Multivariable Calculus: Free Course

About this course

Extend single-variable calculus into functions of several variables in this free Multivariable Calculus course from Khan Academy. All 175 source videos remain in the classroom. The curriculum connects multivariable functions with partial derivatives, gradients, optimization, multiple integration and vector-calculus theorems. Visual explanations and worked examples help a prepared learner move between a geometric interpretation and the calculations used to describe it.

Course at a glance

What you’ll learn

• Interpret multivariable functions and their geometric representations.
• Use partial derivatives and gradients to describe local change.
• Explore multivariable derivative applications and optimization.
• Study double, triple, line and surface integrals in the demonstrated settings.
• Connect Green’s, Stokes’ and the divergence theorems with their assumptions and interpretations.

Skills you’ll gain

• Multivariable functions
• Partial derivatives
• Gradients
• Multiple integrals
• Vector calculus
• Theorem interpretation

Course Overview

The complete recorded sequence covers the major multivariable-calculus learning areas represented in the source: functions, derivatives, applications, integration and the relationships between integrals and vector fields. Its examples support both calculation and interpretation, including later proof and application recordings. All source videos are retained rather than reducing a multistep explanation to a summary clip. Prior algebra, geometry and single-variable calculus are important because the course extends those ideas. Work through a small case carefully before applying a notation or theorem to a more involved region or field.

How to study the course

• Videos 1–43: this part of the source list includes “Multivariable functions” through “Curvature of a cycloid”. Write definitions and assumptions explicitly. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 44–87: this part of the source list includes “Computing the partial derivative of a vector-valued function” through “Warm up to the second partial derivative test”. Track the mathematical objects used in each operation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 88–131: this part of the source list includes “Second partial derivative test” through “Surface integral example part 3: The home stretch”. Compare a simple example with a less obvious one. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 132–175: this part of the source list includes “Surface integral ex2 part 1: Parameterizing the surface” through “Divergence theorem proof (part 5)”. Verify the solution using its defining conditions. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits prepared college-level learners and returning students studying the specific advanced topic. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

The earlier algebra or calculus used in the recordings is assumed. Keep working notes and review definitions before following a proof or a multistep calculation.

Put the lessons into practice

Choose a simple two-variable function and describe its values using a sketch or table. Compute relevant partial derivatives and explain their meaning. Then work a small integration or vector-field example using a method shown in the course. State the region, orientation and assumptions before calculating. Compare with an easier case and check that the interpretation matches the quantities involved. For a theorem application, identify the conditions that make the relationship usable rather than treating its formula as an automatic shortcut.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.