Prof. Ben Brubaker defines and explores the properties of the linear approximation of a function at a point. The linear approximation is then applied to solve a simple differential equation encountered in chemical kinetics.
After watching this video students will be able to:
- Recognize the linear approximation of a function as the tangent line to the function.
- Apply linear approximations to solve a simple differential equation.
- Explain the limitations of linear approximations mathematically and graphically.
Funding provided by the Singapore University of Technology and Design (SUTD)
Developed by the Teaching and Learning Laboratory (TLL) at MIT for SUTD
MIT © 2012
It is highly recommended that the video is paused when prompted so that students are able to attempt the activities on their own and then check their solutions against the video.
During the video, students will:
- Find the equation to the tangent line.
- Posit why the tangent line is not a good approximation at any intersection point, but only tangent intersections.
- Compute the error between the exact and approximated solutions to a reaction rate problem from chemistry.