What Is Calculus? A Beginner’s Guide to Limits and Differentiation

The first part in a two part introductory guide to calculus.

© Eugene Brennan

Calculus is a study of rates of change of functions and accumulation of infinitesimally small quantities. It can be broadly divided into two branches:

• Differential Calculus. This concerns rates of changes of quantities and slopes of curves or surfaces in 2D or multidimensional space.
• Integral Calculus. This involves summing infinitesimally small quantities.

What’s Covered in this Tutorial

In this first part of a two-part tutorial you will learn about:

• Limits of a function
• How the derivative of a function is derived
• Rules of differentiation
• Derivatives of common functions
• What the derivative of a function means
• Working out derivatives from first principles
• 2nd and higher-order derivatives
• Applications of differential calculus
• Worked examples

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