Concepts inAccurate numerical derivatives in MATLAB
MATLAB
MATLAB (matrix laboratory) is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, and Fortran.
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Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). One of the earliest mathematical writings is a Babylonian tablet from the Yale Babylonian Collection(YBC 7289), which gives a sexagesimal numerical approximation of, the length of the diagonal in a unit square.
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Array data structure
In computer science, an array data structure or simply array is a data structure consisting of a collection of elements, each identified by at least one array index or key. An array is stored so that the position of each element can be computed from its index tuple by a mathematical formula.
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Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity.
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Implementation
Implementation is the realization of an application, or execution of a plan, idea, model, design, specification, standard, algorithm, or policy.
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Object-oriented programming
Object-oriented programming (OOP) is a programming paradigm using "objects" â data structures consisting of data fields and methods together with their interactions â to design applications and computer programs. Programming techniques may include features such as data abstraction, encapsulation, messaging, modularity, polymorphism, and inheritance. Many modern programming languages now support OOP, at least as an option.
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector- or scalar-valued function with respect to another vector. Suppose FÂ : R â R is a function from Euclidean n-space to Euclidean m-space. Such a function is given by m real-valued component functions, F1(x1,... ,xn), ... , Fm(x1,... ,xn).
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Complex number
A complex number is a number which can be put in the form a + bi, where a and b are real numbers and i is called the imaginary unit, where . In this expression, a is called the real part and b the imaginary part of the complex number. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number can be identified with the point (a, b).
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