Week
Dates

Section & Topic

Lecture

Homework Assignments

Week 1

9/4 – 9/7

    Week 2

        9/10-9/14

Introduction: Sets and Functions

1

1.1-1.2

Ordered Fields and the Number System

Completeness and the Real Number System

1.3-1.4

Least Upper Bounds and Cauchy Sequences

2

1.5-1.6

Cluster Points: lim inf and lim sup. and

 Euclidean Space.

Week 3
9/17 – 9/21

1.7-1.8

Norms, Inner products, and Metrics.

The Complex Numbers

3

2.1-2.3

Open Sets, Interior of a Set, and Closed Sets

Week 4
9/24 – 9/28

2.4-2.6

Accumulation Points, Closure of a Set, and Boundary of a Set.

4

2.7-2.10

Sequences, Completeness, and Series of Real Numbers and Vectors.

Week 5
10/1 – 10/5

3.1-3.2

Compactness, The Heine-Borel Theorem

5

3.4-3.5

Path-Connected Sets and Connected Sets

Week 6
10/8 – 10/12

REVIEW FOR EXAM #1

6

└►  STUDY FOR EXAM #1

MIDTERM EXAM I: FRIDAY ~ October 12, 2012

Week 7
10/15 – 10/19

4.1-4.3

Continuity, Images of Compact and Connected Sets and Operations on Continuous mappings

7

4.4-4.6

The Boundedness of Continuous Functions on Compact Sets, The Intermediate value Theorem, and Uniform Continuity.

Week 8
10/22 – 10/26

4.7-4.8

Differentiation of Function of One variable and Integration of Function of One Variable

8

5.1-5.3

Pointwise and Uniform Convergence, The Weierstrass M test and Integration and Differentiation of Series

Week 9
10/29 – 11/2

5.4-5.5

The Elementary Functions and the Space of Continuous Functions

9

5.7-5.8

The Contraction Mapping and its applications and Stone-Weierstrass Theorem

Week 10
11/5 – 11/9

Last Day to Withdraw from this course

5.9-5.10

The Direchlet and Abel Tests, Power Series and Cesaro and Abel Summability

10

6.1-6.3

Definition of Derivative and Matrix Representation, and Continuity of Differentiable Mappings.

Week 11
11/12 – 11/16

REVIEW FOR EXAM #2

11

└►  STUDY FOR EXAM #2

MIDTERM EXAM II:  FRIDAY ~ November 16, 2012

Week 12
11/26 – 11/30

6.4-6.6

.Conditions for Differentiability, the Chain Rule, and Product Rule and Gradients..

12

6.7-6.8

The mean value Theorem and Taylor’s Theorem and Higher Derivatives

Week 13
11/21 – 11/24

6.9, 8.1

Maxima and Minima and integrable Functions

13

Week 14
11/28 – 12/1

8.2-8.3

Volume and Sets of Measure Zero and Lebesgue’s Theorem

14

Week 15
12/5 – 12/9

REVIEW FOR FINAL EXAM

15

└►  STUDY FOR FINAL EXAM

Week 16
12/12

Final EXAM WEEK:  December 14-20, 2012