Numerical analysisNumerical analysis is the study of algorithms for the problems of continuous mathematics. These algorithms involve real or complex variables (in contrast to discrete mathematics), and typically use numerical approximation in addition to symbolic manipulation. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts.
Finite element methodNumerical method for solving physical or engineering problemsVisualization of how a car deforms in an asymmetrical crash using finite element analysis
Differential equationType of functional equation (mathematics) 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.
System of linear equationsIn mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. For example, {3x+2y−z=12x−2y+4z=−2−x+12y−z=0{\displaystyle {\begin{cases}3x+2y-z=1\\2x-2y+4z=-2\\-x+{\frac {1}{2}}y-z=0\end{cases}}} is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied.Nonlinear partial differential equationIn mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture.
Partial differential equationType of differential equation
DiscretizationIn applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers.
Finite differenceDiscrete analog of a derivative A finite difference is a mathematical expression of the form f(x + b) − f(x + a). Finite differences (or the associated difference quotients) are often used as approximations of derivatives, such as in numerical differentiation.
Linear algebraBranch of mathematicsLinear algebra is the branch of mathematics concerning linear equations such as a1x1+⋯+anxn=b,{\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b,}linear maps such as the following: (x1,…,xn)↦a1x1+⋯+anxn,{\displaystyle (x_{1},\ldots ,x_{n})\mapsto a_{1}x_{1}+\cdots +a_{n}x_{n},}and their representations in vector spaces and through matrices.
DerivativeInstantaneous rate of change (mathematics)The graph of a function, drawn in black, and a tangent line to that graph, drawn in red. The slope of the tangent line is equal to the derivative of the function at the marked point.The derivative at different points of a differentiable function. In this case, the derivative is equal to sin(x2)+2x2cos(x2){\displaystyle \sin \left(x^{2} ight)+2x^{2}\cos \left(x^{2} ight)}.
Ordinary differential equationIn mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions.
Matrix ringIn abstract algebra, a matrix ring is a set of matrices with entries in a ringR that form a ring under matrix addition and matrix multiplication. The set of all n × n matrices with entries in R is a matrix ring denoted Mn(R) (alternative notations: M(n, R), Matn(R) and R). Some sets of infinite matrices form infinite matrix rings. A subring of a matrix ring is again a matrix ring. Over a rng, one can form matrix rngs.*As an Amazon Associate I earn from qualifying purchases.