György Bicsák, Dávid Sziroczák, Aaron Latty

Numerical methods


Anti-differentiation

When only the first derivative of a given function is known, in order to get the function itself, the opposite of the differentiation has to be carried out, which is the so-called anti-differentiation. We could be suspicious, since it is really sounds like the integration, and it actually is, but from a different point of view. Our goal is to carry out an integration process without the general integration rules, and relying only on the difference-calculation. Going back to equation (4.29.), the anti-differentiation can be given in the following general form:

Numerical methods

Tartalomjegyzék


Kiadó: Akadémiai Kiadó

Online megjelenés éve: 2019

ISBN: 978 963 454 283 4

This book on Numerical Methods is part of the Transportation and Vehicle Engineering Faculty’s curriculum at the Budapest University of Technology and Economics, created under the Stipendium Hungaricum Scholarship Programme. The book demonstrates the aim of developing and using numerical methods. Instead of relying on more complicated and expensive analytical solution methods, simpler arithmetical equations are used to approximate the accurate solution with the required level of accuracy. After discussing the various sources and propagation of solution errors, the book discusses the solution of single variable equations and system of equations. Following chapters describe the two main curve fitting methods; approximation and interpolation. These chapters are followed by the numerical differentiation and integration methods, then finally the numerical solutions for ordinary and partial differentiation equations are outlined. MATLAB is one of the most popular choice today for numerical computing, with its user friendly, yet powerful computing capability. It is practically an industry standard for prototyping and new developments, and there is great value for students to be introduced to solving problems with MATLAB. Many chapters in the notes show examples implemented in MATLAB, with actual working code available to use and practice.

Hivatkozás: https://mersz.hu/bicsak-numerical-methods//

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