Animal Form and Function: Breathing https://youtu.be/EWnXld8l_u4

In this video I do an overview of how animals breathe via the respiratory system. Oxygen is absorbed from the air via millions of small air sacs called alveoli (atria in birds), and pumped to the heart as oxygen rich blood, which then gets pumped throughout the body.

#science #biology #breathing #animals #education

Exercise 4: Parametric Equations of a Trochoid https://youtu.be/AbC3V1M7Voo

In this video I derive the parametric equations of a trochoid, which is the shape obtained by tracing a point as a circle rotates. If the point traced is on the circle itself, then the shape is the famous cycloid.

#math #trochoid #cycloid #desmos #calculus

Jeane Manning 1996 Presentation: The Coming Energy Revolution https://youtu.be/i_8FKS3VC0E

In this video I have posted the 1996 presentation that Jeane Manning gave at the International Symposium on New Energy in Denver, Colorado. Jeane discusses several alternative energy researchers, and includes photos she took of John Hutchison's free energy crystal converter device. Jeane has also personally observed THE Hutchison Effect in 2007 while visiting John's Vancouver lab with Dr. Thorsten Ludwig. While the world continues to ignore that cheap, abundant, and clean energy exists, pioneers such as Jeane Manning, John Hutchison, and many others continue to shine the light on a better reality that is right around the corner...

#HutchisonEffect #technology #AntiGravity #FreeEnergy #science

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

Exercise 1: Precise Definition of a Vector Function Limit https://youtu.be/mVJ4wviwDs8

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 a vector function limit as well as the 3D distance formula, to prove the difference inequalities of the precise definition. The 2nd solution is the reverse: it involves assuming the precise definition difference inequalities and then working backwards to prove the vector function limit exists. Lastly, I show that the precise definition of a vector function limit in 3D can be visualized as a sphere which gets indefinitely smaller as the interval shrinks.

This is probably the only in-depth precise definition of limits for vector functions anywhere in the internet, so buckle up!

#math #vectorfunctions #limits #science #calculus