Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics, numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology.
The TI-89 and the TI-89 Titanium are graphing calculators developed by Texas Instruments (TI). They are differentiated from most other TI graphing calculators by their computer algebra system, which allows symbolic manipulation of algebraic expressions—equations can be solved in terms of variables, whereas the TI-83/84 series can only give a numeric result.
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.
Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language. It covers several areas of technical computing, such as symbolic mathematics, numerical analysis, data processing, visualization, and others. A toolbox, MapleSim, adds functionality for multidomain physical modeling and code generation.
Macsyma is one of the oldest general-purpose computer algebra systems still in wide use. It was originally developed from 1968 to 1982 at MIT's Project MAC.
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.
In mathematics, an expression is in closed form if it is formed with constants, variables and a finite set of basic functions connected by arithmetic operations and function composition. Commonly, the allowed functions are nth root, exponential function, logarithm, and trigonometric functions. However, the set of basic functions depends on the context.
TK Solver is a mathematical modeling and problem solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc.
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).
Mathcad is computer software for the verification, validation, documentation and re-use of mathematical calculations in engineering and science, notably mechanical, chemical, electrical, and civil engineering. Released in 1986 on DOS, it introduced live editing (WYSIWYG) of typeset mathematical notation in an interactive notebook, combined with automatic computations. It was originally developed by Mathsoft, and since 2006 has been a product of Parametric Technology Corporation.
Finite-difference time-domain (FDTD) or Yee's method is a numerical analysis technique used for modeling computational electrodynamics. Since it is a time-domain method, FDTD solutions can cover a wide frequency range with a single simulation run, and treat nonlinear material properties in a natural way.
Mathomatic is a free, portable, general-purpose computer algebra system (CAS) that can symbolically solve, simplify, combine, and compare algebraic equations, and can perform complex number, modular, and polynomial arithmetic, along with standard arithmetic. It does some symbolic calculus (derivative, extrema, Taylor series, and polynomial integration and Laplace transforms), numerical integration, and handles all elementary algebra except logarithms. Trigonometric functions can be entered and manipulated using complex exponentials, with the GNU m4 preprocessor. Not currently implemented are general functions like f(x), arbitrary-precision and interval arithmetic, and matrices.
Computational electromagnetics (CEM), computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment.
Xcas is a user interface to Giac, which is an open source computer algebra system (CAS) for Windows, macOS and Linux among many other platforms. Xcas is written in C++. Giac can be used directly inside software written in C++.
Ch is a proprietary cross-platform C and C++ interpreter and scripting language environment. It was originally designed by Harry H. Cheng as a scripting language for beginners to learn mathematics, computing, numerical analysis, and programming in C/C++. Ch is now developed and marketed by SoftIntegration, Inc, with multiple versions available, including a freely available student edition and Ch Professional Edition for Raspberry Pi is free for non-commercial use.
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to more than one independent variable.
Symbolic regression (SR) is a type of regression analysis that searches the space of mathematical expressions to find the model that best fits a given dataset, both in terms of accuracy and simplicity.
