Definitions

• Function
  • Domain, codomain, range, image, pre-image
  • Injection, surjection, bijection
  • Continuous function, differentiable function
  • Increasing function (as defined on pg 328), decreasing function
• Limit
• Derivative
• Local minimum, local maximum
• Upper bound, lower bound, least upper bound, greatest lower bound
• Completeness property

Theorems

• Limits
  • Linearity of limit
  • Limit of product and quotient
  • Approximation property of supremum (and infimum)
• Continuity
  • Persistence of sign Lemma (73.2)
  • Intermediate Value Theorem
  • A continuous injective function is monotone
• Derivatives
  • Linearity of derivative
  • Lagrange's Theorem
  • Continuity of differentiable functions
  • Derivative of product and quotient
  • Derivative of composite function (Chain Rule)
  • Uphill-at-a-point Lemma
  • First Derivative necessary condition for an extremum
  • Function with positive derivative on an interval is increasing
  • Mean Value Theorem for derivatives
  • First derivative test, second derivative test

alex at iastate dot edu

Document last modified on Fri Oct 26 2007