A year-long sequence in single-variable calculus should include the following topics:

  • Derivatives of polynomial, rational, trigonometric, exponential, and logarithmic functions
  • Maximum-minimum problems
  • Curve sketching, and other applications (velocity, acceleration)
  • Antiderivatives and simple motion problems.
  • Definite integrals,
  • Integral tables and basic techniques of integration
  • Polar coordinates
  • Applications to areas, volumes, force, work
  • Growth and decay problems.
  • Indeterminate forms
  • Improper integrals
  • Sequences and series, especially Taylor's formula and power series