CALCULUS

Calculus

Definition Of Calculus

Calculus is the branch of mathematics that studies continuously changing quantities.
Calculus deals with limits, differentiation, and integration of functions of one or more variables.
Calculus is a method of analysis or calculation using a special symbolic notation for limits, differentiation, and integration.
Calculus is the combined mathematics of differential calculus and integral calculus.

Video Examples:What is Calculus?

Related terms for Calculus

Variables
Limits
Differentiation
Integration
Differential Calculus
Integral Calculus
Derivatives
Integrals
Functions
Differential Equation
Continuity
Argument of a Function
Maxima and Minima

Quick Summary

Calculus studies rates of change and accumulation.
It is divided into differential and integral calculus.
It uses limits to define derivatives and integrals.

\[ \frac{dy}{dx} = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \]

🍎 Teacher Insights

Emphasize the connection between the geometric interpretation of derivatives and integrals. Use visual aids and real-world examples to illustrate the concepts.

🎓 Prerequisites

Algebra
Trigonometry
Analytic Geometry
Precalculus

Check Your Knowledge

Q1: What is the derivative of x^2?

x 2x x^3 1

Q2: What is the integral of 1?

0 x x^2 C

Frequently Asked Questions

Q: What is the difference between differential and integral calculus?
A: Differential calculus deals with rates of change and slopes of curves, while integral calculus deals with accumulation of quantities and areas under curves.

Q: Why is calculus important?
A: Calculus is fundamental to many areas of science, engineering, and economics, providing tools for modeling and solving problems involving change and optimization.