These are the more important topics (I'm excluding the very basic stuff like functions, domain and range, limits and continuity, which I assume you know well):

  • Derivative of a function, differentiation rules (including the Chain Rule), table of elementary derivatives
  • Implicit differentiation
  • Related rates
  • Finding local/global max/min of a given function on a given interval, increase/decrease, concavity of a graph, critical and inflection points
  • Optimization
  • Linear approximation
  • Anti-derivatives (aka indefinite integrals)
  • The relation between the position, velocity, and acceleration of a moving object
  • Definite integral as area, properties
  • Fundamental Theorem of Calculus I and II
  • Average value of a function over an interval
  • Application of integral in finding areas between two curves
  • Application of integral in finding volumes
  • Inverse functions and derivatives
  • Natural log, its properties, its derivative
  • The exponential function, its properties, its derivative
  • Exponential growth and decay
  • L'Hospital's Rule
  • Inverse trigonometric functions and their derivatives
  • Basic integration formulas (Table 7.1)
  • Integration by substitution
  • Integration by Parts
  • Partial fractions (simple cases, e.g. when you have two linear factors in the denominator)
  • Trigonometric substitution (simple cases, e.g. when you have a2-x2 or a2+x2 in your integral)
  • Improper integrals (very simple cases as we briefly discussed in class, no ``comparison tests'')