M408M Learning Module Pages
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Chapter 10: Parametric Equations and Polar Coordinates
Learning module LM 10.1: Parametrized Curves:
3 kinds of functions, 3 kinds of curves
The cycloid
Visualizing parametrized curves
Tracing curves and ellipses
Lissajous figures
Learning module LM 10.2: Calculus with Parametrized Curves:
Slope and area
Arc length and surface area
Summary and simplification
Higher Derivatives
Learning module LM 10.3: Polar Coordinates:
Definitions of polar coordinates
Graphing polar functions
Computing slopes of tangent lines
Learning module LM 10.4: Areas and Lengths of Polar Curves:
Area inside a polar curve
Area between polar curves
Arc lengths of polar curves
Learning module LM 10.5: Conic Sections:
Slicing a cone
Ellipses
Hyperbolas
Parabolas and directrices
Completing the square
Learning module LM 10.6: Conic Sections in Polar Coordinates:
Foci and directrices
Visualizing eccentricity
Polar equations for conic sections
Astronomy
Chapter 12: Vectors and the Geometry of Space
Chapter 13: Vector Functions
Chapter 14: Partial Derivatives
Chapter 15: Multiple Integrals
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Chapter 10: Parametric Equations and Polar Coordinates
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