Free Resources to Learn Calculus: A Course, Textbooks, Notes

You do not need a tuition bill to get a first-year calculus education. A university-grade video course, three open textbooks and a full set of worked notes all cost nothing¹²⁴. What costs something is time, so this page ranks the free options by what they give you and then lays the best one out as a calendar.

How can I learn calculus for free?

Pair a course with a textbook and a bank of extra problems. The course supplies order and deadlines, the textbook offers a second explanation, and the notes add problems you have not seen.

The full course: MIT OpenCourseWare 18.01SC

The course covers differentiation and integration of functions of one variable and ends with a short look at infinite series¹. Its audience is the independent learner: OCW Scholar courses were designed for that group¹. The materials include worked examples and interactive applets for key ideas¹. It was taught in fall 2010¹.

Calculus matters outside the classroom for a plain reason: it is fundamental to physics, engineering and economics¹. If you want a gentler start, the Highlights series was made for high school students, college students or anyone who needs help with the subject⁸. Its instructor, Gilbert Strang, has taught at MIT since 1962⁸.

Free textbooks

OpenStax Calculus is written for the standard calculus sequence and is free in web view or PDF². Volume 1 covers functions, limits, derivatives and integration². Its examples are followed by a checkpoint question so you can test yourself at once, and answers to selected exercises sit in the answer key². The applications reach probability, biology, ecology, business and economics, plus physics and engineering². The book is under a Creative Commons license².

Active Calculus is the better pick if you learn by trying problems first. Every section has activities, and the web version adds interactive WeBWorK exercises³. Both books are open: you can read them in a browser and they carry Creative Commons licenses²³. A library guide from Sacramento State lists more open books, including a calculus text for the life sciences and an applied calculus text⁹.

Notes with practice problems

Paul’s Online Notes is a full set of material for the topics usually found in Calculus I, II and III⁴. Calculus I covers limits, derivatives and basic integration⁴. Calculus II adds advanced integration techniques, parametric equations, polar coordinates, series, vectors and 3D space, and Calculus III covers partial derivatives, multiple integrals and line and surface integrals⁴. The review chapter is the part to open first if algebra and trigonometry have faded: it covers the topics from those subjects that matter for calculus⁴.

An 18-week plan from the free course

The syllabus of 18.01SC lists 5 units, 13 parts and 5 exams, counting the final¹. Giving each part and each exam one week is a calendar you can start tonight.

Worked example (our arithmetic): weeks and hours for the MIT course¹

The UC Davis math department advises two to four hours on each homework assignment⁵. If each of the 13 parts counts as one assignment, that is 13 × 2 = 26 to 13 × 4 = 52 hours of homework over the 18 weeks, or about 1.4 to 2.9 hours a week on average (our arithmetic)⁵. Add lecture time on top of that. The point of the sum is the shape: calculus is a habit measured in months, not an evening.

Read the OpenStax chapters beside the units, as the diagram shows: chapters 2 to 4 for derivatives, chapters 5 and 6 for integrals, and Volume 2 for the techniques and series².

What is the best source to learn calculus?

No single free source wins every learner, so choose by how you learn. If you want a schedule with exams, take the MIT course¹. If you want to read at your own speed with checkpoint questions, take OpenStax². If you prefer to try problems before reading, take Active Calculus³. If you are stuck on one topic, take the matching section of Paul’s Online Notes and its practice problems⁴. Use the course as the main road and the others as side roads, which is also how MIT frames its own path: read the material for a unit, do the recommended problems, take a sample test⁷.

Can I teach myself calculus?

Yes, and a path for it has been online for decades. The MIT World Web Math path was written to study calculus in a self paced fashion⁷. It splits the subject into 10 units, from limits and continuity to infinite series⁷. The page was last modified July 28, 1998, so use it as a map of the topics and not as a modern course⁷. Each unit repeats the same loop: read, do as many problems as you need to feel comfortable, take a sample test⁷.

Three habits from the UC Davis tips page fit self-study well⁵. Work on calculus every day, because daily practice makes concepts, definitions and theorems familiar⁵. Memorize definitions, formulas and theorems as they appear, because waiting slows down your homework and gets in the way of deeper understanding⁵. When a problem stumps you, give it time, because being stumped is a chance for growth even if you never solve it alone⁵. Preparing for a test with new problems works better than rereading ones you have solved⁵.

If you study alone, the “study partner” advice still helps: UC Davis suggests finding one or two others to do homework and prepare for exams with⁵. An online forum or a friend who reads along does the same job.

Is a high IQ required to learn calculus?

The best evidence points to effort, not IQ. A study followed 3,520 students in grades 5 to 10 over six annual waves of data⁶. Intelligence was linked to math achievement only in the initial development of competence⁶. Students who felt competent, were intrinsically motivated and used strategies such as summarizing, explaining and connecting ideas grew more, and intelligence had no relation to that growth⁶. The study measured school students and not adults learning calculus, so read it as evidence about how math skill grows and not as a promise about any one person⁶.

Where to go next

Soon the ideas get easier to spot in daily life. Read what a derivative is for the core idea, keep the derivative rules cheat sheet open while you practice, and see why math education struggles for the data on how students learn math. More ways to study live in the Learning section. Open MIT OpenCourseWare, OpenStax or Paul’s Online Notes and begin this week.