Lesson 1 Ch1 The ordered field (R,+,*,<) ; Definition of Sup and inf; completeness axiom.
Lesson 2 Ch1 Definition of inf; examples;Properties of sup and inf;
Lesson 3 Ch 1 square root of 2; Q is dense in R
Lesson 4 Ch 2 Useful identities/inequalities. Review of Induction Definition of limit of a sequence Examples
Lesson 5 Ch 2 Example of limits , limit laws, squeeze theorem
Lesson 6 Ch 2 Proofs of limit theorems. Some other general theorems
Lesson 7 Ch 2 Proof of limit theorem #4. Sequences divergent to infinity
Lesson 8 Ch 2 Monotone sequences. Subsequences
Lesson 9 Ch 2 Subsequence theorem. Sets dense in R . Open and closed sets
Lesson 10 Ch 2 Open and closed sets. Sequentially compact sets . The number e (optional)
Lesson 11 Ch 9 Cauchy sequences. Series definition. Geometric series
Lesson 12 Ch 9 Series . Geometric series. Harmonic series
Next Monday will be a review day. No lesson will be posted for Monday . We may do some problems from this exam Beykel Win 2016
Lesson 13 Ch 9 Comparison test. Limit test
Lesson 14 Ch 9 Alternating series test. Absolute convergence
Lesson 15 Ch 9 Ratio test
Lesson 16 Ch 3 Limit of a function. Limit laws. Limit of composition
Lesson 17 Ch 3 Continuity. Examples. Sum, product, quotient of continuous functions.
Lesson 18 Ch 3 Continuity of composition. More examples.
Lesson 19 Ch 3 Extreme value theorem.
Proof review problems we did not do on Monday in class
Lesson 20 Ch 3 Intermediate value theorem.
Lesson 21 Ch 3 Uniform continuity.
Lesson 22 Ch 3 Monotonic functions. Inverses
Lesson 23 Ch 9 Sequences of functions. Pointwise and Uniform convergence
Lesson 24 Ch 9 Sequences of functions. Examples