Definition of Derivative for Vector Functions https://youtu.be/LAXaiYA5p1k

In this video I go over the definition of derivative for a vector function, which is very similar to the definition for real valued functions. The derivative of a vector function is defined as the limit as h approaches zero of the secant vector (difference of two vectors separated by incrementing the parameter t by h) divided h. As h approaches zero the secant vector approaches a vector that is parallel to the tangent vector to the curve.

#math #science #calculus #vectorfunctions #geogebra

Exercise 3: Manually Graphing the Projection of the Trefoil Knot onto the xy-Plane https://youtu.be/2_Zp2N35lYQ

In this video I manually (and painstakingly) plot an approximation of the projection of the 3D trefoil knot onto the xy-plane. I also plot the trefoil knot in 3D using the amazing GeoGebra graphing calculator as well as the new Desmos' graphing calculator. 

#math #trefoilknot #geogebra #desmos #calculus

Example 7: Using Computers (GeoGebra) to Draw Space Curves https://youtu.be/aBuDScugCXA

In this video I graph out several complicated space curves using GeoGebra's amazing 3D graphing calculator. These curves are the toroidal spiral, trefoil knot, and a twisted cubic.

#math #3D #spacecurves #GeoGebra #calculator

Problems Plus 6: Largest Sphere in a Sphere https://youtu.be/uefSE-rXFw4

In this video I find the largest sphere that passes through a given point while every point inside is also inside a larger sphere.

A Hyperbolic Paraboloid Can Be Generated by Straight lines https://youtu.be/-nxmXc1GD-U

In this video I show that a hyperbolic paraboloid can be generated entirely by two sets of lines, thus classifying it as a Ruled Surface. The only quadric surfaces that are ruled surfaces are cylinders, cones, and hyperboloids of one sheet.

Applications of Quadric Surfaces: Telescopes, Car Headlights, Microphones, Nuclear Power Plants https://youtu.be/ceWkMHHr5gw

In this video I go over a quick overview of some of the many applications of quadric surfaces.