Step By Step Calculus » 1.1 - Introduction

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Introduction
Welcome
Hello, and welcome to MuchLearning’s Calculus Courses!
Calculus is used in virtually all areas of Science, Engineering, and Business. Understanding calculus gives insight into the world around us from Zeno’s paradox (you can never travel from point A to B because you will have to first travel half that distance, and half the distance of the half and so on), to finding the area or volume of an object to how objects heat and cool down, to the change in stock prices over time. Calculus is fundamental in describing problems involving infinitesimal quantities, infinite sums, and instantaneous behaviour (e.g. velocity from distance). With well known contributors such as Archimedes, Fermat, Descartes and Newton to other great mathematicians such as Leibniz, Bernoulli and Cauchy, calculus has paved the road to our understanding of finance, networks, electrical circuits, chemical reactions, physics, geometry, numbers as well as analysis and is still an active area of research today.
Course Material
The goal of this series of courses is to build a foundation and understanding of calculus and to provide the fundamental tools for using calculus in the fields of Applied Mathematics, Engineering, Sciences and Mathematical Finance. This series of courses begins with a review of numbers, sets, and trigonometry then introduces induction and takes a formal look at functions. We use this knowledge from the earlier chapters to understand the theory of limits, which is the foundation of calculus. We continue with differentiation and some of its applications, followed by integration and its applications. Finally we take a look at how everything works with functions of two variables and polar co-ordinates.
This series is neither meant to be elementary nor all-encompassing. Naturally, the amount of effort required for this course depends upon your background and experience. If the going gets tough, don’t despair - we have many tools to keep you on track!
Good luck - we hope you enjoy calculus as much as we do!