This 16-minute video shows that the line integral of a scalar field is independent of path direction.

This 10-minute video lesson provides a second example of using path independence of a conservative vector field to solve a line integral.

This 13-minute video lesson provides a concrete example of the derivative of a vector valued function to better understand what it means.

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

Investigate collisions on an air hockey table. Set up your own experiments: vary the number of discs, masses and initial conditions. Is momentum conserved? Is kinetic energy conserved? Vary the elasticity and see what happens.

This magnetism teacher‰Ûªs guide is one of four activity guides‰ÛÓplus a background guide for teachers‰ÛÓthat provide students with the opportunity to build on science concepts related to Earth‰Ûªs magnetism and its changes, as detected by THEMIS magnetometers located in schools across the U.S. The four activity guides have been used in different types of classes, from physical science and physics classes, to geology classes and astronomy classes. The excitement of actually participating in the THEMIS project helps motivate the students to learn challenging physical science concepts.

The background guide for teachers, the THEMIS GEONS Users Guide describes the important role that terrestrial magnetism plays in shaping a number of important Earth systems. It also explains the basic operating principles behind magnetometers‰ÛÓparticularly the system you are now in the process of using to investigate magnetic storms at your school.

Earth‰Ûªs Magnetic Personality is the fourth and final guide, which was developed with the goal that students can work directly with the THEMIS magnetometer data. The guide covers vectors, the x-y-z magnetometer plots, creating a prediction for aurora using the magnetometer data, calculating the total magnetic field strength and observing it over months, and the waves in Earth‰Ûªs magnetic field excited by large magnetic storms.

Play hockey with electric charges. Place charges on the ice, then hit start to try to get the puck in the goal. View the electric field. Trace the puck's motion. Make the game harder by placing walls in front of the goal. This is a clone of the popular simulation of the same name marketed by Physics Academic Software and written by Prof. Ruth Chabay of the Dept of Physics at North Carolina State University.

Play ball! Add charges to the Field of Dreams and see how they react to the electric field. Turn on a background electric field and adjust the direction and magnitude. (Kevin Costner not included).

Explore the forces at work when you try to push a filing cabinet. Create an applied force and see the resulting friction force and total force acting on the cabinet. Charts show the forces, position, velocity, and acceleration vs. time. View a Free Body Diagram of all the forces (including gravitational and normal forces).

Explore the forces at work when you try to push a filing cabinet. Create an applied force and see the resulting friction force and total force acting on the cabinet. Charts show the forces, position, velocity, and acceleration vs. time. View a Free Body Diagram of all the forces (including gravitational and normal forces).

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.

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.

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]