Math 5C - Multivariable Calculus

Homework Even Answers

 

 

Course Overview

Study Suggestions

Sample Exams

• Sample Exams | 1 solutions| 2 solutions | 3 solutions another version solns| 4 4solns| Final with answers | Sample Final v2 - Solutions

Graphing Tools

• Blank grid in R3
• CalcPlot3D
• CalcPlot instructions by MathisPower4U, Larry Green, Paul Seeburger
• 3D grapher
• Geogebra 3D grapher

My Favorite Resources:

• Professor Leonard (Very good full video lecture, except the one onf triple integrals)
• Mathispower4U (good power point style videos)
• Khan Academy Multivariable (videos)
• Professor Clark Powerpoints with computer graphics
• Dr Trevor Bazett videos
• Pauls's Notes (Explanations and sample problems)
• Online book -Whitman college
• Additional Online Resources

Course Content:

• Vectors and 3-D (Ch 12)

  • Note outlines Chapter 12, 13
  • Moveable Points in R3
  • Proof of right hand rule 1 2 
  • Geometric illustration of cross product
  • Quadric Surfaces (with cross section sliders) requires Java. Good visualization of graphing window domain.
  • Quadric Surfaces: What is a trace? Cross Section Animation

• Vector Valued Funtions and Space Curves (Ch 13)

  • Curve Sketching Tool: CalcPlot space curves| 3 (geogebra)| 4 (geogebra with r(t))
  • Acceleration vector animation
  • TNB example
  • TNB animation

• Multivariable Functions (Ch 14)

  • Unit 2 Note Outlines
  • a surface with its traces, and the resulting level curves
    (courtesy of Professor John Putz, Alma College)
  • Limits geogebra
  • Directional Derivative Animation
  • Directional Derivative (geobebra) and gradient
  • Illustration of partials (geogebra)
  • Tangent plane (geogebra)
  • Directional Derivative Video (Mathispower4u)
  • Gradient Video (Mathispower4u)
  • Relative Extrema Video (Mathispower4u)
  • Absolute Max on Closed Domain Video
  • Illustration Absolute extrema on closed domain
  • Example: Absolute Extrema on Closed Domain
  • Wolfram Max/Min subject to constraint
  • Lagrange Multiplier development graph
  • Lagrange Multipliers sample problems
  • Lagrange Widget
• 

  Integrals of Multivariable Functions (Ch 15, 16.2i, 16.7i)

  • Unit 3 Note Outlines
  • Double Integral Example Geogebra Graphic
  • Double integral rdr
  • Triple Integral Example Geogebra
  • Triple Integral Example 3 Geogebra | Notes ***
  • Triple Integral Examples 1 | 2 | | 3 (scroll down
  • Triple Integral Videos 1 (Mathispower4u) | 2 (PatrickJMT)
  • Review of double, triple, and line integrals powerpoint| 2
  • Spherical Coordinates Animation another
  • Spherical Coordinates range gif
  • Simple Spherical Coordinate Solids
  • Spherical dV
  • Animation of finding limits of integration for "snow cone"
  • Types of Integrals
• 

  Vector Fields (Ch 16)

  • Unit 4 Note Outlines
  • Vector Field Plotter
  • Geogebra 3D Vector Field Plotter
  • Line Ingegral with respect to arc length animation
  • Line Integral (courtesy Israel Castro)
  • Work Illustration (courtesy Israel Castro)
  • Divergence and Curl - Subtleties about curl
  • Intuitive idea of how curl is related to work. (Khan)
  • Khan has a lot of good videos related to this chapter
  • Grad Div Curl in environmemtal science
  • Divergence and curl (3 blue 1 brown)
  • Stokes' Theorem
  • Stokes Theorem video part 1 part 2 (Mathispower4u)
  • Divergence Theorem video part 1 part 2 (Mathispower4u)

 

Math 5C - Multivariable Calculus