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Calculus

Calculus
History[edit] Modern calculus was developed in 17th century Europe by Isaac Newton and Gottfried Wilhelm Leibniz (see the Leibniz–Newton calculus controversy), but elements of it have appeared in ancient Greece, China, medieval Europe, India, and the Middle East. Ancient[edit] The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. Medieval[edit] Modern[edit] In Europe, the foundational work was a treatise due to Bonaventura Cavalieri, who argued that volumes and areas should be computed as the sums of the volumes and areas of infinitesimally thin cross-sections. These ideas were arranged into a true calculus of infinitesimals by Gottfried Wilhelm Leibniz, who was originally accused of plagiarism by Newton.[13] He is now regarded as an independent inventor of and contributor to calculus. Leibniz and Newton are usually both credited with the invention of calculus. Foundations[edit]

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Related:  System Theory

Dynamical system The Lorenz attractor arises in the study of the Lorenz Oscillator, a dynamical system. Overview[edit] Before the advent of computers, finding an orbit required sophisticated mathematical techniques and could be accomplished only for a small class of dynamical systems. Quadratic function A quadratic function, in mathematics, is a polynomial function of the form The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis. The expression ax2 + bx + c in the definition of a quadratic function is a polynomial of degree 2, or a 2nd degree polynomial, because the highest exponent of x is 2. This expression is also called a quadratic polynomial or quadratic.

Calculus - Integration Introduction Integration is a major parts of calculus. It is an extension of the concept of summation. In fact the integration symbol derrivesfrom an elongated letter S, first used by Leibniz, to stand for Summa meaning sum in Latin.

Feedback "...'feedback' exists between two parts when each affects the other."[1](p53, §4/11) Algebra "Algebraist" redirects here. For the novel by Iain M. Banks, see The Algebraist. Even more maths Functions Limits Differentiation Differentiation Max and Min Profit, Cost, and Revenue Linear Programming Integration I will try to add on more each week, so keep looking at this space.If you find a mistake, please tell me. I may give you a surprise. Integration State-space representation In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. "State space" refers to the space whose axes are the state variables. The state of the system can be represented as a vector within that space. To abstract from the number of inputs, outputs and states, these variables are expressed as vectors. Additionally, if the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.[1][2] The state-space representation (also known as the "time-domain approach") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With

Group (mathematics) Groups share a fundamental kinship with the notion of symmetry. For example, a symmetry group encodes symmetry features of a geometrical object: the group consists of the set of transformations that leave the object unchanged and the operation of combining two such transformations by performing one after the other. Lie groups are the symmetry groups used in the Standard Model of particle physics; Point groups are used to help understand symmetry phenomena in molecular chemistry; and Poincaré groups can express the physical symmetry underlying special relativity.

Indefinite Integral An integral of the form i.e., without upper and lower limits, also called an antiderivative. The first fundamental theorem of calculus allows definite integrals to be computed in terms of indefinite integrals. In particular, this theorem states that if Conceptual model A conceptual model is a model made of the composition of concepts, which are used to help people know, understand, or simulate a subject the model represents. Some models are physical objects; for example, a toy model which may be assembled, and may be made to work like the object it represents. The term conceptual model may be used to refer to models which are formed after a conceptualization (generalization)[1] process in the mind.

Modular arithmetic Time-keeping on this clock uses arithmetic modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00.

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