Motion in Space: Velocity and Acceleration https://3speak.tv/watch?v=mes/e443f9d3 & https://youtu.be/c9wE-BMvaY4

In this video, I go over further into vector functions, and this time look at motion in space in terms of the velocity, acceleration, and position of objects moving in 2D or 3D space. Using the fact that the rate of change of the position of an object is the velocity, and likewise that the rate of change of velocity is the acceleration, I show we can write the velocity and acceleration of an object just in terms of the derivatives of the position vector. Likewise, going backwards via vector integrals, we can obtain the velocity from the acceleration vector, and the position from the velocity vector.

#math #vectors #calculus #space #physics

Vector Functions: Arc Length and Curvature https://youtu.be/i9ForOVH5Bk

In this video, I go over further into vector functions and this time do a deep dive into the arc length and curvature of a space curve. I also go over normal, binormal vectors, as well as the TNB frame, normal & osculating planes, and much more, so buckle up!

#math #vectors #calculus #arclength #curvature

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