GeoGebra
GeoGebra
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
Cube of a Binomial - Volume Model
Thin Slice: Using Trig Ratios to Solve for R.Triangle Sides
How to Assign Color Objects Inside the List? II
Oriented Angles and the Unit Circle
Binomial Coefficient and Symmetry
Discover Resources
Modeling with Quadratics
Reeve Test 1
Quadrado
Volume (3D)
Comparing Apples and Oranges with Ratios
Discover Topics
Stochastic Process or Random Process
Fractal Geometry
Line Segment
Isosceles Triangles
Confidence Interval