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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
အခြေခံ data အခေါ်အဝေါ်များ
Marion's Theorem
Dilation + Rotation of Pentagons
Translation in 3D (via x, y, z)
bewijs stelling van Pythagoras
Discover Resources
CCGPS AG 1.2.2 Example 2
PMC 2008-09 Q12
Untitled
breakaxe
utilisation de geogebra: exercise 2
mirka_sophia
Discover Topics
Correlation
Functions
Similarity Transformation or Similarity
Median Line
Integral Calculus
