In this lesson, students will learn how great navigators of the past stayed on course that is, the historical methods of navigation. The concepts of dead reckoning and celestial navigation are discussed.

Figuring out the acceleration of ice down a plane made of ice. Created by Sal Khan.

Figuring out the components of the force due to gravity that are parallel and perpendicular to the surface of an inclined plane. Created by Sal Khan.

This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB® in particular.

This course will survey physics concepts and their respective applications; it is intended as a basic introduction to the current physical understanding of our universe. In this course, the student will study physics from the ground up, learning the basic principles of physical law, their application to the behavior of objects, and the use of the scientific method in driving advances in this knowledge. This course focuses on Newtonian mechanics--how objects move and interact--rather than Electromagnetism or Quantum Mechanics. While mathematics is the language of physics, the student need only be familiar with high school-level algebra, geometry, and trigonometry; the small amount of additional math needed will be developed during the course. (Physics 101; See also: Biology 109, Chemistry 001, Mechanical Engineering 005)

The difference between vectors and scalars. ​Introduction to distance, displacement, speed, and velocity. Created by Sal Khan.

Join the ladybug in an exploration of rotational motion. Rotate the merry-go-round to change its angle, or choose a constant angular velocity or angular acceleration. Explore how circular motion relates to the bug's x,y position, velocity, and acceleration using vectors or graphs.

Join the ladybug in an exploration of rotational motion. Rotate the merry-go-round to change its angle, or choose a constant angular velocity or angular acceleration. Explore how circular motion relates to the bug's x,y position, velocity, and acceleration using vectors or graphs.

Welcome to this online course on Linear Algebra.

Linear Algebra is a branch of mathematics that plays a fundamental to role in many parts of Science and Engineering, such as Quantum Mechanics, Coding Theory, Signal Processing and Control Theory .

As Linear Algebra is a common component of many university programmes in Science or Engineering, this course can be used as additional study or preparation for on campus courses on Linear Algebra. Please note that we cannot guarantee that this course can replace an on campus course.

The course has no preliminaries other than basic high school mathematics. Furthermore, the course is self contained; it can be studied without extra resources. Nevertheless, for each topic you can find some references to standard literature that you can consult for further reading.

This 14-minute video lesson shows how to determine the equation for a plane in R3 using a point on the plane and a normal vector.

This 25-minute video lesson introduces the idea of an angle between two vectors.

This 17-minute video lesson shows how to express a projection on to a line as a Matrix Vector prod. [Linear Algebra playlist: Lesson 61 of 143]

This 12-minute video lesson provides an introduction to the null space of a matrix and shows that the null space of a matrix is a valid subspace. [Linear Algebra playlist: Lesson 34 of 143]

This 10-minute video lesson shows how to figure out a normal vector to a plane from its equation. [Linear Algebra playlist: Lesson 141 of 143]

This 13-minute video lesson shows how to calculate the null space of a matrix. [Linear Algebra playlist: Lesson 35 of 143]

This 12-minute video lesson discusses how to understand how the null space of a matrix relates to the linear independence of its column vectors. [Linear Algebra playlist: Lesson 36 of 143]

This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.

This 9-minute video lesson provides definitions of the vector dot product and vector length.