List of Free Online Calculus Courses and Lessons

Free online courses and lessons in calculus are offered by real schools. Learn which calculus courses are available, what topics they cover and which ones lead to real college credit.

Online Calculus Courses for Credit

Students can find plenty of free online calculus courses that don't require registration or tuition, but these courses generally don't award college credit. Students interested in courses that can lead to credit might consider options that charge a fee in exchange for access to online lessons. Study.com offers this type of online learning with engaging video lessons and self-assessment quizzes available to registered members.

Students who want to study calculus can check out the Math 104: Calculus course. Some of the chapters in this course include:

  • Continuity - Learn about continuity in a function, discontinuities and intermediate value theorem.
  • Rate of Change - Examine velocity, slopes, the mean value theorem and derivatives.
  • Area Under the Curve and Integrals - Topics include using Riemann sums, the trapezoid rule, definite integrals and the average value theorem.
  • Integration Applications - See methods for finding simple areas and areas between functions and calculating volumes using single intervals.
  • Differential Equations - Learn how to solve equations with the separation of variables method, calculate exponential growth and solve related rates problems.

Free Online Non-Credited Calculus Courses

Free online calculus courses are available that don't lead to college credit. Those planning to take these courses should have a calculator that can perform simple and complex calculations in order to complete the assignments. Additionally, many of these courses have associated textbooks that may need be purchased to fulfill class assignments.

Massachusetts Institute of Technology (MIT)

  • Big Picture of Calculus is designed to show students how calculus is used in real life situations. The course consists of an introductory video, 5 highlights of calculus videos and 12 derivative videos.
  • Calculus with Applications covers quadratic approximations, differentiable functions, vectors, higher derivatives and many other topics. The course site also includes links to relevant calculus tools in areas such as curves and vectors, linear geometry and algebra. Other learning tools include a glossary of calculus terminology, online textbook with lecture notes and an interactive Java applet.
  • Single Variable Calculus is a self-contained course so a textbook is not required, although it may be helpful. OCW users can download exams and assignments after learning about differentiation and integration applications. The course also offers students the opportunity to join an online study group. High school algebra and trigonometry are prerequisites for this course.
  • Calculus of Several Variables offers participants an in-depth study of math concepts. In addition to lecture notes, students also have assignments and exams, both offering solutions. A textbook is required for this course. Single variable calculus is a prerequisite course.
  • Differential Equations combines course notes, lecture videos and exams with solutions. Additionally, students can perform practice problems and view problem-solving videos. This course focuses on equations and solutions most common in engineering and science.
  • Calculus with Theory is an advanced calculus course covering axioms for the real numbers, fundamental theorems of calculus, infinite series and the Riemann integral. Course notes, problem sets and assignments are available on the course site.
  • Multivariable Calculus with Theory focuses on vector integral calculus and linear algebra. Additional topics include partial differentiation, triple integrals, Stokes' theorem and multivariable calculus. Two textbook purchases are suggested for this course.

University of California - Irvine

  • CSET Mathematics III: Trigonometry and Calculus prepares prospective teachers for their CSET (California Subject Examinations for Teachers), which is required of individuals who wish to teach in California. Topics include sequences and series, derivatives and applications, trigonometry and integrals.

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