Shareable link to the document (has all of the mathematical examples that will be discussed in both this episode and the following episode):

https://docs.google.com/document/d/1VfEVBscCPTfoyTDyv4ZRFJYL9Luzyd1UHvjxzz-uwpg/edit?usp=sharing

References:

Derivative - Wikipedia

https://en.wikipedia.org/wiki/Derivative

Power Rule - Wikipedia

https://en.wikipedia.org/wiki/Power_rule

All derivative calculations were checked using this website

https://www.derivative-calculator.net/

Product Rule - Wikipedia

https://en.wikipedia.org/wiki/Product_rule

Quotient Rule - Wikipedia

https://en.wikipedia.org/wiki/Quotient_rule

Chain Rule - Wikipedia

https://en.wikipedia.org/wiki/Chain_rule

Integral - Wikipedia

https://en.wikipedia.org/wiki/Integral

Line Integral (AKA a Contour Integral in Complex Analysis) - Wikipedia

https://en.wikipedia.org/wiki/Line_integral

All integral calculations were checked using this calculator (can also calculate derivatives, but I was not near the calculator when I was working on the derivative portion of the chapter):

https://www.amazon.com/Texas-Instruments-TI-84-Graphing-Calculator/dp/B00TFYYWQA

Reverse Power Rule - KhanAcademy

https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8a/e/intro-to-integration

Riemann Integral - Wikipedia

https://en.wikipedia.org/wiki/Riemann_integral

Fundamental Theorem(s) of Calculus - Wikipedia

https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus

Differential Equation - Wikipedia

https://en.wikipedia.org/wiki/Differential_equation

Partial Differential Equation - Wikipedia

https://en.wikipedia.org/wiki/Partial_differential_equation