Week  Topics  Study Materials  Materials 
1 
Ordered fields and the number system, completeness and the real number system.


Elementary Classical Analysis, J. E. Marsden.

2 
Least upper bounds, Cauchy sequences.


Elementary Classical Analysis, J. E. Marsden.

3 
Cluster points; lim inf and lim sup, Euclidean space.


Elementary Classical Analysis, J. E. Marsden.

4 
Open sets, interior of a set, closed sets, accumulation points.


Elementary Classical Analysis, J. E. Marsden.

5 
Closure of a set, boundary of a set, sequences, series in R and R^n.


Elementary Classical Analysis, J. E. Marsden.

6 
Compact sets; the HeineBorel and the BolzanoWeierstrass Theorems, nested set theory.


Elementary Classical Analysis, J. E. Marsden.

7 
Pathconnected sets, connected sets.


Elementary Classical Analysis, J. E. Marsden.

8 
Continuity, images of compact and connected sets.


Elementary Classical Analysis, J. E. Marsden.

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


Elementary Classical Analysis, J. E. Marsden.

10 
The IntermediateValue theorem, uniform continuity.


Elementary Classical Analysis, J. E. Marsden.

11 
Pointwise and uniform convergence, the Weierstrass Mtest, integration and differentiation of series.


Elementary Classical Analysis, J. E. Marsden.

12 
The space of continuous functions,The ArzoliAscoli Theorem, fixed points and integral equations.


Elementary Classical Analysis, J. E. Marsden.

13 
StoneWeierstrass Theorem, the Drichlet and Abel Tests, MeanValue and Taylor Theorems.


Elementary Classical Analysis, J. E. Marsden.

14 
Inverse function theorem, Implicit function theorem.


Elementary Classical Analysis, J. E. Marsden.
