This course on Plane Curves covers topics such as Conic Sections, Parametric Equations, Parametric Calculus, and Polar Coordinates. By the end of the course, learners will be able to understand and work with various types of curves, including parabolas, ellipses, hyperbolas, and polar curves. They will also learn how to plot points, find parametrizations, calculate arc lengths, and determine areas between curves. The course employs a combination of introductory explanations, examples, and sketching exercises to help students grasp the concepts effectively. This course is intended for individuals interested in advancing their knowledge of calculus and its applications in analyzing and interpreting different types of curves in mathematics.
Overview
Syllabus
Plane Curves: Conic Sections - 01. Intro.
Plane Curves: Conic Sections - 02. Parabolas - Intro.
Plane Curves: Conic Sections - 03. Parabolas - Example 1.
Plane Curves: Conic Sections - 04. Parabolas Example 2.
Plane Curves: Conic Sections - 05. Ellipses - Intro.
Plane Curves: Conic Sections - 06. Ellipses - Example: Finding an Equation.
Plane Curves: Conic Sections - 07. Ellipses - Example: Sketching.
Plane Curves: Conic Sections - 08. Hyperbolas - Intro.
Plane Curves: Conic Sections - 09. Hyperbolas - Example: Sketch 1.
Plane Curves: Conic Sections - 10. Hyperbolas Example - Sketch 2.
Plane Curves: Parametric Equations - 01. Intro.
Plane Curves: Parametric Equations - 02. Example: Plotting Points.
Plane Curves: Parametric Equations - 03 Example: Finding a Parametrization.
Plane Curves: Parametric Equations - 04. Example: Eliminating the Parameter.
Plane Curves: Parametric Equations - 05. Example: Parametric Ellipse.
Plane Curves: Parametric Equations - 06 Example: Non-smooth curve.
Plane Curves: Parametric Calculus - 01. Intro.
Plane Curves: Parametric Calculus - 02. Example: Tangent and Normal Lines.
Plane Curves: Parametric Calculus - 03. Example: the Unit Circle.
Plane Curves: Parametric Calculus - 04. Example: Tangent at a cusp of an astroid.
Plane Curves: Parametric Calculus - 05. Example: Concavity.
Plane Curves: Parametric Calculus - 06. Example: Sketching.
Plane Curves: Parametric Calculus - 07. Arc Length.
Plane Curves: Parametric Calculus - 08. Example: Arc Length.
Plane Curves: Parametric Calculus - 09. Example: Arc Length 2.
Plane Curves: Parametric Calculus - 10. Example: Area.
Plane Curves: Polar Coordinates - 01. Intro.
Plane Curves: Polar Coordinates - 02. Example: Polar Equations.
Plane Curves: Polar Coordinates - 03. Example: Polar Curve - Cardioid.
Plane Curves: Polar Coordinates - 04. Example: Polar Curve - Rose.
Plane Curves: Polar Coordinates - 05. Example: Converting between coordinate systems.
Plane Curves: Polar Coordinates - 06. Example: Intersection.
Plane Curves: Polar Calculus - 01. Intro.
Plane Curves: Polar Calculus - 02. Example: Limacon Tangent.
Plane Curves: Polar Calculus - 03. Example: Polar Tangents, Part 1.
Plane Curves: Polar Calculus - 04. Example: Polar Tangents, Part 2.
Plane Curves: Polar Calculus - 05. Area.
Plane Curves: Polar Calculus - 06. Example: Circle Area.
Plane Curves: Polar Calculus - 07. Example: Cardioid Area.
Plane Curves: Polar Calculus - 08. Example: Area Between Curves 1.
Plane Curves: Polar Calculus - 09. Example: Area Between Curves 2.
Plane Curves: Polar Calculus - 10. Arc Length.
Taught by
Sean Fitzpatrick
