Overview
This course covers the proofs of essential differentiation rules such as the product rule, quotient rule, and chain rule. Students will also learn about the applications of differentiation through the Mean Value Theorem, Rolle's Theorem, and L'Hôpital's Rule. The course emphasizes understanding the theoretical foundations of calculus and applying them to solve problems without relying on L'Hôpital's Rule. The intended audience for this course is individuals seeking a deeper understanding of calculus and differentiation techniques.
Syllabus
Proof of the product rule.
Quotient Rule Proof.
Proof of the Chain Rule.
Rolle’s Theorem Proof.
Mean Value Theorem Proof.
The Mean Value Theorem and Fixed Points.
Hopital rule proof.
lim sin(x)/x = 1 as x goes to 0.
Banach Fixed Point Theorem.
Nice L'Hôpital Problem.
Hopital Counterexample.
COOL Quotient Rule Proof.
Exponential Properties.
Don't use L’Hopital.
Taught by
Dr Peyam