Free MIT Courses Online : Single Variable Calculus Classes Free Online

This Single Variable Calculus free online course from MIT covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.


Single Variable Calculus is a first-year, first-semester course at MIT. The prerequisites are high school algebra and trigonometry. Prior experience with calculus is helpful but not essential.

Single Variable Calculus Course Overview:

Calculus is a foundational course at MIT; it plays an important role in the understanding of science, engineering, economics, and computer science, among other disciplines. This introductory calculus course covers differentiation and integration of functions of one variable, with applications. Topics include:

  • Concepts of Function, Limits and Continuity
  • Differentiation Rules, Application to Graphing, Rates, Approximations, and Extremum Problems
  • Definite and Indefinite Integration
  • The Fundamental Theorem of Calculus
  • Applications to Geometry: Area, Volume, and Arc Length
  • Applications to Science: Average Values, Work, and Probability
  • Techniques of Integration
  • Approximation of Definite Integrals, Improper Integrals, and L’Hôspital’s Rule

Course Goals:

After completing this course, students should have developed a clear understanding of the fundamental concepts of single variable calculus and a range of skills allowing them to work effectively with the concepts.

The basic concepts are:

  1. Derivatives as rates of change, computed as a limit of ratios
  2. Integrals as a “sum,” computed as a limit of Riemann sums

After completing this course, students should demonstrate competency in the following skills:

  • Use both the limit definition and rules of differentiation to differentiate functions.
  • Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity.
  • Apply differentiation to solve applied max/min problems.
  • Apply differentiation to solve related rates problems.
  • Evaluate integrals both by using Riemann sums and by using the Fundamental Theorem of Calculus.
  • Apply integration to compute arc lengths, volumes of revolution and surface areas of revolution.
  • Evaluate integrals using advanced techniques of integration, such as inverse substitution, partial fractions and integration by parts.
  • Use L’Hospital’s rule to evaluate certain indefinite forms.
  • Determine convergence/divergence of improper integrals and evaluate convergent improper integrals.
  • Determine the convergence/divergence of an infinite series and find the Taylor series expansion of a function near a point.

Course Structure:

This course, designed for independent study, has been organized to follow the sequence of topics covered in an MIT course on Single Variable Calculus. The content is organized into five major units:

  1. Differentiation
  2. Applications of Differentiation
  3. The Definite Integral and its Applications
  4. Techniques of Integration
  5. Exploring the Infinite

Each unit has been further divided into parts (A, B, C, etc.), with each part containing a sequence of sessions. Because each session builds on knowledge from previous sessions, it is important you progress through the sessions in order. Each session covers an amount you might expect to complete in one sitting.

Within each unit you will be presented with sets of problems at strategic points, so you can test your understanding of the material. As you begin each part of a unit, review the problem set at its end so that you may work toward solving those problems as you learn new material.

MIT expects its students to spend about 150 hours on this course. More than half of that time is spent preparing for class and doing assignments. It’s difficult to estimate how long it will take you to complete the course, but you can probably expect to spend an hour or more working through each individual session.

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One Response to Free MIT Courses Online : Single Variable Calculus Classes Free Online

  1. Rita Aghadiuno says:


    My daughter needs to take this course in Single Variable Calculus online. Can she take it at your institution? Will it be free? Will a certificate showing college credits be issued?
    Please reply.

    Thank you.

    Rita Aghadiuno.

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