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

In this video I prove the main properties of vector function limits, namely the addition, constant multiplication, as well as the dot and cross products of their limits. YouTube - Summary - Notes - Playlist

In this video I prove the main properties of vector function limits, namely the addition, constant multiplication, as well as the dot and cross products of their limits. These properties are identical

In this video I go over the precise definition of a vector function limit and prove it in 2 different ways. The 1st solution involves assuming the vector exists, and then using the basic definition of

In this video I show that space curves can be used to model charged particle motion in orthogonally oriented electric and magnetic fields. Depending on the speed and position of a charged particle, the

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. YouTube - Summary -

In this video I go over an example on determining the vector function of the curve of intersection between a vertical cylinder and a slanted plane. I first find an equation of the intersection by plugging

In this video I go over an example on determining the vector function of the curve of intersection between a vertical cylinder and a slanted plane. YouTube - Summary - Notes - Playlist - Vector Functions

In this video I go over an example in obtaining the vector and parametric equations of a line segment between two given points. I first recap on the vector equation of a line segment, which involves a

In this video I go over an example in obtaining the vector and parametric equations of a line segment between two given points. I first recap on the vector equation of a line segment, which involves a

In this video I go over the definition of the limit of a vector function, which involves taking the limit of each of its component functions. If the limit exists, then so does the limit of each component

In this video I go over the definition of the limit of a vector function, which involves taking the limit of each of its component functions. If the limit exists, then so does the limit of each component

In this video I introduce vector functions and show how they differ from the real-value functions that we are used to. Vector functions have domain of real numbers and a range of vectors. Compare this

In this video I introduce vector functions and show how they differ from the real-value functions that we are used to. Vector functions have domain of real numbers and a range of vectors. Compare this

In this video I deep dive nearly 5 hours into vector functions and space curves. A vector function has a domain (or input) of real numbers and a range (or outputs) of vectors. Compare this with the real-valued

“Collinearity of vectors is the silent language of geometry, where lines speak in unison and points align wit....

*Komplexe Datentypen Vektoren Diese könnte man als die erweiterte Version von Arrays bezeichnen. Ein bisschen analog zu &str und Strings. Vielleicht stellt sich jemand die Frage, warum man dann nicht

In this video I show that if the dot or cross products are zero then neither vector has to be zero, but if BOTH the dot and cross products are zero then at least one of the vectors has to be zero. - notes

In this video I show that if the dot or cross products are zero then neither vector has to be zero, but if BOTH the dot and cross products are zero then at least one of the vectors has to be zero. If the

In this video I show that a formula has different meanings when plotted in 2D vs 3D, such as the equation of a circle in 2D which becomes a circular cylinder in 3D. - notes - playlist