Detailed Proofs# Here we list more detailed proofs of theorems and lemmas that are not included in the main text. Cauchy-Schwarz Inequality Bolzano-Weierstrass Theorem Extreme Value Theorem Rolle's Theorem Mean Value Theorem Chain Rule for Scalar-Scalar Functions Squeeze Theorem First Fundamental Theorem of Calculus Second Fundamental Theorem of Calculus Clairaut's Theorem
