Standard syllabus
Calculus I · Undergraduate · Math
Learning objectives from the Calculus I syllabus, grouped by unit. Click an objective for study materials.
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Calculus I — scope drawn from OpenStax Calculus Volume 1 (functions, limits, derivatives, integration).
Review and limits
- Functions, graphs, and review of algebra and trigonometry — Functions, graphs, and review of algebra and trigonometry
- Limits and continuity — Limits and continuity
- Limit laws — Limit laws
Derivatives
- Definition of the derivative — Definition of the derivative
- Rates of change — Rates of change
- Differentiation rules — Differentiation rules
- Chain rule — Chain rule
- Implicit differentiation — Implicit differentiation
- Logarithmic differentiation — Logarithmic differentiation
- Derivatives of exponential and logarithmic functions — Derivatives of exponential and logarithmic functions
- Inverse trigonometric functions — Inverse trigonometric functions
Applications of derivatives
- Related rates — Related rates
- Applied rate-of-change problems — Applied rate-of-change problems
- Applications of derivatives — Applications of derivatives
- Curve sketching — Curve sketching
- Optimization — Optimization
- Applied maximum/minimum problems — Applied maximum/minimum problems
- Linear approximation and differentials — Linear approximation and differentials
Integration
- Antiderivatives and indefinite integrals — Antiderivatives and indefinite integrals
- Definite integrals and Riemann sums — Definite integrals and Riemann sums
- The area problem — The area problem
- Fundamental Theorem of Calculus — Fundamental Theorem of Calculus
- Integration by substitution (u-substitution) — Integration by substitution (u-substitution)
- Applications of integration — Applications of integration
- Average value of a function — Average value of a function
Learning objectives
Click an objective for study materials.
Review and limits
- Functions, graphs, and review of algebra and trigonometry — Functions, graphs, and review of algebra and trigonometry
- Limits and continuity — Limits and continuity
- Limit laws — Limit laws
Derivatives
- Definition of the derivative — Definition of the derivative
- Rates of change — Rates of change
- Differentiation rules — Differentiation rules
- Chain rule — Chain rule
- Implicit differentiation — Implicit differentiation
- Logarithmic differentiation — Logarithmic differentiation
- Derivatives of exponential and logarithmic functions — Derivatives of exponential and logarithmic functions
- Inverse trigonometric functions — Inverse trigonometric functions
Applications of derivatives
- Related rates — Related rates
- Applied rate-of-change problems — Applied rate-of-change problems
- Applications of derivatives — Applications of derivatives
- Curve sketching — Curve sketching
- Optimization — Optimization
- Applied maximum/minimum problems — Applied maximum/minimum problems
- Linear approximation and differentials — Linear approximation and differentials
Integration
- Antiderivatives and indefinite integrals — Antiderivatives and indefinite integrals
- Definite integrals and Riemann sums — Definite integrals and Riemann sums
- The area problem — The area problem
- Fundamental Theorem of Calculus — Fundamental Theorem of Calculus
- Integration by substitution (u-substitution) — Integration by substitution (u-substitution)
- Applications of integration — Applications of integration
- Average value of a function — Average value of a function
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Review and limits
Functions, graphs, and review of algebra and trigonometry
Coming soon - Derivatives
Definition of the derivative
Coming soon - Applications of derivatives
Related rates
Coming soon - Integration
Antiderivatives and indefinite integrals
Coming soon
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