applied mathematics

Written by

The Information Architects of Encyclopaedia Britannica

Last updated

June 18, 2026

Quick Summary

Applied mathematics is a branch of mathematics that focuses on the tools and techniques used in physics and engineering. It emphasizes areas such as vector spaces, matrix algebra, differential and integral equations, and complex variables. This field is crucial for solving problems that arise in various scientific disciplines, including electromagnetism, classical mechanics, and quantum mechanics.1

Numerical analysis, a related area, combines mathematics and computer science to create and analyze algorithms for finding numerical solutions to problems with continuous variables. This is essential for solving complex mathematical models used in science and engineering, especially with the advent of powerful digital computers. Numerical analysis is concerned with the accuracy, stability, and efficiency of these computational methods, and it plays a vital role in fields like computer-aided engineering and atmospheric modeling. Analysis, in general, deals with continuous change, limits, differentiation, and integration, with applications extending to sciences, finance, economics, and sociology.23

Summary created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

3 Britannica Sources

Ask Britannica AI about this topic

Britannica doesn't have a full article on this topic, so we've curated a list of our relevant coverage.

economics
Postwar developments
First of all, mathematics came to permeate virtually every branch of the field. As economists moved from a limited use of differential and integral calculus, matrix algebra represented an attempt to add a quantitative dimension to a general equilibrium model of the economy. Matrix algebra was also associated…
Read More
First of all, mathematics came to permeate virtually every branch of the field. As economists moved from a limited use of differential and integral calculus, matrix algebra represented an attempt to add a quantitative dimension to a general equilibrium model of the economy. Matrix algebra was also associated…
Read More

John von Neumann
Later years and assessment
” Von Neumann’s shift to applied mathematics after the midpoint of his career mystified colleagues, who felt that a genius of his calibre should concern himself with “pure” mathematics. In an essay written for James Newman’s The World of Mathematics (1956), von Neumann made an eloquent defense of applied mathematics.…
Read More
” Von Neumann’s shift to applied mathematics after the midpoint of his career mystified colleagues, who felt that a genius of his calibre should concern himself with “pure” mathematics. In an essay written for James Newman’s The World of Mathematics (1956), von Neumann made an eloquent defense of applied mathematics.…
Read More