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. These fee-based classes prepare students to earn alternative forms of credit.
Study.com offers this type of online learning with timely, engaging video lessons and self-assessment quizzes available to registered members. Free transcripts are also available for Study.com's video lessons. Both of these options can help students earn college credit. Students who want to study calculus can check out the Math 104: Calculus course. Some of the lessons 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
- Calculus with Applications
- Calculus of Several Variables
- Differential Equations
- Single Variable Calculus
- Calculus with Theory
- Multivariable Calculus with Theory
Professor Gilbert Strang teaches Big Picture of Calculus, an online course 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. Professors Strang's free calculus textbook is available for online download.
Prior high school calculus coursework is recommended to individuals interested in the Calculus with Applications course. Topics covered include 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.
Although very similar to the multivariable calculus course, Calculus of Several Variables offers participants a more 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.
The Differential Equations course 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. 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.
The first of a 2-part course, 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 is the second of the 2-part course series offered in the area of calculus theory at MIT. The course 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
This free online course prepares prospective teachers for their CSET (California Subject Examinations for Teachers), which is required of individuals who wish to teach in California. Topics in CSET Mathematics III: Trigonometry and Calculus include sequences and series, derivatives and applications, trigonometry and integrals.
University of Notre Dame
The Elements of Calculus I course is designed for students who want to learn about calculus and its connection with modern society. Topics examine functions, limits, derivatives and natural logarithm. Activities for each topic discussed during the lectures are available for download online.
The Calculus II for Business course delves into the fundamental theorem of calculus, differential equations, partial derivatives, producer surplus and logistic growth. This course helps students obtain problem-solving skills used in business today. The elements of calculus I is a prerequisite for this course.
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