MTHT 530 Analysis for Teachers II

Key Concepts

You should be comfortable with all of the key definitions.
You should be able to state and apply all of the key results.
You should be able to sketch the proof of the key results marked with (*).


Key Concepts (Chapters 5,6,7,8) Key Theorems


Key Concepts (Chapter 22) Key Theorems

The Derivative

Key Concepts (Chapters 9,10,11,12) Key Results

Uniform Continuity

Key Concepts (Chapter 8 appendix) Key Results


Key Concepts (Chapters 13,14,18) Key Results

Series and Sequences of Functions

Key Concepts (Chapters 23,24) Key Results
  • Convergence of the geometric series (*)
  • Divergence of the harmonic series
  • A sequence converges if and only if it is Cauchy (*)
  • If a series converges, the limit of the terms is 0 (*)
  • Comparision Test (*)
  • Ratio Test
  • Integral Test
  • Alternating Series Test
  • Absolutely convergent series are convergent
  • Continuity of limits of uniformly convergent series of functions (*)
  • Integrability and differentiability of of limits of uniformly convergent series
  • Weierstrass M-test
  • If the series sum a_nR^n converges, then the power series sum a_nx^n converges uniformly on [-a,a] for all 0 continuity, differentiability and integrability of power series.

    Last Updated 3/29/06