- Introduction: definition, basic properties, total differential.
- Mean value theorem and related topics (l'Hospital's rule, derivative and monotonicity/concavity).
- Graphing functions including monotonicity, concavity and asymptotes; for practical approach see Methods Survey.
- Applications: tangent line, global extrema and optimization, Taylor polynomial, approximation; for practical approach see Methods Survey.
- Implicit and parametric functions (derivative, sketching); for practical approach see Methods Survey.