18.02SC | Fall 2010 | Undergraduate

Multivariable Calculus

Part B: Chain Rule, Gradient and Directional Derivatives

Session 36: Proof

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Overview

In this session you will:

  • Watch a lecture video clip and read board notes
  • Read course notes and examples
  • Do problems and use solutions to check your work

Lecture Video

Video Excerpts

Clip: Proof

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

Reading and Examples

Proof the Gradient is Perpendicular to Level Curves and Surfaces (PDF)

Problems and Solutions

Problems: Gradient and Level Curves (PDF)

Solutions (PDF)

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Course Info

Fall 2010
Exam Solutions
Exams
Lecture Notes
Lecture Videos
Problem Set Solutions
Problem Sets