Explore an in-depth video series on plane curves in calculus, covering conic sections, parametric equations, and polar coordinates. Begin with an introduction to parabolas, ellipses, and hyperbolas, learning how to find equations and sketch these curves. Dive into parametric equations, mastering techniques for plotting points, finding parametrizations, and eliminating parameters. Apply calculus concepts to parametric curves, including tangent and normal lines, concavity, arc length, and area calculations. Transition to polar coordinates, understanding how to convert between coordinate systems and analyze polar curves like cardioids and roses. Conclude with advanced topics in polar calculus, such as finding tangent lines, calculating areas, and determining arc lengths for various polar curves.
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
