COURSE CHART
Weeks

Course Topics

1

The Real line and Euclidean space (ordered field, distance, Schwarz Inequality, The topology of Euclidean space 
2

Open sets, Interior of a set, closed sets

3

Accumulation points, Boundary and closure of a set 
4

Sequences in R^n, Convergent Sequences, Cauchy Sequence, Completeness, Infinite Series 
5

Compactness, the HeineBorel theorem,

6

Connected sets,Nested set property, Pathconnected sets 
7

Continuous Mappings ;continuity, Images of compact and connected sets 
8

Operations on continuous mappings, the boundedness of continuous functions on compact sets, 
9

Continuous Mappings ;Uniform continuity, Examples 
10  Pointwise convergence, Uniform convergence 
Midterm Exam  
11

Uniform convergence of sequences of functions, Ttest Uniform convergence of series of functions,

12

The Weierstrass Mtest, Interchanging the places of limits and integrals of sequences of functions, 
13

Integration and differentiation of series, Power series, Interval of convergence, Taylor's expansion

14

Equicontinuity, Arzela  Ascoli Theorem, Examples, Review 