Calculus I
Free Online Course • Single-Variable Calculus • Self-Paced Learning
Welcome to Calculus I
This comprehensive course covers single-variable calculus from limits through integration techniques. Whether you are preparing for STEM coursework or strengthening your mathematical foundations, each module includes detailed lessons with worked examples, interactive practice problems, self-check quizzes, and printable study materials.
Self-Paced
Learn on your schedule. All materials available 24/7.
Interactive
Practice problems with instant feedback and detailed solutions.
Comprehensive
Study guides, quick reference cards, and step-by-step worked examples.
Research-Based
Designed using evidence-based learning principles.
Course Modules
Limits and Continuity
Build the foundation of calculus by understanding limits, computing them algebraically, and exploring continuity.
- The intuitive idea of a limit
- Computing limits algebraically
- Limits at infinity and asymptotes
- Continuity and the Intermediate Value Theorem
The Derivative
Discover rates of change, the formal definition of the derivative, and basic differentiation rules.
- Average and instantaneous rates of change
- The derivative: definition and notation
- Differentiability and local linearity
- Basic differentiation rules
Differentiation Rules
Master the product, quotient, and chain rules, plus derivatives of trigonometric functions and implicit differentiation.
- Product and quotient rules
- The chain rule
- Derivatives of trig functions
- Implicit differentiation
Applications of Derivatives I
Apply derivatives to related rates, linear approximation, extreme values, and the Mean Value Theorem.
- Related rates
- Linear approximation and differentials
- Extreme values and critical points
- The Mean Value Theorem
Applications of Derivatives II
Use derivatives for curve sketching, concavity analysis, and solving optimization problems.
- First derivative test
- Second derivative and concavity
- Curve sketching
- Optimization problems
Integration
Learn antiderivatives, Riemann sums, the definite integral, and the Fundamental Theorem of Calculus.
- Antiderivatives and indefinite integrals
- Riemann sums and area
- Definite integral and FTC Part 1
- FTC Part 2 and Net Change Theorem
Applications of Integration
Find areas between curves, compute volumes of solids of revolution, and calculate average values.
- Area between curves
- Volumes: disk and washer methods
- Volumes: shell method
- Average value of a function
Techniques of Integration
Master u-substitution, trigonometric integrals, integration by parts, and numerical methods.
- u-Substitution
- Integrals involving trig functions
- Integration by parts
- Numerical integration
Ready to Get Started?
Begin with Module 1 to build a strong foundation in limits and continuity. All materials are completely free!
Learning Tips
- Work through modules in order — each one builds on the previous
- Do every practice problem before moving to the quiz
- Use the study guide to review key formulas and concepts
- Sketch graphs by hand to build intuition about derivatives and integrals
- Take your time — understanding beats memorization
- Use Desmos to visualize functions and verify your work