Session 25: Level Curves and Contour Plots

• Course Home
• Syllabus
• 1. Vectors and Matrices

  • Part A: Vectors, Determinants and Planes
  • Part B: Matrices and Systems of Equations
  • Part C: Parametric Equations for Curves
  • Exam 1
• 2. Partial Derivatives

  • Part A: Functions of Two Variables, Tangent Approximation and Opt
  • Part B: Chain Rule, Gradient and Directional Derivatives
  • Part C: Lagrange Multipliers and Constrained Differentials
  • Exam 2
• 3. Double Integrals and Line Integrals in the Plane

  • Part A: Double Integrals
  • Part B: Vector Fields and Line Integrals
  • Part C: Green's Theorem
  • Exam 3
• 4. Triple Integrals and Surface Integrals in 3-Space

  • Part A: Triple Integrals
  • Part B: Flux and the Divergence Theorem
  • Part C: Line Integrals and Stokes' Theorem
  • Exam 4
  • Physics Applications
• Final Exam

  • Practice Final Exam
  • Review
  • Final Exam
• Download Course Materials

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Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Read course notes and examples
• Watch two recitation videos
• Work with a Mathlet to reinforce lecture concepts
• Do problems and use solutions to check your work

Lecture Video

Video Excerpts

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» Clip: Level Curves and Contour Plots (16 min)

From Lecture 8 of 18.02 Multivariable Calculus, Fall 2007

Download the complete lectures from this course:

» iTunes U
» Internet Archive

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

Reading and Examples

Level Curves and Contour Plots (PDF)

Recitation Video

Level Curves

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Download this video:
» iTunes U (MP4 - 23MB)
» Internet Archive (MP4 - 23MB)
» Transcript (PDF)

 

Level Curves and Critical Points

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Download this video:
» iTunes U (MP4 - 18MB)
» Internet Archive (MP4 - 18MB)
» Transcript (PDF)

Related Resources

Functions of Two Variables Mathlet

Problems and Solutions

Problems: Contour Plots (PDF)

Solutions (PDF)

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