T
Tan :
Abbreviation of tangent.
Tangent
A line
that meets a smooth curve at a single point and does not cut across the curve.
ii) In Trigonometry, the tangent is function defined as tan x = sinx / cosx. In
a right angle triangle, the tangent of an angle θ is the ratio of the length of the sides opposite and adjacent
to the angle. Tan θ = Perpendicular / Base. Value of Tan
varies from 0 to infinity for the angles
from zero to 900
Tangent Line : The tangent line is represented a the limit of secant
line.
Tangent Plane : A Tangent plane is a plane that touches a surface defined
in 3dimensional coordinate system at a given point p. The normal vector of the
tangent plane is perpendicular to the surface at the point p. the surface
should be smooth near the surface at the
point p. the tangent plane contains all the lines tangent to a specific point
on a surface.
Tanh : Hyperbolic of tan.
Tautology : A statement
of proportional logic which can be inferred from any proposition whatsoever that is true because of its logical structure.
Taylor’s Series : According to Taylor’s series or theorem, a
polynomial f(x) can be expanded as
given below around a point ‘a’ valid for an integer n .
F(x) = f(a) + f’(a) 9 x –a) + f”(a) (x – a)2
/ 2! + f”’(a) (x – a)3 / 3! + ………+ fn(a) (x – a)n
/ n! + ……..
When a
= 0 , the series is called Maclaurin series .
Tensor : A set of quantities that obey certain
transformation laws relating the bases in one generalized coordinate system to
those of another and involving partial derivative sums . vectors are simple
tensors.
Tera : Symbol T. A prefix having meaning 1012.
Term : A mathematical expression of the form rxn,
pxnyr, where n,p,r are numbers and x and y are variable.
Terminating :To come to an end. E.g., 8.5 is a terminating
decimal, while 1.733333.. is non terminating decimal.
Terminating
continued fraction : A continuous fraction having finite
number of terms.
Terminating
decimal : A decimal that terminates is a
terminating decimal. All Terminating decimal are Rational numbers but not all rational numbers are terminating decimal
expression .
Terrestrial triangle : The Terrestrial triangle is formed on the earth
by the great circles connecting the pole and two palces on the earth.
Tessellation
: A Tessellation is a repeated
geometric design that covers a plane without gaps or overlaps.
Tetrahedron
: A polyhedron with four faces.
Tetromino
: A four-square polyomino.
THEOREM : A Theorem is a
statement which is stated in natural language and can be proved on the basis
explicitly states or precisely known confusions.
Theorem
of Parallel axis : The moment of inertia of any object about an axis through its
centre of mass is the minimum moment of inertia for an axis in that direction
in space. The moment of inertia about any axis parallel to the axis is given by
Ipa = Icm + Md2
Where Ipa
is moment of inertia of the body
about an axis passing through centre of mass, M is the body of mass and d is
the distance between the two axes.
Theoretical Probability : The
chances of events happening as determined by calculating results that would
occur under ideal circumstances.
Theory of Equations :
Theory of equations includes the study of equations, polynomials , algebraic expressions,
algebraic equations, separation of roots, approximation of roots and the
application of matrices and determinants for solving the equations etc.
Theory of Games : The
study of ways in which strategic interactions among rational players produce
outcomes with respect of the preferences of the players, none of which might
have been introduced by any one of them.
Theory of Indices :
Theory of indices describes the laws for multiplication and division of quantities
having same base as given below.
1.am an = am + n 2.
am /an = am - n 3.
(am )n = am n 4. (ab)n = an b n
5. (a/b)n
= an /b n
6. a0 =1 7. a-m =1/am 8.
am/n = 
m
Theory of Probability : A
theory of Probability is a way of understanding probability statements. A theory
of probability connects the mathematics of probability, which is the set of
consequences of axioms of probability, with real world of observation and experimentation.
Therm : A unit of energy
equal to 105.
Time series : Times
series analysis accounts for the fact that data points taken over time may have
an internal structure ( such as autocorrelation, correlation, trend or seasonal
variation ) that should be accounted for the value of the variable is generated
successively in time. A continuous graph trace is an example of continuous time
series.
Ton : 1. Long Ton – unit of weight
used in U.K., equal to 2240 lbs or 1016 kg. (2) short Ton ; unit of weight used in U.S.A., equal to 2000
pounds or 907.18 kg. (3) Metric Ton :
usually referred to as tone equal to 1000 kg.
Topological space : A
set with topology defined upon it is called a topological space .
Topology : Generally Topology is the study of those
proportions of space which are invariant under continuous deformations, that is
, deformations which do not create’tears’ or ‘holes’. More specifically, given
set X , a Topology on X is a collection of subsets of X, such that the empty
set and X itself are included in the collection, and such that the collection
is closed under the formation of finite intersection and arbitrary unions.
Torque : Symbol T, Torque
about an axis is the product of force and the distance of its line of action
from the axis
Toeplitz
matrix : A matrix in which all the elements are the same along any
diagonal that slopes from northwest to southeast.
Torus :
A geometric solid in the shape of a donut.; A surface of
revolution generated by revolution of a circle in three dimensional spaces
about an axis passing through its centre and perpendicular to the plane of the
circle and it do or not touch the circle .
Total Derivative : The
rate of change of a function of two or more variables with respect to a
paprameter on which these variables depend.
If Z =
f(x,y,t), x= θ(t) and y = Ø(t),
the total derivative of z with respect to t.
Total Differential : In
analogy with the differential of a function of one variable, the total
differential of a function Z = f( x,y) of more than one variable is
Dz = 
dx + dy
Totally ordered Set : A
set with total order defined on it. An order relation on a set S is a total
order exactly if, for any two elements x and y of S, either x< y , x = y or
y< x , but no two of the three.
Trace :
The trace of a matrix is the sum of the terms along the
principal diagonal.
Transcendental
Function : A function that cannot be expressed as
algebraic function. E.g. , In x, sinx, ex etc., and any function
containing them are Transcendental functions.
Transcendental
number : A real
or complex number that is not algebraic.
Transform of Element of Group : The
transform of an element ‘K’ by an element ‘X’ is X-1 is X-1
KX.
Transform of Matrix : A
matrix B related to a given matrix A by the expression B = Q-1 AQ, Q
being a non-singular matrix. Eigen values remain same.
Transformation : The
changing of an algebraic expression or equation into an equivalent one with a
different form.
Transformation of Axis : Let
the coordinate of a point be (x,y,z)
in a coordinate system of axes. The axis can be transformed in three ways. One ,
the origin is shifted keeping the axes parallel. Two , the origin is kept as it
is , but the axes are rotated. Third , the origin shifting and rotation of axes
take place simultaneously. The coordinate of the point with respect to new
coordinate axes will be different.
Transformation of Coordinate : A
coordinate transformation is conversion from one system to another, to describe
the same space. E.g. Cartesian coordinates may be converted to spherical
coordinates or vice versa.
Transitive Property : The
property that states that if a=b and b = c , then a =c .
Transitive relation : A
binary relation R over a set X is Transitive if it holds for a,b,c in X, that
is . if a is related to b and b is related to c, then a is related to c . e.g.
a>b, and b>c , then a>c ( > relation
is transitive ).
Transitive Set : A set
is called Transitive if it is equal to
its Transitive closure. That is, X is a Transitive set if whenever y is an
element of X and z is an element of Y, then z is an element of X.
Translation : A function which we obtain if we add the same constant
to each value of the variable of the given function and move the graphs of the
function by a constant distance.
Transpose: To
move a term from one side of an equation to another side , with change of sign.
Transpose of Matrix : The Transpose
of a matrix A is obtained by interchanging its rows and columns. It is usually
denoted by AT, if A is the original matrix.
Transversal : A line
that intersects two or more other lines in the same plane.
Trapezium
: A quadrilateral in which no sides are parallel.
Trapezoid
: A quadrilateral in which two sides are parallel.
Tree : A tree
is a graph with the property that there is a unique path from any vertex to any
other vertex traveling along the edges.
Triangle
: A geometric figure with three sides.
Triangular
number : A number of the form n(n+1)/2.
Triangular
prism : A polyhedron-a prism with two identical, triangular bases.
Trinomial
: An algebraic expression consisting of 3 terms.
Tromino
: A three-square polyomino.
Truncated
pyramid : A section of a pyramid between its base and a plane parallel to
the base.
Twin
primes : Two prime numbers that differ by 2. For example, 11 and 13 are
twin primes.
