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Lecture
Parametrized Curves in 2D: Examples and Properties
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Parametrized Curves in 2D
Covers the concept of parametrized curves in 2D and their properties.
Regular Curves and Constant Speed
Covers regular curves and constant speed, with examples of circles and helices.
Real Functions: Definitions and Properties
Explores real functions, covering parity, periodicity, and polynomial functions.
Curvature and Osculating Circle
Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.
Functions and Periodicity
Covers functions, including even and odd functions, periodicity, and function operations.
Surface of Revolution
Explains the parametric equations of surfaces of revolution generated by curves in space.
Functions Composition: Continuity & Elements
Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.
Derivatives and Functions: Definitions and Interpretations
Covers the definition of derivative functions and their interpretation, focusing on differentiability, velocity, and curve lengths.
Arc Length Approximation
Explores arc length calculation for curves and polygons inscribed in circles using trigonometry and parametric equations.
Symmetries of Trigonometric Functions
Explores the symmetries of trigonometric functions, periodicity, and properties of even and odd functions.