Detailed Schedule -- Principles of Analysis

Fall 2004, 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 (from Lay)
9/1 Course introduction, basic logic Sections 1,2
9/3 Basic strategies of proof Section 3
9/6 More strategies of proof Section 4
9/8 Set operations Section 5
9/10 Relations and functions Sections 6, 7
9/13 More on functions Section 7
9/15 Cardinality and countability Section 8
9/17 The natural numbers and induction Section 10
9/20 Ordered fields Section 11
9/22 The Completeness Axiom in R Section 12
9/24 Topology of R Section 13
9/27 Compactness Section 14
9/29 Theorems of Heine-Borel and Bolzano-Weierstrass Section 14
10/1 Exam I Sections 1 - 13 (9 omitted)
10/4 Convergence of sequences Section 16
10/6 Limit theorems for sequences Section 17
10/8 Monotone sequences and convergence Section 18
10/11 Columbus Day Break (no class)
10/13 Subsequences, ``sequential compactness'' Section 19
10/15 Spare Day Section 20
10/18 Limits of functions Section 20
10/20 Continuity Section 21
10/22 Properties of continuous functions Section 22
10/25 More properties of continuous functions Section 22
10/27 Uniform continuity Section 23
10/29 Exam II Sections 14 - 22 (15 omitted)
11/1 The derivative Section 25
11/3 The Mean Value Theorem and consequences Section 26
11/5 Why L'Hopital's Rule ``works'' Section 27
11/8 Taylor polynomials and Taylor's Theorem Section 28
11/10 Definition of the Riemann integral Section 29
11/12 Properties of integrals Section 30
11/15 More properties of integrals Section 30
11/17 Fundamental Theorem of Calculus Section 31
11/19 Convergence of infinite series Section 32
11/22 First convergence tests Section 33
11/24 Thanksgiving Vacation (no class) Section 33
11/26 Thanksgiving Vacation (no class) Section 33
11/29 More on convergence tests Section 33
12/1 Power series and radius of convergence Section 34
12/3 Exam III Sections 23 - 33 (24 omitted)
12/6 Course wrap-up Section 34

The final exam for this course will be given at 8:30am on Wednesday, December 15.

Last modified: August 14, 2000