Math 412, Winter 2004

Lesson Schedule: We will try to follow the attached schedule closely. You will probably find the lectures more valuable if you read the material and attempt some of the problems before coming to class.


 
M  1/5
Chapter 1 Quantifiers, Sets, and DeMorgan's Laws
T  1/6
Chapter 1 Functions
Th   1/8
Chapter 1 Cardinality
F   1/9
Chapter 2 Introduction to the real numbers:
Field axioms, ordering, and useful inequalities

 
 
M  1/12
Chapter 2 Completeness Axiom and the Archimedean Principle
T  1/13
Chapter 2 Applications of the Archimedean Principle
Th   1/15
Chapter 3 Introduction to sequences
F   1/16
Chapter 3 Elementary properties of sequences

 
 
M  1/19
NO CLASS
  MARTIN LUTHER KING JR. DAY
T  1/20
Chapter 3 Monotone sequences, the number e, and Cauchy
Th  1/22
Chapter 3 Convergence iff Cauchy and intro to subsequences
F   1/23
Chapter 3 More subsequences and infinite limits

 
 
M   1/26
Chapter 4 Infinite series
T  1/27
Chapter 4 Convergence criteria for series with positive terms
Th  1/29
Chapter 4 Cauchy condensation test and corollaries
FRIDAY  1/30
 EXAM 1 TODAY
IN CLASS		  On material through Tuesday, 1/27

 
 
M  2/2
Chapter 4 Ratio and Root Tests
T  2/3
Chapter 4 Absolute convergence, Alternating Series
Th   2/5
Chapter 4 Conditional convergence and rearrangements
F   2/6
Chapter 4 Further results on series

 
 
M  2/9
Chapter 5 Introduction to Euclidean space
T  2/10
Chapter 5 Sequences in n-space
Th   2/12
Chapter 5 More sequences in n-space
F   2/13
Chapter 6 Introduction to limits of functions

 
 
M  2/16
NO CLASS
  GEORGE WASHINGTON'S BIRTHDAY
T  2/17
Chapter 6 More on limits, R^m-valued functions
Th  2/19
Chapter 6 Still more on limits, infinite limits
F   2/20
Chapter 7 Continuity, sequential characterization of continuity

 
 
M   2/23
Chapter 7 Operations on continuous functions, uniform continuity
T  2/24
Chapter 7 Still more about continuity
Th  2/26
Chapter 8 Introduction to topology, Bolzano-Weierstrass theorem
FRIDAY  2/27
 EXAM 2 TODAY
IN CLASS		  On material through Tuesday, 2/24

 
 
M  3/1
Chapter 8 Compactness, various Heine-Borel theorems
T   3/2
Chapter 8 Proof of Heine-Borel theorem,
Intro to continuous functions on compact sets
Th   3/4
Chapter 8 More about continuous functions on compact sets
F  3/5
Chapter 9 Introduction to Differentiation: Chain Rule, Mean Value Theorem

 
 
M  3/8
Chapter 9 Consequences of MVT, Generalized MVT, and L'Hospital's Rule
T  3/9
Chapter 9 Differentiation of inverses, Taylor's Theorem
Th   3/11
Chapter 9 Finish Taylor's theorem, begin Optimization
F   3/12
Chapter 9 More on optimization

 
 
 
 FINAL EXAMINATION

TUESDAY AFTERNOON, MARCH 16

1:10 - 4:00 PM