Best Free Calculus Courses

Find the best online Free Calculus Courses for you. The courses are sorted based on popularity and user ratings. We do not allow paid placements in any of our rankings.

Differentiation Made Easy: Learn to differentiate – Calculus

​Learn to take derivative of functions (trigonometric, exponential, logarithmic & ...) ,Test your knowledge on Quizzes

Created by Alireza Eshghi - Math Instructor


Students: 8405, Price: Free

Videos: Every video covers a topic of differentiation. For every topic I solve some examples from simple to hard. I believe that we learn better with more exercises.  

Quizzes: You can test your understanding and knowledge about a topic by taking a quiz ( All of them have complete solutions) . If you pass, congratulation. If not, you can review the videos again or look at the solutions of questions or ask me for help in the Q&A section.

Integration Made Easy (Short Version) – Calculus

Calculus 2 -Learn different techniques of integration, U substitution, Part by Part, Partial fractions and much more...

Created by Alireza Eshghi - Math Instructor


Students: 3415, Price: Free

Videos: Every video covers a topic of Integration. For every topic I solve many many  examples from very simple to hard. I believe that we learn better with more and more exercises.

1. Integrations Formulas

2. U Substitution

3. Integration by Parts

4. Integration of Rational Functions by Partial Fractions

5. Integration of Trigonometric Functions

6. Trigonometric Substitutions

& much more...

Introduction to Calculus 2: Area Estimation

Learn the basic method of area estimation: Riemann Sum

Created by Gina Chou - Physics PhD candidate


Students: 603, Price: Free


This course, Introduction to Calculus 2: Area Estimation, includes the first section you will learn in Calculus 2, including video, notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and theorems. The course is organized into the following topics:

  • Area Estimation (Riemann Sum)

  • Sigma Notation

  • Summation Rules

  • Summation Formulas

  • Evaluating Summation

  • Limit of a Riemann Sum (Signed Area)


Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.

Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).

Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again.

BONUS #1: Downloadable lecture notes so you can review the lectures without having a device to watch/listen.

BONUS #2: Step-by-step guide to help you solve problems.

BONUS #3: A secret Facebook group for you to ask questions and discuss with your classmates.

See you inside the course!

- Gina :)

Calculus (Integration part 1)

Integration for secondary school

Created by Kuldeep Yadav - Director at UrbanGuru India


Students: 214, Price: Free

In this method of integration by substitution, any given integral is transformed into a simple form of integral by substituting the independent variable by others.

Take for example an equation having an independent variable in x, i.e. ∫sin (x3).3x2.dx———————–(i),

In the equation given above the independent variable can be transformed into another variable say t.

Substituting x3 = t ———————-(ii)

Differentiation of above equation will give-

3x2.dx = dt ———————-(iii)

Substituting the value of (ii) and (iii) in (i), we have

∫sin (x3).3x2.dx = ∫sin t . dt

Thus the integration of the above equation will give

∫sin t . dt= -cos t + c

Again putting back the value of t from equation (ii), we get

∫sin (x3).3x2.dx = -cos x3 + c

The General Form of integration by substitution is:

∫ f(g(x)).g'(x).dx = f(t).dt, where t = g(x)

Usually the method of integration by substitution is extremely useful when we make a substitution for a function whose derivative is also present in the integrand. Doing so, the function simplifies and then the basic formulas of integration can be used to integrate the function.

When to Use Integration by Substitution Method?

In calculus, the integration by substitution method is also known as the “Reverse Chain Rule” or “U-Substitution Method”. We can use this method to find an integral value when it is set up in the special form. It means that the given integral is of the form:

∫ f(g(x)).g'(x).dx = f(u).du

Here, first, integrate the function with respect to the substituted value (f(u)), and finish the process by substituting the original function g(x).

Course on Vector Calculus

Vector Differential Calculus

Created by Rutika Bhatia - Instructor Prof Bhatia Rutika R


Students: 59, Price: Free

Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields, and fluid flow and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields, and fluid flow.

The objective of the course is to introduce and develop the methods of vector analysis. These methods provide a natural aid to the understanding of geometry and some physical concepts. They are also a fundamental tool in many theories of Applied Mathematics.

After completion of the course, students will have adequate background, conceptual clarity and knowledge of mathematical principles related to Vector differentiation

By the end of the course, students should be able to:

• Calculate scalar and vector products.

• Find the vector equations of lines and planes.

• Understand the parametric equations of curves and surfaces.

• Differentiate vector functions of a single variable.

• Calculate velocity and acceleration vectors for moving particles.

• Understand and be able to find the unit tangent vector, the unit principal normal and the curvature of a space curve.

• Find the gradient of a function.

• Find the divergence and curl of a vector field and prove identities involving these.

• Use the gradient operator to calculate the directional derivative of a function.

• Calculate the unit normal at a point on a surface.

• Recognise irrotational and solenoidal vector fields.

• Evaluate line and surface integrals.

• Understand the various integral theorems relating line, surface and volume integrals.

Few applications of Vector Differential Calculus

Because vectors and matrices are used in linear algebra, anything that requires the use of arrays that are linear dependent requires vectors. A few well-known examples are:

  1. Internet search

  2. Graph analysis

  3. Machine learning

  4. Graphics

  5. Bioinformatics

  6. Scientific computing

  7. Data mining

  8. Computer vision

  9. Speech recognition

  10. Compilers

  11. Parallel computing