Module 4: Parametric and Polar Curves Topic 1 – Parametric Equations and Curves Parametric Equations and Curves – The Main Idea Example 1 – Variant #4 from The Main Idea Example 2 Example 3 – Finding Parametric Equations from a Rectangular Curve Example 4 – Smooth and Non-Smooth Curves using Desmos Topic 2 – Calculus with Parametric Curves Derivatives of Parametric Curves – The Main Idea Derivatives of Parametric Curves – Ex2 (part 1) Derivatives of Parametric Curves – Ex2 (part 2, IPs) Arc Length of Parametric Curves Example Area of a Region given by a Parametric Curve Example Topic 3 – Polar Coordinates and Graphs Polar Coordinates Review Polar Graphs and Symmetry Review Tangent Lines of a Polar Graph Example Tangent Lines of a Lemniscate Example Topic 4 – Areas and Lengths in Polar Coordinates Area of a Region given by a Polar Curve – The Main Idea Area of a Shaded Region given by a Polar Curve Area of Lemniscate Loops Arc Length of a Polar Curve Topic 5 – Conic Sections Review The Parabola (Lecture) The Ellipse (Lecture) The Hyperbola (Lecture) Analyzing a Parabola Example Analyzing an Ellipse Example Analyzing a Hyperbola Example Topic 6 – Conic Sections in Polar Coordinates Conic Sections in Polar Coordinates – The Main Idea Polar Form of an Ellipse Example
