Introductory Electrical Engineering With Math Explained in Accessible Language

2Infinitesimal Calculus: A Brief Introduction

2.1 Introduction

In this chapter we will do a brief introduction to infinitesimal calculus or differential and integral, known as simply, calculus.

Wikipedia has as good definition about calculus:

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.

It has two major branches, differential calculus (concerning instantaneous rates of change and slopes of curves) and 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 convergence of infinite sequences and infinite series to a well‐defined limit.

Generally, modern calculus is considered to have been developed, independently, in the 17^th century by Isaac Newton and Gottfried Wilhelm Leibniz.

Today, Calculus has widespread uses in science, engineering, and economics.

Calculus is a part of modern mathematics education.

2.2 The Concept Behind Calculus

Suppose we have a car traveling in a straight line for 1 h, at a constant speed of 100 km/h, and later reducing the speed in half and traveling for another hour. What is the average speed of that car?

The answer is

Now let us see a ...