Unit 0: Intro to Calculus

Intro

As you probably know, geometry is the study of shapes and algebra is the study of relationships and generalizations of arithmetic operations.

So, what is calculus all about?

Calculus is the mathematical study of change. In fact, it is all about infinitesimally small change.

Calculus has two major branches:

• Differential calculus (concerning instantaneous rates of change and slopes of curves)

• Integral calculus (concerning accumulation of quantities and the areas under and between curves)

These two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of limits which is basically what separates algebra from calculus. Further calculus courses focus on convergence of infinite sequences and infinite series.

Calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Calculus has widespread uses in science, engineering, and economics.

Today, calculus has widespread uses in science, engineering and economics and can help solve many problems that elementary algebra alone cannot.