Lecture 12: Gradient, directional derivative, and tangent plane
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Lesson Description:
Learn about the gradient vector, directional derivative, and more on the tangent plane.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 15, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.
Additional Resources:
- Transcript of Lesson - Written transcript from this lesson.
- Lecture Notes - Lecture Notes from this lesson.
- Problem Set - A problem set with some problems from this lecture.
Questions answered by this video:
- What is the gradient vector and how do you find it?
- What does the gradient vector mean, what does it measure, and what can you do with it?
- How do you find the normal vector to a plane?
- How do you find the level curve of a function?
- What is the proof that the gradient is perpendicular to the level surface for a function?
- How do you find the tangent plane to a surface using a gradient?
- What are directional derivatives and how do you find them?
- What do directional derivatives mean geometrically?
- How can you determine the direction that a gradient vector is pointing?
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Staff Review
The gradient vector is discussed and explained in depth after being introduced in the previous lecture. This idea is very important to the idea of vector fields, which are discussed later in this course. Directional derivatives are also explained and shown very using pictures and problems.
