How would you like to follow in the footsteps of Euclid and Archimedes? Would you like to be able to determine precisely how fast Usain Bolt is accelerating exactly 2 seconds after the starting gun? Differential calculus deals with the study of the rates at which quantities change. It is one of the two principle areas of calculus. The fathers of modern calculus, Isaac Newton and Gottfried Leibniz, independently formulated the fundamental theorem of calculus relating differentiation and integration. Differential calculus and integral calculus are connected by the fundamental theorem of calculus, which states that differentiation is the reverse process to integration.
Limit introduction, squeeze theorem, and epsilon-delta definition of limits
Calculating derivatives. Power rule. Product and quotient rules. Chain Rule. Implicit differentiation. Derivatives of common functions.
Minima, maxima, and critical points. Rates of change. Optimization. L'Hopital's rule. Mean value theorem.