# ⓘ Mathematics - Dimension, mathematics an pheesics, Eccentricity, mathematics, EASIAM, Calculus, Sofia Kovalevskaya, Area, Complex analysis, INTLAB, Million, Pi ..

## Dimension (mathematics an pheesics)

In physics an mathematics, the dimension o a space or object is informally defined as the minimum nummer o coordinates needit tae specify ony pynt within it. Thus a line haes a dimension o ane acause anly ane coordinate is needit tae specify a pynt on it. A surface such as a plane or the surface o a cylinder or sphere haes a dimension o twa acause twa coordinates are needit tae specify a pynt on it. The inside o a cube, a cylinder or a sphere is three-dimensional acause three coordinates are needed tae locate a pynt within these spaces.

## Eccentricity (mathematics)

In mathematics, the eccentricity, denotit e or ε {\displaystyle \varepsilon }, is a parameter associated wi every conic section. It can be thoucht o as a measur o hou much the conic section deviates frae bein circular. In pairticular, The eccentricity o an ellipse which is nae a circle is greater nor zero but less nor 1. The eccentricity o a parabola is 1. The eccentricity o a hyperbola is greater nor 1. The eccentricity o a circle is zero. Furthermore, twa conic sections are seemilar if an anly if thay hae the same eccentricity.

## EASIAM

EASIAM is the eastern Asian branch o the US-basit Society for Industrial and Applied Mathematics.EASIAM is aimin tae advance studies o appleed mathematics i eastern Asia

## Calculus

Calculus is a mathematical or logical formal seestem. It wis cleckit in the 17t century bi Isaac Newton an Gottfried Wilhelm Leibniz an uises infineetesimal quantities for tae find the tangent o curves - differential calculus - for tae calculate lenths an areas o curved feegurs - integral calculus. Thir operations is inverses, frae the fundamental theorem o calculus. Introduction coorses in calculus for ordinar includes the study o logarithms, exponential functions an trigonometric functions Amang the important areas o calculus is: infineetesimal calculus - a brainch o mathematics includin ...

## Sofia Kovalevskaya

Sofia Vasilyevna Kovalevskaya, born Sofia Vasilyevna Korvin-Krukovskaya, wis a Roushie mathematician that made noteworthy contreibutions tae analysis, pairtial differential equations an mechanics.

## Area

Area is a pheesical meisur expressin the size o a pairt o a surface. The term can be uised in a nane-mathematical context for tae mean "naur haund" an aw. Surface area is the soum o the areas o the ooter sides o an object.

## Complex analysis

Complex analysis is the area o mathematical analysis thon looks at functions on the complex nummers. Cauchy is normally creditit wi foundin complex analysis, buildin on the work o Gauss an Leonhard Euler.

## International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics

International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics is an international conference aboot numerical analysis. It is held once i 2 years.

## INTLAB

INTLAB is an interval arithmetic library usin MATLAB. INTLAB wis usit tae develop other MATLAB-basit libraries such as VERSOFT an INTSOLVER, an it wis usit tae solve some problems i the Hundred-dollar, Hundred-digit Challenge problems".

## Million

Ae million, or ae thoosand thoosand, is the naitural nummer efter 999.999 an afore 1.000.001. In scienteefic notation, its written as 10 6. The million is whiles uised as a metaphor for a gey muckle nummer, as in "Neer in a million year", or a hyperbole, as in "Av walked a million mile". Hence, a "millionaire" can mean juist a rich bodie, nae maiter the actual siller or the exact quantity. Il Milione is the teetle o Marco Polos narration o his traivels tae Cheenae. The name is jaloused tae come frae Polos byname efter his tales o riches an multitudes. The wird "million" is common tae the d ...

## Ordinary differential equation

Chicone, C. 2006. Ordinary differential equations with applications. Springer Science & Business Media. Wolfgang Walter, Ordinary differential equations. Springer. Hermann, M., & Saravi, M. 2014. A First Course in Ordinary Differential Equations. Analytical and Numerical Methods, Springer India. Hartman, P. 2002. Ordinary differential equations, Classics in Applied Mathematics, Philadelphia: Society for Industrial and Applied Mathematics, ISBN 978-0-89871-510-1. Logemann, H., & Ryan, E. P. 2014. Ordinary differential equations: Analysis, qualitative theory and control. Springer. Teschl, G. ...

## Pi

Pi, kent as Ludolphs nummer or Archimedes constant an aw, is an irraitional nummer thats gey uissfu in mathematics an naitural philosophy. The seembol uised for it comes frae the 16t letter o the Greek ABC, π

## Validatit numerics

Validatit numerics is a numerical analysis wi mathematically strict error evaluation. I order tae dae sae, a technology callit interval arithmetic is usit. Validatit numerics is needit for the followin reasons. It is difficult tae avoid numerical errors i numerical computation, an computation without error evaluation may cause unfortunate results. It can be appliit tae computer-assistit proofs for mathematical problems such as pairtial differential equations. Ane o the most known implementation o validatit numerics is INTLAB Interval Laboratory. INTLAB wis usit tae create other numerical l ...

## Wolfram Mathematica

Today, Wolfram Mathematica is usit for the followin purposes: Numerical methods for ordinary differential equations Numerical linear algebra Computer science Numerical analysis Geometry Numerical methods for pairtial differential equations

## ⓘ Mathematics

• Mathematics is the studie o feck, structur, room, an chynge. Historically, Mathematics developed frae coontin, calculation, meisurement, an the studie
• Applee d mathematics is a branch o mathematics that concerns itself wi mathematical methods that are typically uised in science, ingineerin, business
• The Mathematics Genealogy Project is a web - basit database for the academic information o mathematicians includin scientists o stateestics, computer science
• Applied Mathematics SIAM is a perfaisional nonprofit organisation for applee d mathematics SIAM Review SIAM Journal on Applied Mathematics SIAM Journal
• In physics an mathematics the dimension o a space or object is informally defined as the minimum nummer o coordinates needit tae specify ony pynt within
• extensive knawledge o mathematics in his or her wirk such as Cauchy an Gauss teepically tae solve mathematical problems. Mathematics is concerned wi nummers
• In elementary mathematics a variable is an alphabetic character representin a nummer which is aither arbitrary or nae fully specified or unkent. Makin
• In mathematics a matrix plural: matrices is a rectangular array o nummers, seembols, or expressions, arranged in rowes an columns. Anton 1987, p. 23
• In mathematics a function is a relation atween a set o inputs an a set o permissible ootputs wi the property that ilka input is relatit tae exactly ane

## Appleed mathematics

Appleed mathematics is a branch o mathematics that concerns itself wi mathematical methods that are typically uised in science, ingineerin, business, an industry.

## Variable (mathematics)

In elementary mathematics, a variable is an alphabetic character representin a nummer which is aither arbitrary or nae fully specified or unkent. Makin algebraic computations wi variables as if thay wur explicit nummers allaes ane tae solve a range o problems in a single computation. A teepical ensaumple is the quadratic formula, which allaes tae solve every quadratic equation bi simply substitutin the numeric values o the coefficients o the gien equation tae the variables that represent them.

## Function (mathematics)

In mathematics, a function is a relation atween a set o inputs an a set o permissible ootputs wi the property that ilka input is relatit tae exactly ane ootput. An example is the function that relates ilka real nummer x tae its square x 2. The ootput o a function f correspondin tae an input x is denotit bi f. In this example, if the input is −3, then the ootput is 9, an we mey write f = 9. The input variable are sometimes referred tae as the argument o the function.

## Interval (mathematics)

In mathematics, a interval is a set o real nummers wi the property that ony nummer that lies atween twa nummers in the set is an aa includit in the set. For example, the set o aw nummers x satisfyin 0 ≤ x ≤ 1 is an interval which contains 0 an 1, as well as aw nummers atween them. Ither examples o intervals are the set o aw real nummers R {\displaystyle \mathbb {R} }, the set o aw negative real nummers, an the empty set.

## Imre Lakatos

Imre Lakatos wis a Hungarian philosopher o mathematics an science, kent for his thesis o the fallibility o mathematics an its methodology o pruifs an refutations in its pre-axiomatic stages o development, an aa for introducin the concept o the resairch programme in his methodology o scienteefic resairch programmes.

## Mathematical analysis

Mathematical analysis is a branch o mathematics that studies conteenous chynge an includes the theories o differentiation, integration, meisur, leemits, infinite series, an analytic functions.

## Hilary Putnam

Hilary Putnam wis a American filosofer, mathematicker an computer scientist that wis at the heid o the analytic filosofie fae the 60s on. In the filosofie o mathematics, he is maist kent fur the Quine–Putnam indispensability thesis, whaur he an W. V. Quine threaps that mathematical entities is real. In mathematics itsel, he is maist kent fur the Davis–Putnam algorithm, that he proponed wi Martin Davis, an fur reddin up Hilberts tent quirk.

## Smaa angle approximation

Smaw angle approximation is a wey o estimatin angles in radians, whaur the angle is smaw. Whan x is smaw, an in radians, the follaein formulae is true: sin ⁡ x ≃ x {\displaystyle \sin x\simeq x} cos ⁡ x ≃ 1 − x 2 {\displaystyle \cos x\simeq 1-{\frac {x^{2}}{2}}} tan ⁡ x ≃ x {\displaystyle \tan x\simeq x}