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