Numerical mathematics | Wikipedia audio article
Channel: wikipedia tts
Date: 19/01/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Numerical_analysis


00:02:24 1 General introduction
00:03:52 1.1 History
00:05:36 1.2 Direct and iterative methods
00:07:23 1.2.1 Discretization and numerical integration
00:07:59 1.3 Discretization
00:08:20 2 Generation and propagation of errors
00:08:39 2.1 Round-off
00:10:51 2.2 Truncation and discretization error
00:12:16 2.3 Numerical stability and well-posed problems
00:12:45 3 Areas of study
00:13:19 3.1 Computing values of functions
00:19:03 3.2 Interpolation, extrapolation, and regression
00:19:19 3.3 Solving equations and systems of equations
00:19:57 3.4 Solving eigenvalue or singular value problems
00:20:47 3.5 Optimization
00:22:43 3.6 Evaluating integrals
00:23:14 3.7 Differential equations
00:24:03 4 Software
00:24:56 5 See also
00:25:45 6 Notes
00:27:11 7 References



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SUMMARY
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Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business and even the arts have adopted elements of scientific computations. As an aspect of mathematics and computer science that generates, analyzes, and implements algorithms, the growth in power and the revolution in computing has raised the use of realistic mathematical models in science and engineering, and complex numerical analysis is required to provide solutions to these more involved models of the world. Ordinary differential equations appear in celestial mechanics (planets, stars and galaxies); numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.
Before the advent of modern computers, numerical methods often depended on hand interpolation in large printed tables. Since the mid 20th century, computers calculate the required functions instead. These same interpolation formulas nevertheless continue to be used as part of the software algorithms for solving differential equations.
One of the earliest mathematical writings is a Babylonian tablet from the Yale Babylonian Collection (YBC 7289), which gives a sexagesimal numerical approximation of the square root of 2, the length of the diagonal in a unit square. Being able to compute the sides of a triangle (and hence, being able to compute square roots) is extremely important, for instance, in astronomy, carpentry and construction.Numerical analysis continues this long tradition of practical mathematical calculations. Much like the Babylonian approximation of the square root of 2, modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors.