Math 414 Analysis II
Week to Week Sylabus
- Week 1:
Integration: Riemann-Darboux Integration, upper and lower sums,
criteria for integrability, integrability of continuous functions,
Read sections 7.1 and 7.2
- Week 2 Properties of Integrals
Read section 7.4 pg 195-197
- Week 3 Fundamental Theorem of Calculus approximating integrable functions by step
functions and continuous functions,
Read section 7.5
- Week 4 integrating Thomae's function, general Riemann sums,
equivalence of Riemann-Darboux and Riemann definitions of integral
Read section 8.1 pg 214-216
- Week 5 measure zero sets, Lebesgue's Criterion
Read sections 7.3 and 7.6 pg 203-207, supplementary notes on Topology
of Reals pg 21-25
- Week 6 infinite series, convergence tests, absolute vs.
conditional convergence
Read sections 2.7
- Week 7 rearrangements of series, products of convergent series,
sequences of functions, pointwise covergence
Read sections 2.8, 6.2
- Week 8 uniform convergence, review,
Midterm 1 March 5
- Week 9 uniform convergences and continuity, integrability
and differentiability
Read sections 6.2, 6.3 and 7.4 (pg 197-198)
- Week 10 nowhere differentiable continuous functions,
Read sections 5.4 of the text
and 2.7 of the notes on Topology of the Reals
SPRING BREAK
- Week 11 series of functions, power series
Read sections 6.4 and 6.5
- Week 12 power series, Taylor series
- Week 13 Contraction Mappings and Differential Equations
Read section 2.8 of Quick Tour of Topology of R and pg 170-171,
177-180 of Rosenlicht's Introduction to Analysis
- Week 14 Implicit Function Theorem,
Inverse Function Theorem Midterm II on Friday
April 23
Read section 2.9
of Quick Tour of Topology of R and pg 173-177
of Rosenlicht's Introduction to Analysis
- Week 15 Baire Category Theorem for the space
of continuous functions, "most" continuous fuctions are nowhere differentiable
Read 8.2 and Lecture Notes
Last Updated 4/12/04