Difference between revisions of "ModelCourses/Multivariate Calculus"

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:[[ModelCourses/Calculus/Vectors/setUnit2|Download Set Definition File]]
  
:[[ModelCourses/Calculus/Vectors/setUnit2|Download Set Definition File]]
   
−
=== Unit 3 - Non-rectangular coordinates ===
 +
=== Unit 3 - [[ModelCourses/Calculus/Vectors/Coordinate Systems|Non-rectangular Coordinate Systems]] ===
−
*[[ModelCourses/Calculus/Vectors/Coordinate Systems|Coordinate Systems]]
 +
−
** Surfaces in Space
 +
* Surfaces in Space
−
** Cylindrical Coordinates
 +
* Cylindrical Coordinates
−
** Spherical Coordinates
 +
* Spherical Coordinates
−
** Applications
 +
* Applications
   
 
:[[ModelCourses/Calculus/Vectors/setUnit3|Download Set Definition File]]
  
:[[ModelCourses/Calculus/Vectors/setUnit3|Download Set Definition File]]
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:[[ModelCourses/Calculus/VectorFunctions|Download this entire collection of problem sets]]
  
:[[ModelCourses/Calculus/VectorFunctions|Download this entire collection of problem sets]]
   
−
=== Unit 1 - Vector Functions ===
 +
=== Unit 1 - [[ModelCourses/Calculus/VectorFunctions/CalculusBasics|Calculus of Vector Functions]] ===
−
* [[ModelCourses/Calculus/VectorFunctions/CalculusBasics|Calculus of Vector Functions]]
 +
−
** Vector Functions and Space Curves
 +
* Vector Functions and Space Curves
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** Derivatives and Integrals of Vector Functions
 +
* Derivatives and Integrals of Vector Functions
 
:[[ModelCourses/Calculus/VectorFunctions/setUnit1|Download Set Definition File]]
  
:[[ModelCourses/Calculus/VectorFunctions/setUnit1|Download Set Definition File]]
   
−
=== Unit 2 - Vector Function Properties ===
 +
=== Unit 2 - [[ModelCourses/Calculus/VectorFunctions/Properties|Vector Function Properties ]] ===
−
* [[ModelCourses/Calculus/VectorFunctions/Properties|Properties]]
 +
−
** Arc Length
 +
* Arc Length
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** Curvature
 +
* Curvature
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** Unit Tangent and Unit Normal vectors
 +
* Unit Tangent and Unit Normal vectors
   
 
:[[ModelCourses/Calculus/VectorFunctions/setUnit2|Download Set Definition File]]
  
:[[ModelCourses/Calculus/VectorFunctions/setUnit2|Download Set Definition File]]
   
−
=== Unit 3 - Vector Function Applications ===
 +
=== Unit 3 - [[ModelCourses/Calculus/VectorFunctions/Applications|Vector Function Applications ]] ===
−
* [[ModelCourses/Calculus/VectorFunctions/Applications|Applications]]
 +
−
** Computing equation of osculating circle
 +
* Computing equation of osculating circle
−
** Motion in Space: Velocity and Acceleration
 +
* Motion in Space: Velocity and Acceleration
   
 
:[[ModelCourses/Calculus/VectorFunctions/setUnit3|Download Set Definition File]]
  
:[[ModelCourses/Calculus/VectorFunctions/setUnit3|Download Set Definition File]]
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== <span style="color:blue">Partial Derivatives</span> ==
  
== <span style="color:blue">Partial Derivatives</span> ==
 
:[[ModelCourses/Calculus/PartialDerivatives|Download this entire collection of problem sets]]
  
:[[ModelCourses/Calculus/PartialDerivatives|Download this entire collection of problem sets]]
−
=== Unit 1 - Partial Derivatives - Definition ===
 +
=== Unit 1 - [[ModelCourses/Calculus/PartialDerivatives/Definition|Partial Derivatives - Definition ]]===
−
* [[ModelCourses/Calculus/PartialDerivatives/Definition|Definition]]
 +
−
** Functions of Several Variables and Level Curves
 +
* Functions of Several Variables and Level Curves
−
** Limits and Continuity
 +
* Limits and Continuity
−
** Partial Derivatives by Definition
 +
* Partial Derivatives by Definition
   
 
:[[ModelUnits/Calculus/PartialDerivatives/Unit1|Download Set Definition File]]
  
:[[ModelUnits/Calculus/PartialDerivatives/Unit1|Download Set Definition File]]
   
−
=== Unit 2 - Partial Derivatives - Rules ===
 +
=== Unit 2 - [[ModelCourses/Calculus/PartialDerivatives/Rules|Partial Derivatives - Rules ]]===
−
* [[ModelCourses/Calculus/PartialDerivatives/Rules|Rules]]
 +
−
** Partial Derivatives using Rules
 +
* Partial Derivatives using Rules
−
** The Chain Rule
 +
* The Chain Rule
−
** Directional Derivatives and the Gradient Vector
 +
* Directional Derivatives and the Gradient Vector
   
 
:[[ModelUnits/Calculus/PartialDerivatives/Unit2|Download Set Definition File]]
  
:[[ModelUnits/Calculus/PartialDerivatives/Unit2|Download Set Definition File]]
   
−
=== Unit 3 - Partial Derivatives - Applications ===
 +
=== Unit 3 - [[ModelCourses/Calculus/PartialDerivatives/Applications|Partial Derivatives - Applications ]]===
−
* [[ModelCourses/Calculus/PartialDerivatives/Applications|Applications]]
 +
−
** Tangent Planes and Linear and Other Approximations
 +
* Tangent Planes and Linear and Other Approximations
−
** Maximum and Minimum Values
 +
* Maximum and Minimum Values
−
** Lagrange Multipliers
 +
* Lagrange Multipliers
   
 
:[[ModelUnits/Calculus/PartialDerivatives/Unit3|Download Set Definition File]]
  
:[[ModelUnits/Calculus/PartialDerivatives/Unit3|Download Set Definition File]]
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:[[ModelCourses/Calculus/MultipleIntegrals|Download this entire collection of problem sets]]
  
:[[ModelCourses/Calculus/MultipleIntegrals|Download this entire collection of problem sets]]
   
−
=== Unit 1 - Double Integrals Rectangular ===
 +
=== Unit 1 - [[ModelCourses/Calculus/MultipleIntegrals/Rectangular|Double Integrals Rectangular ]]===
−
* [[ModelCourses/Calculus/MultipleIntegrals/Rectangular|Rectangular Coordinates]]
 +
−
** Iterated Integrals
 +
* Iterated Integrals
−
** Setting up Double Integrals over General Regions
 +
* Setting up Double Integrals over General Regions
−
** Applications of Double Integrals in Rectangular Coordinates
 +
* Applications of Double Integrals in Rectangular Coordinates
   
 
:[[ModelUnits/Calculus/MultipleIntegrals/Unit1|Download Set Definition File]]
  
:[[ModelUnits/Calculus/MultipleIntegrals/Unit1|Download Set Definition File]]
   
−
=== Unit 2 - Double Integral Polar ===
 +
=== Unit 2 - [[ModelCourses/Calculus/MultipleIntegrals/Polar|Double Integral Polar Coordinates]]===
−
* [[ModelCourses/Calculus/MultipleIntegrals/Polar|Polar Coordinates]]
 +
−
** Double Integrals in Polar Coordinates
 +
* Double Integrals in Polar Coordinates
−
** Applications of Double Integrals in Polar Coordinates
 +
* Applications of Double Integrals in Polar Coordinates
   
 
:[[ModelUnits/Calculus/MultipleIntegrals/Unit2|Download Set Definition File]]
  
:[[ModelUnits/Calculus/MultipleIntegrals/Unit2|Download Set Definition File]]
   
−
=== Unit 3 - Triple Integrals ===
 +
=== Unit 3 - [[ModelCourses/Calculus/MultipleIntegrals/TripleIntegrals|Triple Integrals]] ===
−
* [[ModelCourses/Calculus/MultipleIntegrals/TripleIntegrals|Triple Integrals]]
 +
−
** Triple Integrals
 +
* Triple Integrals
−
** Triple Integrals in Cylindrical Coordinates
 +
* Triple Integrals in Cylindrical Coordinates
−
** Triple Integrals in Spherical Coordinates
 +
* Triple Integrals in Spherical Coordinates
−
** Change of Variables in Multiple Integrals
 +
* Change of Variables in Multiple Integrals
−
** Applications of Triple Integrals
 +
* Applications of Triple Integrals
   
 
:[[ModelUnits/Calculus/MultipleIntegrals/Unit3|Download Set Definition File]]
  
:[[ModelUnits/Calculus/MultipleIntegrals/Unit3|Download Set Definition File]]
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== <span style="color:blue">Vector Calculus</span> ==
  
== <span style="color:blue">Vector Calculus</span> ==
 
:[[ModelCourses/Calculus/VectorCalculus|Download this entire collection of problem sets]]
  
:[[ModelCourses/Calculus/VectorCalculus|Download this entire collection of problem sets]]
−
=== Unit 1 - Vector Fields ===
 +
=== Unit 1 - [[ModelCourses/Calculus/VectorCalculus/VectorFields|Vector Fields]] ===
−
*[[ModelCourses/Calculus/VectorCalculus/VectorFields|Vector Fields]]
 +
−
** Vector Fields in 2D
 +
* Vector Fields in 2D
−
** Vector Fields in 3D
 +
* Vector Fields in 3D
   
 
:[[ModelUnits/Calculus/VectorCalculus/Unit1|Download Set Definition File]]
  
:[[ModelUnits/Calculus/VectorCalculus/Unit1|Download Set Definition File]]
   
−
=== Unit 2 - Line Integrals in 2D ===
 +
=== Unit 2 - [[ModelCourses/Calculus/VectorCalculus/LineIntegrals|Line Integrals in 2D ]] ===
−
* [[ModelCourses/Calculus/VectorCalculus/LineIntegrals|Line Integrals]]
 +
−
** Line Integrals of a scalar function
 +
* Line Integrals of a scalar function
−
** Line Integrals over a vector field
 +
* Line Integrals over a vector field
−
** The Fundamental Theorem of Calculus for Line Integrals
 +
* The Fundamental Theorem of Calculus for Line Integrals
−
** Green's Theorem
 +
* Green's Theorem
   
 
:[[ModelUnits/Calculus/VectorCalculus/Unit2|Download Set Definition File]]
  
:[[ModelUnits/Calculus/VectorCalculus/Unit2|Download Set Definition File]]
   
−
=== Unit 3 - Line Integrals in 3D ===
 +
=== Unit 3 - [[ModelCourses/Calculus/VectorCalculus/LineIntegrals3D|Line Integrals in 3D]] ===
−
* [[ModelCourses/Calculus/VectorCalculus/LineIntegrals3D|Line Integrals in 3D]]
 +
−
** Parametric Surfaces and Areas (sometimes optional due to time constraints)
 +
* Parametric Surfaces and Areas (sometimes optional due to time constraints)
−
** Curl and Divergence (sometimes optional due to time constraints)
 +
* Curl and Divergence (sometimes optional due to time constraints)
−
** Surface Integrals (sometimes optional due to time constraints)
 +
* Surface Integrals (sometimes optional due to time constraints)
−
** Stokes' Theorem (often optional)
 +
* Stokes' Theorem (often optional)
−
** The Divergence Theorem (often optional)
 +
* The Divergence Theorem (often optional)
   
 
:[[ModelUnits/Calculus/VectorCalculus/Unit3|Download Set Definition File]]
  
:[[ModelUnits/Calculus/VectorCalculus/Unit3|Download Set Definition File]]

Revision as of 11:33, 12 December 2011

Multivariate Calculus Model Course Units

A user of this material should locate appropriate units below that fit their particular course in multivariate calculus.

Instructions for importing problem sets Instructions for exporting problem sets


Within each Unit below, specific problem types should be described. Complete problem sets for each unit will eventually be collected and made available from this site (and perhaps from within the WebWork system itself) but these have not been made available yet. Also, the specific problems suggested could be directly linked if desired although this might be a bit too much!


Vectors in Space

Download this entire collection of problem sets

Unit 1 - Vectors

  • Space Coordinates
  • The Dot Product of Two Vectors
  • The Cross Product of Two Vectors in Space
Download Set Definition File

Unit 2 - Vector Applications

  • Projections
  • Lines and Planes in Space
  • Distances in Space
Download Set Definition File

Unit 3 - Non-rectangular Coordinate Systems

  • Surfaces in Space
  • Cylindrical Coordinates
  • Spherical Coordinates
  • Applications
Download Set Definition File

Vector Functions

Download this entire collection of problem sets

Unit 1 - Calculus of Vector Functions

  • Vector Functions and Space Curves
  • Derivatives and Integrals of Vector Functions
Download Set Definition File

Unit 2 - Vector Function Properties

  • Arc Length
  • Curvature
  • Unit Tangent and Unit Normal vectors
Download Set Definition File

Unit 3 - Vector Function Applications

  • Computing equation of osculating circle
  • Motion in Space: Velocity and Acceleration
Download Set Definition File

Partial Derivatives

Download this entire collection of problem sets

Unit 1 - Partial Derivatives - Definition

  • Functions of Several Variables and Level Curves
  • Limits and Continuity
  • Partial Derivatives by Definition
Download Set Definition File

Unit 2 - Partial Derivatives - Rules

  • Partial Derivatives using Rules
  • The Chain Rule
  • Directional Derivatives and the Gradient Vector
Download Set Definition File

Unit 3 - Partial Derivatives - Applications

  • Tangent Planes and Linear and Other Approximations
  • Maximum and Minimum Values
  • Lagrange Multipliers
Download Set Definition File

Multiple Integrals

Download this entire collection of problem sets

Unit 1 - Double Integrals Rectangular

  • Iterated Integrals
  • Setting up Double Integrals over General Regions
  • Applications of Double Integrals in Rectangular Coordinates
Download Set Definition File

Unit 2 - Double Integral Polar Coordinates

  • Double Integrals in Polar Coordinates
  • Applications of Double Integrals in Polar Coordinates
Download Set Definition File

Unit 3 - Triple Integrals

  • Triple Integrals
  • Triple Integrals in Cylindrical Coordinates
  • Triple Integrals in Spherical Coordinates
  • Change of Variables in Multiple Integrals
  • Applications of Triple Integrals
Download Set Definition File

Vector Calculus

Download this entire collection of problem sets

Unit 1 - Vector Fields

  • Vector Fields in 2D
  • Vector Fields in 3D
Download Set Definition File

Unit 2 - Line Integrals in 2D

  • Line Integrals of a scalar function
  • Line Integrals over a vector field
  • The Fundamental Theorem of Calculus for Line Integrals
  • Green's Theorem
Download Set Definition File

Unit 3 - Line Integrals in 3D

  • Parametric Surfaces and Areas (sometimes optional due to time constraints)
  • Curl and Divergence (sometimes optional due to time constraints)
  • Surface Integrals (sometimes optional due to time constraints)
  • Stokes' Theorem (often optional)
  • The Divergence Theorem (often optional)
Download Set Definition File

Packaged Courses

Moodle

https://test.webwork.maa.org/moodle/

Stewart

Stewart_packaged

Hughes-Hallett

Hughes_Hallett_packaged

Smith and Minton

Smith_Minton_packaged

Larson

Larson_packaged

Other Model Course Pages

``Future Work: A rubric needs to be developed that helps instructors determine the hardness level of a particular problem.``

  • Development Workgroup: Mei Qin Chen, Dick Lane and John Travis
  • To Do:
    • Finish choosing problem sets for remaining units
    • Add features to problems to include:
      • Hints
      • Solutions
      • MetaTags
      • Improvements such as changing multiple choice problems to fill in the blank, etc.


[Other Webwork Course Templates]

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