There is a way to solve a problem using calculus. Getting an exact solution is impractical though, because it requires a long time, or many resources. An example for this is calculating power series.
One of the earliest known uses of numerical analysis is a Babylonianclaytablet, which approximates the squareroot of 2. In a unit square, the diagonal has this length. Being able to compute the sides of a triangle is extremely important, for instance, in carpentry and construction.[6]
Numerical analysis continues this long tradition of practical mathematical calculations. Much like the Babylonian approximation of , 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.
Computers greatly helped this task. Before there were computers, numerical methods often depended on hand interpolation in large printed tables. Since the mid 20th century, computers calculate the required functions instead.[18] These same interpolation formulas nevertheless continue to be used as part of the software algorithms for solving differential equations.[19][20][21]
In order to support numerical analysts, many kinds of numerical software has been created:
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M. Nakao, M. Plum, Y. Watanabe (2019) Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations (Springer Series in Computational Mathematics).
Barnes, B., & Fulford, G. R. (2011). Mathematical modelling with case studies: a differential equations approach using Maple and MATLAB. Chapman and Hall/CRC.
Zimmermann, P., Casamayou, A., Cohen, N., Connan, G., Dumont, T., Fousse, L., ... & Thiéry, N. M. (2018). Computational mathematics with SageMath. Society for Industrial and Applied Mathematics.
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