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Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
Eigenvalues and eigenvectors. In linear algebra, it is often important to know which vectors have their directions unchanged by a given linear transformation. An eigenvector ( / ˈaɪɡən -/ EYE-gən-) or characteristic vector is such a vector. Thus an eigenvector of a linear transformation is scaled by a constant factor when the linear ...
Integral equations as a generalization of eigenvalue equations. Certain homogeneous linear integral equations can be viewed as the continuum limit of eigenvalue equations. Using index notation, an eigenvalue equation can be written as. where M = [Mi,j] is a matrix, v is one of its eigenvectors, and λ is the associated eigenvalue.
Lotka–Volterra equations. The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear [disambiguation needed] differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.
Engineering Equation Solver (EES) is a commercial software package used for solution of systems of simultaneous non-linear equations. It provides many useful specialized functions and equations for the solution of thermodynamics and heat transfer problems, making it a useful and widely used program for mechanical engineers working in these ...
Broyden's method. In numerical analysis, Broyden's method is a quasi-Newton method for finding roots in k variables. It was originally described by C. G. Broyden in 1965. [1] Newton's method for solving f(x) = 0 uses the Jacobian matrix, J, at every iteration. However, computing this Jacobian is a difficult and expensive operation.
Quadratically constrained quadratic program. In mathematical optimization, a quadratically constrained quadratic program ( QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions. It has the form. where P0, ..., Pm are n -by- n matrices and x ∈ Rn is the optimization variable.
An autonomous system is a system of ordinary differential equations of the form. where x takes values in n -dimensional Euclidean space; t is often interpreted as time. It is distinguished from systems of differential equations of the form. in which the law governing the evolution of the system does not depend solely on the system's current ...