Detailed Schedule -- Principles of Analysis

Fall 2000, Prof. Little

As always, topics may be added, deleted, or rearranged during the course of the semester. Any changes will be announced in class and here.

DateClass Topic Reading (Bilodeau and Thie)
8/30 Course introduction, sets and functions 1.1-2
9/1 Algebraic and order properties 1.3
9/4 N and the principle of induction 1.4
9/6 Upper and lower bounds 1.5
9/8 The completeness axiom for R 1.5
9/11 Sequences and limits 2.1
9/13 Definition of convergence of a sequence 2.1
9/15 Limit theorems 2.2
9/18 Limit theorems, continued 2.2
9/20 Monotonic sequences 2.3
9/22 Inductively defined sequences 2.4
9/25 Subsequences of a sequence 2.5
9/27 Cauchy sequences 2.5
9/29 Limits for functions 3.1
10/2 More on limits 3.1
10/4 Limit theorems for functions 3.2
10/6 Midterm I Chapters 1 and 2
10/9 Columbus Day Break (no class) 3.3
10/11 One-sided and infinite limits 3.3
10/13 Continuity 3.4
10/16 Intermediate Value Theorem 3.5
10/18 Extreme Value Theorem 3.5
10/20 Uniform Continuity 3.6
10/23 Definition of the derivative 4.1
10/25 Derivative rules 4.2
10/27 Rolle's Theorem 4.3
10/30 The Mean Value Theorem and consequences 4.3
11/1 Definition of the definite integral 5.1
11/3 More on definition of the definite integral 5.1
11/6 Properties of integrals 5.2
11/8 Existence theory for integrals 5.3
11/10 Fundamental Theorem of Calculus 5.4
11/13 Convergence of infinite series 6.1
11/15 First convergence tests 6.1
11/17 Midterm II Chapters 3 - 5
11/20 Alternating series 6.2
11/22 Thanksgiving Vacation (no class) 6.2
11/24 Thanksgiving Vacation (no class) 6.2
11/27 Absolute convergence and the ratio test 6.2
11/29 Power series 6.3
12/1 CEF's given out this day, radius of convergence 6.3
12/4 Taylor series and Taylor's theorem 6.4

The final exam for this course will be given at 2:30pm on Friday, December 15 -- the last possible time this exam week!.

Last modified: August 14, 2000