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Outline
Unit 1: Paths and Curves
1.1 Plane Curves
1.2 Calculus of Plane Curves
1.3 Speed and Arclength
1.4 Curvature
1.5 Space Curves
1.6 The Frenet Frame
Unit 1: Paths and Curves
Author:
Sarah Harrelson
Topic:
Vectors 2D (Two-Dimensional)
,
Vectors 3D (Three-Dimensional)
,
Calculus
,
Parametric Curves
,
Vectors
Unit 1 of a high school Multivariable Calculus Class for LASA High School:
https://www.lasahighschool.org/
Table of Contents
1.1 Plane Curves
1.1.1 Introduction to parameterized curves
1.1.2 A subtlety
1.1.3 Properties of paths
1.1.4 Directed Lines and Line Segments
1.1.5 Transformations of paths (part 1)
1.1.6 Transforming the Parameter (Circles)
1.1.7 Transforming the parameter (directed lines)
1.1.8 Circles and Ellipses
1.2 Calculus of Plane Curves
1.2.1 The Cycloid Problem
1.2.2 The Velocity Vector
1.2.3 Tangent Line to a Plane Curve
1.2.4 A few product and chain rules
1.3 Speed and Arclength
1.3.1 Speed
1.3.2 Estimating length via line segments
1.3.3 Creating an integral
1.3.4 Arc length
1.3.5 Arc length parameterization
1.4 Curvature
1.4.1 The Unit Tangent Vector
1.4.2 Curvature (round 1)
1.4.3 Curvature (Round 2)
1.4.4 The Unit Normal
1.4.5 The Osculating Circle
1.5 Space Curves
1.5.1 Intro to Space Curves
1.5.2 Directed Lines
1.5.3 Circles
1.5.4 Projections onto Coordinate Planes
1.6 The Frenet Frame
1.6.1 The Osculating Circle for Space Curves
1.6.2 Acceleration
1.6.3 The Binormal Vector
1.6.4 Torsion
Next
1.1.1 Introduction to parameterized curves
New Resources
Conformal mapping: Visualization
The Cosine Formula - Proof Without Words
Free fall
Cobb-Douglas Production Function
Untitled
Discover Resources
Conic Form of Vertical parabola
Poli_Reg_Cfr_Circoscr
Solution to Parallel Lines & Angles Problem
Vertical Angle Exploration
Gamma Command
Simplifying Radicals (I)
Discover Topics
Random Experiments
Indefinite Integral
Numbers
Hypothesis Testing
Intersection
