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

Exercise 2: Properties of Vector Function Limits https://youtu.be/y5e8Xhdt39Q 

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.

#math #vectorfunctions #limits #science #calculus

Example 5: Vector and Parametric Equations of a Line Segment https://youtu.be/dSIfPYi3q4U

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 parameter t between 0 and 1.

#math #vectorfunctions #geogebra  #science #calculus

Limit of a Vector Function https://youtu.be/z48K6YRJ3Jc

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 function.

#math  #limits #vectorfunctions #education #calculus

Introduction to Vector Functions https://youtu.be/Qi2hVnKN-5c

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 with real-valued functions which have both domain and range being single values, aka numbers.

#math #science #vectorfunctions #education #calculus

Vector Functions and Space Curves https://youtu.be/Qi2hVnKN-5c

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 functions that we are used to, which have inputs of real numbers (typically x) and the outputs are also real numbers (typically y = f(x)).

#math #science #education #vectorfunctions #calculus