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Contenuti
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
Autore:
Sarah Harrelson
Argomento:
Vettori 2D (Due dimensioni)
,
Vettori 3D (tridimensionali)
,
Analisi
,
Curve parametriche
,
Vettori
Unit 1 of a high school Multivariable Calculus Class for LASA High School:
https://www.lasahighschool.org/
Sommario
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
Successivo
1.1.1 Introduction to parameterized curves
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