Unit 0: Intro to Calculus

Intro

Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

Calculus has two major branches:

Differential calculus deals with instantaneous rates of change and the slopes of curves.

Integral calculus deals with accumulation of quantities and areas under or between curves.

These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit.

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.

Intro

As you probably know, geometry is the study of shapes and algebra is the study of relationships. 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:

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.

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