Intro to Calculus
About this free Intro to Calculus course
Intro to Calculus is a free online calculus course that introduces the three big ideas of calculus, limits, derivatives, and integrals, in simple and engaging ways. It explains each concept visually before moving to the rules and techniques, so students understand why the math works, not just how to do it.
The course follows the flow of a first-semester college calculus or AP Calculus AB class. It runs from the tangent problem and limits through differentiation rules, integration techniques, analyzing functions, and an introduction to differential equations, building a strong foundation and the tools to solve real-world problems with confidence.
Who this course is for
This course is designed for high school juniors and seniors (grades 11-12) who have completed precalculus, and for anyone preparing for AP Calculus AB. You should be comfortable with functions, graphs, and trigonometry.
Course outline
- Introduction to calculus. What calculus is and a preview through the tangent problem.
- Limits. Understanding limits, unpredictable limits, and calculating limits.
- Derivatives. Rate of change, the definition of the derivative, basic derivatives, and the product and quotient rules.
- Further differentiation. Trigonometric derivatives, further rules, and connecting position, velocity, and acceleration.
- Integrals. Integration concepts, the Fundamental Theorem of Calculus, u-substitution, area under a curve, and integrating common functions.
- Advanced integration. Long division, completing the square, inverse trig integrals, and trig identity integration.
- Analyzing functions and applications. The Mean Value and Extreme Value Theorems, critical points, concavity, optimization, slope fields, and average value.
What you'll learn
- Evaluate limits graphically and algebraically
- Differentiate functions with the power, product, quotient, and chain rules
- Use derivatives to analyze motion and to find extrema and inflection points
- Evaluate integrals using the Fundamental Theorem of Calculus and u-substitution
- Solve optimization problems and sketch slope fields
How long it takes
Plan on about 25 hours: three to four hours per unit including practice problems. Integration techniques and optimization take the most practice, so budget extra time there.
Frequently asked questions about Intro to Calculus
Is Intro to Calculus really free?
Yes. Intro to Calculus is completely free, with no fees, subscriptions, or account required. STEM for Others is a 501(c)(3) nonprofit, and every course in our curriculum library is free for students, families, and teachers.
Does this course prepare me for AP Calculus AB?
It covers most AP Calculus AB topics, including limits, derivatives, integrals, the Fundamental Theorem of Calculus, analyzing functions, optimization, and slope fields. It isn't an official AP course, so pair it with College Board practice exams.
How do I start the course?
Click Begin Course at the top of this page to open the full slide deck in a new tab. You can also flip through the slides embedded above. Work through one unit at a time and try the practice questions before moving on.
Do I get a certificate?
The self-paced Intro to Calculus materials don't include an official certificate. If you're taking the course through a STEM for Others chapter program, ask your chapter leader about recognizing your completion.
Can teachers and clubs use this curriculum?
Yes. Teachers, homeschool families, libraries, and after-school clubs are welcome to use the Intro to Calculus materials with their students at no cost. STEM for Others volunteers also teach our curriculum in partner schools and libraries. You can find a chapter near you or start one at your school.
Related free courses
