13, 16, 18, 20

1. Sets, Ordered sets
2. Real numbers, sup and inf
3. Completeness, Archimedean property
4. Absolute value, inequalities

Homework will be assigned on Sept. 18
Homework Assignment(dvi file)
Solution for HW1, problem 8(dvi file)
Solution for HW1, problem 8(pdf file)
 

1. Neighborhood, open and closed intervals
2. Nested interval property, decimal expansion
3. Open and closed sets, limits

1. Properties of open, closed sets
2. Heine-Borel Theorem; Weierstrass Property
3. Covergent sequences

1. Convergent of some special sequences
2. Subsequence, Cauchy sequences
3. Series, geometric series

1. Ratio, Root and integral tests for series
2. Absolute convergence, alternating series, power series
3. limits, limits of functions

1. Continuous functions
2. Property of continuous functions
3. Continuity and connectedness

1. Maximum-Minimum theorem
2. Uniform continuiuty, monotonic functions
3. Derivative of a real function

1. Chain rule, inverse functions
2. Mean value theorem, L'Hospital's rule
3. Taylor's theorem

1. Definition of the Riemann integral
2. Integrability of monotone and continuous functions

1. Fundamental Theorem of Calculus
2. Evaluation of integrals

1. Sequence and series of functions
2. Uniform convergence
3. Uniform convergence and continuity, integration

1. Uniform convergence and differentiation
2. Power series
3. logarithm and exponential functions