Difference between revisions of "ModelCourses/Multivariate Calculus"
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:[[ModelCourses/Calculus/VectorCalculus|Download this entire collection of problem sets]] |
:[[ModelCourses/Calculus/VectorCalculus|Download this entire collection of problem sets]] |
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=== Unit 1 - Vector Fields === |
=== Unit 1 - Vector Fields === |
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| − | * Vector Fields in 2D |
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| + | *[[ModelCourses/Calculus/VectorCalculus/VectorFields|Vector Fields]] |
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| − | ** Basic Graphing |
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| + | ** Vector Fields in 2D |
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| − | ** Gradient vector fields and tests for conservative vector fields |
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| + | ** Vector Fields in 3D |
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| − | * Vector Fields in 3D |
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| − | ** Basic Graphing tricks and software |
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| − | ** Gradient vector fields and tests for conservative vector fields |
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:[[ModelUnits/Calculus/VectorCalculus/Unit1]] |
:[[ModelUnits/Calculus/VectorCalculus/Unit1]] |
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=== Unit 2 - Line Integrals in 2D === |
=== Unit 2 - Line Integrals in 2D === |
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| + | * [[ModelCourses/Calculus/VectorCalculus/LineIntegrals|Line Integrals]] |
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* Line Integrals of a scalar function |
* Line Integrals of a scalar function |
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** Simple computations with respect to ds, dx, dy and dz |
** Simple computations with respect to ds, dx, dy and dz |
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=== Unit 3 - Line Integrals in 3D === |
=== Unit 3 - Line Integrals in 3D === |
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| + | * [[ModelCourses/Calculus/VectorCalculus/LineIntegrals3D|Line Integrals in 3D]] |
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* Parametric Surfaces and Areas (sometimes optional due to time constraints) |
* Parametric Surfaces and Areas (sometimes optional due to time constraints) |
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* Curl and Divergence (sometimes optional due to time constraints) |
* Curl and Divergence (sometimes optional due to time constraints) |
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Revision as of 11:18, 10 December 2011
Contents
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
Unit 1 - Vectors
- Vectors in Space
- Space Coordinates
- The Dot Product of Two Vectors
- The Cross Product of Two Vectors in Space
Unit 2 - Vector Applications
- Vector Applications
- Projections
- Lines and Planes in Space
- Distances in Space
Unit 3 - Non-rectangular coordinates
- Coordinate Systems
- Surfaces in Space
- Cylindrical Coordinates
- Spherical Coordinates
- Applications
Vector Functions
Unit 1 - Vector Functions
- Calculus of Vector Functions
- Vector Functions and Space Curves
- Derivatives and Integrals of Vector Functions
Unit 2 - Vector Function Properties
- Properties
- Arc Length
- Curvature
- Unit Tangent and Unit Normal vectors
Unit 3 - Vector Function Applications
- Applications
- Computing equation of osculating circle
- Motion in Space: Velocity and Acceleration
Partial Derivatives
Unit 1 - Partial Derivatives - Definition
- Definition
- Functions of Several Variables and Level Curves
- Limits and Continuity
- Partial Derivatives by Definition
Unit 2 - Partial Derivatives - Rules
- Rules
- Partial Derivatives using Rules
- The Chain Rule
- Directional Derivatives and the Gradient Vector
Unit 3 - Partial Derivatives - Applications
- Applications
- Tangent Planes and Linear and Other Approximations
- Maximum and Minimum Values
- Lagrange Multipliers
Multiple Integrals
Unit 1 - Double Integrals Rectangular
- Rectangular Coordinates
- Iterated Integrals
- Setting up Double Integrals over General Regions
- Applications of Double Integrals in Rectangular Coordinates
Unit 2 - Double Integral Polar
- Polar Coordinates
- Double Integrals in Polar Coordinates
- Applications of Double Integrals in Polar Coordinates
Unit 3 - Triple Integrals
- Triple Integrals
- Triple Integrals
- Triple Integrals in Cylindrical Coordinates
- Triple Integrals in Spherical Coordinates
- Change of Variables in Multiple Integrals
- Applications of Triple Integrals
Vector Calculus
Unit 1 - Vector Fields
- Vector Fields
- Vector Fields in 2D
- Vector Fields in 3D
Unit 2 - Line Integrals in 2D
- Line Integrals
- Line Integrals of a scalar function
- Simple computations with respect to ds, dx, dy and dz
- Application to Total Mass and Lateral Surface Area
- Line Integrals over a vector field
- Simple computations
- Application to Work
- The Fundamental Theorem of Calculus for Line Integrals
- Relationship with conservative fields and independence of path.
- Green's Theorem
- Simple calculations
- Changing orientations, holes
- Applications in Physics
Unit 3 - Line Integrals in 3D
- 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)
Packaged Courses
Moodle
https://test.webwork.maa.org/moodle/
Stewart
Hughes-Hallett
Smith and Minton
Larson
``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.
