Curated OER
Worksheet 21 Spring 1996
In this math worksheet, students consider a path around the unit circle parameterized by σ on the interval [0, 1] with σ(t) = sin(5πt − π), cos(5πt − π). Then they find the vector.
Curated OER
Complex Analysis: Understanding Contour Integration
In this integration instructional activity, students evaluate contour integrals using the parameterization method. They describe various related theorems. This two-page instructional activity contains approximately eight problems.
Curated OER
Math 312 Spring 98. Contour Integration
In this contour integration worksheet, students compute the value of integrals, sketch the contour and list the parameterization used. This two-page worksheet contains three problems.
Curated OER
Math 312 Spring 2004: Complex Integration
In this complex integration worksheet, students compute the value of the integral, sketch the contour and identify the parameterizations used. This two-page worksheet contains approximately five problems.
EngageNY
Motion Along a Line – Search Robots Again
We can mathematically model the path of a robot. Learners use parametric equations to find the location of a robot at a given time. They compare the paths of multiple robots looking for parallel and perpendicular relationships and...
EngageNY
Linear Transformations of Lines
Discover the extension of parametric equations to model linear transformations. Scholars first write parametric equations to model lines through two points. They then find the parametric equations that represent a linear transformation.
Curated OER
Stokes' Theorem (and some review!)
In this calculus activity, students answer 4 short answer questions each about Green's Theorem and Stokes' Theorem. Questions require students to rephrase each theorem and tell when they may be used. Students solve questions using...
Curated OER
Worksheet 19
In this math worksheet, students use the following descriptions of a spring system to write a differential equation of the form my + γy + ky = F(x).
Curated OER
Worksheet 34
In this math activity, students find the plane perpendicular to the path (t2, t, cos 2πt) at time t = 1/4. Then they determine the location in which the object is moving the fastest.
Curated OER
Worksheet 29
In this math learning exercise, students investigate how time is related to the concept of increasing or decreasing velocity. Then they consider times and answer the questions of whether the velocity is changing.
Curated OER
Worksheet 31
For this math worksheet, students investigate vectors and polar coordinates. They convert the paths of polar coordinates to Euclidian points.
Texas Instruments
Texas Instruments: Dynamic Algebra
This Computer Algebra System (CAS) activity shows how the method of dynamization by parameterization works with almost all classical math problems, which produces problems for CAS calculators quickly.
Khan Academy
Khan Academy: Solve for T
In this seven-problem quiz/practice students parameterize rays by solving for t.
Wolfram Research
Wolfram Math World: Smooth Surface
This site gives the terms which must be met in order for a surface to be a smooth surface. There are related links on this page.
Khan Academy
Khan Academy: Ray Intersection With Line
In this seven-question quiz/practice students find where a ray intersects with a line in implicit form.
Khan Academy
Khan Academy: Parametric Ray Intuition
This is a seven-question quiz/practice review the parametric representation of a ray.