Standard syllabus
Calculus I · Undergraduate · Math
Topics
Review and limits
- Functions, graphs, and review of algebra and trigonometry
- Limits, continuity, and limit laws; indeterminate forms
Derivatives
- Definition of the derivative; tangent lines and rates of change
- Differentiation rules: power, product, quotient, and chain rule
- Implicit differentiation and logarithmic differentiation
- Derivatives of exponential, logarithmic, and inverse trigonometric functions
Applications of derivatives
- Related rates and applied rate-of-change problems
- Applications of derivatives: extrema, mean value theorem, and curve sketching
- Optimization and applied maximum/minimum problems
- Linear approximation and differentials
Integration
- Antiderivatives and indefinite integrals
- Definite integrals, Riemann sums, and the area problem
- Fundamental Theorem of Calculus
- Integration by substitution (u-substitution)
- Applications of integration: area between curves and average value of a function
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