Representing Cartesian coordinate curves using explicit and implicit forms. Representing curves using parametric equations which define x and y in terms of a third variable. Includes examples of parametric equations for a circle, ellipse, and projectile fired at an angle.
18.01 Single Variable Calculus, Fall 2005
Prof. Jason Starr
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Nine questions which involve finding equations in rectangular coordinates for those given in parametric form, or putting a rectangular equation in parametric form.
18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
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Finding implicit forms for parameterized curves. Uses examples from the previous section of the notes.
18.01 Single Variable Calculus, Fall 2005
Prof. Jason Starr
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Definition, with examples of circles and a horizontal line defined in polar coordinates.
18.01 Single Variable Calculus, Fall 2005
Prof. Jason Starr
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Using parametric equations to define a curve in two or three dimensions and properties of parametric equations.
18.013A Calculus with Applications, Spring 2005
Prof. Daniel J. Kleitman
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Three multi-part questions which involve converting rectangular coordinates to polar coordinates, converting polar equations to rectangular equations, and graphing curves given in polar coordinates.
18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
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Sketching a curve in polar coordinates, and labeling the quadrants, endpoints, tangent slopes, and angles for the curve.
18.01 Single Variable Calculus, Fall 2005
Prof. Jason Starr
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Sketching a curve given in polar coordinates and finding the area swept by a line segment as one of the endpoints moves along this curve.
18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
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Sketching a curve defined in polar coordinates and finding the area inside it.
18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
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18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
Course Material Related to This Topic:
Sketching a curve given in polar coordinates and finding points of intersection between that and other curves.
Representing a circle using both rectangular and polar coordinates.
Setting up and evaluating an integral to represent the uncovered area of the two moons involved in a lunar eclipse on another planet.
18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
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Sketching a spiral defined in polar coordinates, counting the times it crosses the x-axis, and finding the area of specific regions of the spiral.
18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
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Finding an equation in polar coordinates and the appropriate range of theta for a line given in rectangular coordinates.
18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
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Applet for showing the graph of a function defined in polar coordinates.
18.013A Calculus with Applications, Spring 2005
Prof. Daniel J. Kleitman
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Applet for plotting curves defined in rectangular or parametric form.
18.013A Calculus with Applications, Spring 2005
Prof. Daniel J. Kleitman
Course Material Related to This Topic: