and L'Hopital's rule
9 Oct 22 6.1.1 Definition of the Riemann integral for continuous functions
Oct 24 6.1.2 Fundamental theorem of calculus
Oct 26 6.2.1 The Riemann integral more generally
10 Oct 29 6.2.2 Basic properties of the general integral
Oct 31 6.2.3 Functions which are Riemann-integrable
Nov 2 6.3 Improper integrals
11 Nov 5 REVIEW Review of Chapters 5-6
Nov 7 EXAM Second midterm exam
Nov 9 7.2.1 Series and convergence tests
12 Nov 12 7.2.2 Rearrangement of series
Nov 14 7.3.1 Pointwise and uniform convergence of functions
Nov 16 7.3.2 Term-by-term differentiation and integration
13 Nov 19 HOLIDAY Fall break
Nov 21 HOLIDAY Fall break
Nov 23 HOLIDAY Fall break
14 Nov 26 7.4.1 Power series and radius of convergence
Nov 28 7.4.2 Analytic continuation of power series
Nov 30 7.4.4 Closure properties of analytic functions
15 Dec 3 7.6.1 Equicontinuity of functions
Dec 5 7.6.2 The Arzela-Ascoli theorem
Dec 7 8.1.1 Definitions of the exponential function
16 Dec 10 8.1.2 Bump functions
Dec 12 8.2.1 Trigonometric functions
Dec 14 REVIEW Review of Chapters 7-8
Final exam Time and date TBA