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Lecture
Intersection between Sphere and Cone
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Sphere, Cone, and Paraboloid
Explores the intersection of a sphere, cone, and paraboloid in 3D space.
Center of Gravity and Variable Change
Discusses center of gravity, variable change, spherical coordinates, and bijectivity in mathematical analysis.
Circular motion: Concepts and Calculations
Explores circular motion concepts, centripetal force, velocity, and acceleration in different coordinate systems, with a focus on auto racing and Formula 1 tire physics.
Dandelin Theorem: Ellipse Construction
Explores ellipse construction using the Dandelin theorem and properties of conics in space.
Multiple Integration: Spherical Coordinates
Explains multiple integration using spherical coordinates to calculate volumes of spheres and ellipsoids.
Surface of Revolution
Explains the parametric equations of surfaces of revolution generated by curves in space.
Perspective of a Sphere & a Circle
Explores conical sections, plane curves, and the perspective of a sphere and a circle.
Graph Surfaces and Sphere in Spherical Coordinates
Covers graph surfaces with an example of a surface defined by a parametric equation.
Circular motion: Friction and Newton's Laws
Explores circular motion, friction, and Newton's laws in various coordinate systems.
Ball Rolling on Hemisphere
Analyzes the motion of a ball on a hemisphere surface with forces and equations of motion.