Math 142B Spring 2021
Terminology and Theorems

Updated 3/26/21

• Chapter 6
  • partition
    • partition point
    • partition interval
  • upper (Darboux) sum, lower (Darboux) sum
  • Refinement Lemma
  • upper integral, lower integral
  • integrable
  • integral
  • Archimedes-Riemann Theorem
  • Archimedean sequence of partitions
  • regular partition
  • gap of a partition
  • step function
  • Leibnitz notation
  • additivity over intervals
  • monotonicity
  • linearity
  • the First Fundamental Theorem
  • antiderivative
  • Mean Value Theorem for Integrals
  • the Second Fundamental Theorem

• Chapter 8
  • contact of order n
  • n^th Taylor polynomial
  • Cauchy Mean Value Theorem
  • Lagrange Remainder Theorem
  • e is irrational
  • Euler's constant γ
  • sequence of partial sums
  • k^th term
  • Taylor series expansion
  • power series for the logarithm
  • nonanalytic, infinitely differentiable function
  • Weierstrass Approximation Theorem
• Chapter 9
  • converge pointwise, pointwise convergence
  • converge uniformly, uniform convergence
  • uniformly Cauchy
  • Weierstrass Uniform Convergence Criterion
  • uniform limit of continuous functions
  • uniform limit of integrable functions
  • uniform limit of differentiable functions
  • power series, power series expansion
  • domain of convergence
  • term-by-term differentiation
  • uniformly convergent power series
  • radius of convergence of a power series
  • ratio test for series