Math 413 Analysis I
Week to Week Sylabus
- Week 1:
Properties of the Reals: ordered fields, completeness axiom,
Read sections 1.3 and 1.4. (pg 13--22)
- Week 2: existence of square roots, the nested interval
property, sequences, convergence
Read sections 2.2 and 2.3.
- Week 3: properties of limits of convergent sequence,
monotone convergence theorem
Read section 2.4 up to and including Example 2.4.5
- Week 4: The Bolzano-Weierstrass Theorem and Cauchy sequences
Read Sections 2.5 and 2.6.
- Week 5: Elementary Topology of the reals: Open sets, Closed
sets
Read Sections 3.2 and 3.1
- Week 6: Elementary Topology of the reals: the Cantor
set, compact sets,
Heine-Borel Theorem
Read Section 3.3
- Week 7: connected sets, limits of functions
Read Sections 3.4 (we will only cover pg 91-92 of 3.4), 4.1 and 4.2
- Week 8: Continuity, Midterm exam Friday October 17
Read Section 4.3
- Week 9: Continuity, Extreme Value Theorem,
Read Sections 4.4
- Week 10: Intermediate Value Theorem, Uniform Continuity
Read Sections 4.4, 4.5
- Week 11: Uniform Continuity, Sets of Discontinuity
Read Sections 4.4, 4.6
- Week 12: Derivatives, Differentiation rules,
finding extremum, Darboux's Theorem
Read Sections 5.2
- Week 13: Mean Value Theorem, Rolle's Theorem,
Read Sections 5.3
- Week 14: Midterm exam Wednesday November 26
- Week 15: L'Hospital's Rules, Newton's Method
Last Updated 11/18/03