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