Session 6: Volumes and Determinants in Space

• 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 a recitation video
• Read course notes
• Do problems and use solutions to check your work
• Watch an additional recitation video
• Do another set of problems and use solutions to check your work

Lecture Video

Video Excerpts

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» Clip: Volumes and Determinants in Space (8 min)

From Lecture 2 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

Computing Determinants (PDF)

Recitation Video

Determinants

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Download this video:
» iTunes U (MP4 - 10MB)
» Internet Archive (MP4 - 10MB)
» Transcript (PDF)

Related Readings

Determinants Area and Volume (PDF)

Problems and Solutions

Problems: 3x3 Determinants (PDF)

Solutions (PDF)

Recitation Video

Volume of a Parallelepiped

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Download this video:
» iTunes U (MP4 - 6MB)
» Internet Archive (MP4 - 6MB)
» Transcript (PDF)

Problems and Solutions

Problems: Volumes and Determinants (PDF)

Solutions (PDF)

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