Session 20: Velocity and Arc Length

• 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
• Review an example
• Watch a recitation video
• Do problems and use solutions to check your work

Lecture Video

Video Excerpts

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» Clip: Velocity and Arc Length (14 min)

From Lecture 6 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.

Related Readings

Velocity, Speed and Arc Length (PDF)

Examples

Velocity, Speed and Arc Length (PDF)

Recitation Video

Parametric Curves: Velocity, Acceleration, Length

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

Problems and Solutions

Problems: Vector Derivatives and Arc Length (PDF)

Solutions (PDF)

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