B
Back Substitution
Back substitution is a technique that is used to solve a system of linear equations that has already been changed to row-echelon form and reduced row-echelon form. After changing the equation, the first equation is solved, then the second last, then the next before that and so forth.
Base (Geometry)
The bottom part of a geometrical figure like a solid object or a triangle is called the base of the object.
Base of an Exponential Expression
Consider the expression ax. Then 'a' can be called as the base of the expression ax.
Base of an Isosceles Triangle
The base of an isosceles triangle is the non-congruent side of the triangle. In other words, it is the side other than the legs of the triangle.
Base of a Trapezoid
The trapezoid has four sides with two sides parallel. Either of the two parallel sides can be considered as the base of the trapezoid.
Base of a Triangle
Base of a triangle is the side at which an altitude can be drawn. It is the side which is perpendicular to the altitude.
Bearing
Bearing is a method used to represent the direction of a line. If there are two points A and B, then we can say that A has a bearing of θ degrees from point B, if the line connecting A and B makes an angle θ with a vertical line drawn through B. The angle is measured in clockwise direction.
Bernoulli Trials
In the field of maths and statistics Bernoulli trials are the experiments where the outcome can be either true or false. In Bernoulli trials all events must be independent. The binomial probability formula is given by p (k successes in n trials) = nCrpkqn – k, where,
n= number of trials,
k = number of successes,
n – k = number of failures,
p = probability of successes in trials,
q = 1 – p, probability of failure in one trial.
Beta (Β β)
A Greek letter used frequently in maths and science as a symbol to denote variables.
Biconditional
It is the method of expressing a mathematical statement containing more than one conditions, that means a condition and its converse. These statements are called as biconditionals. Biconditionals are represented by the symbol ⇔. For example the following statements can be called biconditionals: "A given triangle is equilateral" is same as "All the angles of a triangle measure 60º."
Binomial
A binomial can be simply defined as a polynomial which has two terms, but they are not like terms. For example, 3x – 5z3, 4x – 6y2.
Binomial Coefficients
The coefficients of the various terms in the binomial expansion of the binomial theorem are called as binomial coefficients. Mathematically, a binomial coefficients equals the number of r items that can be selected from a set of n items. They are simply called as the binomial coefficients because they are coefficients of the binomial expanded terms. Generally, they are represented by nCr.
Binomial Coefficients in Pascal's Triangle
Pascal's triangle is an arithmetic triangle that is used to calculate the binomial coefficients of the various numbers. The binomial coefficients (nr) in the pascal's triangle are called as the binomial coefficients in pascal's triangle. Pascal's triangle finds major use in algebra and probability/binomial theorem.
Binomial Probability Formula
The probability of getting m successes in n trials is called binomial probability formula. The formula is given by:
Formula: P(m successes in n trials) = mCpkqn-k, where,
n = number of trials
m = number of successes
n – m = number of failures
p = probability of success in one trial
q = probability of failure in one trial.
Binomial Theorem
A theorem used to expand the powers of polynomial terms and equations. It is given by:
(a + b)n = nC0an + nC1an-1b +..........+nCn -1abn–1 + nCn.
Boolean Algebra
Boolean algebra deals with the logical calculus. Boolean algebra takes only two values in the logical analysis, either 1 or zero.
Back Substitution
Back substitution is a technique that is used to solve a system of linear equations that has already been changed to row-echelon form and reduced row-echelon form. After changing the equation, the first equation is solved, then the second last, then the next before that and so forth.
Base (Geometry)
The bottom part of a geometrical figure like a solid object or a triangle is called the base of the object.
Base of an Exponential Expression
Consider the expression ax. Then 'a' can be called as the base of the expression ax.
Base of an Isosceles Triangle
The base of an isosceles triangle is the non-congruent side of the triangle. In other words, it is the side other than the legs of the triangle.
Base of a Trapezoid
The trapezoid has four sides with two sides parallel. Either of the two parallel sides can be considered as the base of the trapezoid.
Base of a Triangle
Base of a triangle is the side at which an altitude can be drawn. It is the side which is perpendicular to the altitude.
Bearing
Bearing is a method used to represent the direction of a line. If there are two points A and B, then we can say that A has a bearing of θ degrees from point B, if the line connecting A and B makes an angle θ with a vertical line drawn through B. The angle is measured in clockwise direction.
Bernoulli Trials
In the field of maths and statistics Bernoulli trials are the experiments where the outcome can be either true or false. In Bernoulli trials all events must be independent. The binomial probability formula is given by p (k successes in n trials) = nCrpkqn – k, where,
n= number of trials,
k = number of successes,
n – k = number of failures,
p = probability of successes in trials,
q = 1 – p, probability of failure in one trial.
Beta (Β β)
A Greek letter used frequently in maths and science as a symbol to denote variables.
Biconditional
It is the method of expressing a mathematical statement containing more than one conditions, that means a condition and its converse. These statements are called as biconditionals. Biconditionals are represented by the symbol ⇔. For example the following statements can be called biconditionals: "A given triangle is equilateral" is same as "All the angles of a triangle measure 60º."
Binomial
A binomial can be simply defined as a polynomial which has two terms, but they are not like terms. For example, 3x – 5z3, 4x – 6y2.
Binomial Coefficients
The coefficients of the various terms in the binomial expansion of the binomial theorem are called as binomial coefficients. Mathematically, a binomial coefficients equals the number of r items that can be selected from a set of n items. They are simply called as the binomial coefficients because they are coefficients of the binomial expanded terms. Generally, they are represented by nCr.
Binomial Coefficients in Pascal's Triangle
Pascal's triangle is an arithmetic triangle that is used to calculate the binomial coefficients of the various numbers. The binomial coefficients (nr) in the pascal's triangle are called as the binomial coefficients in pascal's triangle. Pascal's triangle finds major use in algebra and probability/binomial theorem.
Binomial Probability Formula
The probability of getting m successes in n trials is called binomial probability formula. The formula is given by:
Formula: P(m successes in n trials) = mCpkqn-k, where,
n = number of trials
m = number of successes
n – m = number of failures
p = probability of success in one trial
q = probability of failure in one trial.
Binomial Theorem
A theorem used to expand the powers of polynomial terms and equations. It is given by:
(a + b)n = nC0an + nC1an-1b +..........+nCn -1abn–1 + nCn.
Boolean Algebra
Boolean algebra deals with the logical calculus. Boolean algebra takes only two values in the logical analysis, either 1 or zero.
Boundary Value Problem
Any differential equation that has constrained on the values of the function (not that on the derivatives) is called as the boundary value problem.
Bounded Function
A function that has a bounded range. For example, in the set [2, 9], 9 the upper bounded number and 2 is the lower bounded number.
Bounded Sequence
A sequence that is bounded with upper and lower bounds. Like the harmonic series, 1, ½, 1/3, ¼,...up to infinity is a bounded function since the function lies between 0 and 1.
Bounded Set of Geometric Points
The bounded set of geometric points is called as the figure or set of points that can be enclosed in a fixed space or co-ordinates.
Bounded Set of Numbers
A set of numbers with lower and upper bound. For example, [3, 7] is called as the bounded set of numbers.
Bounds of Integration
For definite integral, aʃb f(x)dx, a and b are called as the bounds or limits of integration. The bounds of integration also indicate limits of integration.
Box
A rectangular parallelepiped is often referred to as a box. The volume of such a rectangular box is given by the product of length, breadth and height.
Box and Whisker Plot
The box and whisker plot is a beginning lesson for starters, in order to let them understand the basics of handling data value. Box and whisker plot shows certain data, not the complete statistics of the recorded data. Five number summary is another name for visual representation of the box and whisker plot.
Boxplot
A data that displays the five number summary in a diagrammatic form represented as:
Any differential equation that has constrained on the values of the function (not that on the derivatives) is called as the boundary value problem.
Bounded Function
A function that has a bounded range. For example, in the set [2, 9], 9 the upper bounded number and 2 is the lower bounded number.
Bounded Sequence
A sequence that is bounded with upper and lower bounds. Like the harmonic series, 1, ½, 1/3, ¼,...up to infinity is a bounded function since the function lies between 0 and 1.
Bounded Set of Geometric Points
The bounded set of geometric points is called as the figure or set of points that can be enclosed in a fixed space or co-ordinates.
Bounded Set of Numbers
A set of numbers with lower and upper bound. For example, [3, 7] is called as the bounded set of numbers.
Bounds of Integration
For definite integral, aʃb f(x)dx, a and b are called as the bounds or limits of integration. The bounds of integration also indicate limits of integration.
Box
A rectangular parallelepiped is often referred to as a box. The volume of such a rectangular box is given by the product of length, breadth and height.
Box and Whisker Plot
The box and whisker plot is a beginning lesson for starters, in order to let them understand the basics of handling data value. Box and whisker plot shows certain data, not the complete statistics of the recorded data. Five number summary is another name for visual representation of the box and whisker plot.
Boxplot
A data that displays the five number summary in a diagrammatic form represented as:
Smallest | 1st Quartile | Median | 3rd Quartile | Largest |
Braces
The symbolic representation {or} that is used to indicate sets etc.
Brackets
The symbol [ ] which signifies grouping. They work in a similar way parentheses do.
C
Calculus
The branch of mathematics that deals with integration, differentiation and various other forms of derivatives.
Cardinal Numbers
Cardinal numbers are used to indicate the number of elements in an infinite or finite sets.
Cardinality
It is same as cardinal numbers. It is to be noted that cardinality of every infinite set is same.
Cartesian Coordinates
The Cartesian coordinates are the axes that are used to represent the coordinates of a point. (x,y) and (x,y,z) are the Cartesian coordinates.
Cartesian Plane
The planes formed by horizontal and vertical axes like the x and y axis is called the Cartesian plane.
Catenary
The curve formed by a hanging a wire or a ring is called as catenary. Generally, a catenary is confused with a parabola. However, though the looks are similar, it is not same as the parabola. The graph of a hyperbolic cosine function is called the catenary.
Cavalieri’s Principle
A method to find the volume of solids by using the formula V = bh, where b = area of cross section of the base (cylinder/prism) and h = height of the solid.
Central Angle
An angle in a circle with vertex at the circle's center.
Centroid
The intersection point of the three medians of a triangle.
Centroid Formula
The centroid of the points (x1, y1, x2, y2,....xn, yn) is given by:
(x1 + x2 + x3+......xn)/n , (y1 + y2 + y3+ …..yn)/n
Ceva’s Theorem
Ceva's theorem is a way that relates the ratio in which three concurrent cevian divides a triangle. If AB, BC and CA are the three sides of a triangle and and AE, BF and CD are the three cevian of the triangle, then according to Ceva's theorem,
(AD/DB)(BE/EC)(CF/FA) = 1.
Cevian
A line that extends from the vertex of a triangle to the opposite side like altitudes and medians.
Chain Rule
A method used in differential calculus to find the derivative of a composite function.
(d/dx)f(g(x)) = f'((g(x))g'(x) or (dy/dx) = (dy/du)(du/dx)
Change of Base Formula
A very useful formula in logarithm that is used to express a certain logarithmic function in a different base. That's why it is called as base change formula.
Base Change Formula: logax = (logbx/logba)
Check a Solution
Checking a solution means putting the value of corresponding variables in the equation and verify if the equations satisfy the given equation or systems of equation.
Chord
A chord is a line segment that joins the two points on a curve. In a circle, the largest chord is the diameter that joins the two ends of the circle.
Circle
The locus of all points that is always at a fixed distance from a fixed point.
Circular Cone
A cone with a circular base.
The volume of circular cone is given by V = 1/3πr2
Circular Cylinder
A cylinder with circle as bases.
Circumcenter
The center of a circumcircle is called as circumcenter.
Circumcircle
A circle that passes through all the vertices of a regular polygon and triangles is called as circumcircle.
Circumference
The perimeter of a circular figure.
Circumscribable
A plan figure that has a circumcircle.
Circumscribed
A figure circumscribed by a circle.
Circumscribed Circle
The circle that touches the vertices of a triangle or a regular polygon.
Clockwise
The direction of the moving hands of a clock.
Closed Interval
A closed interval is the one in which, both the first and last terms are included while considering the entire set. For example, [3,4].
Coefficient
The constant number that is multiplied with the variables and powers in an algebraic expression. For example, in 234x2yz, 243 is the coefficient.
Coefficient Matrix
The matrix formed by the coefficients of a linear system of equations is called the coefficient matrix
Cofactor
When a determinant is obtained by deleting the rows and columns of a matrix in order to solve the equation, it is called as the cofactors.
Cofactor Matrix
A matrix with the elements of the cofactors, term by term, in a square matrix is called as the cofactor matrix.
Cofunction Identities
Cofunction identities are the identities that show the relation between the trigonometrical functions like the sine, cosine, cotangent,
Coincident
If two figures are superimposed on each other, then they are said to be coincident. In other words, a figure is coincident when all points are coincident.
Collinear
Two points are said to be collinear if they lie on the same line.
Column of a Matrix
The vertical set of numbers in a matrix is called the column of the matrix.
Combination
A selection of objects from a group of objects. The order is irrelevant in the selection of the object.
Combination Formula
A formula that is used to determine the number of possible combinations of r objects from a set of n objects. The formula involves the binomial coefficients and is given as:
nCr. It is read as 'n choose r'
Combinatorics
The branch of mathematics that studies the permutations and combinations of objects and materials.
Common Logarithm
The logarithm to the base 10 is called as common logarithm.
Commutative
An operation is said to be commutative if x ø y = y ø x, for all values of x and y. Addition and multiplication are commutative operations. For example, 4 + 5 = 5 + 4 or 6 X 5 = 5 X 6. Division and subtraction are not commutative.
Compatible Matrices
Two matrices are said to be compatible for multiplication if the number of columns of 1st matrix equals to the number of rows of the other.
Complement of an Angle
The complement of angle say 75º is 90º – 75º = 15º.
Complement of an Event
The set of all outcomes of an event that are not included in the event. The complement of set A is written as Ac. The formula is given as: P(Ac) = 1 – P(A) or P (not A) = 1- P(A).
Complement of a Set
The elements of a given set that are not contained in the given set.
Complementary Angles
If the sum of two angles is 90º, then they are said to be complementary angles. For example, 30º and 60º are complementary to each other as their sum equals 90º.
Composite Number
A positive integer whose factors are the numbers other than 1 and the number itself. For example, 4, 6, 9, 12 etc. 1 is not a composite number.
Compound Fraction
A compound fraction is a fraction that has at least one fraction term in the numerator and denominator.
Compound Inequality
When two or more than two inequalities are solved together it is known as compound inequality.
Compound Interest
While calculating compound interest, the amount that is earned as an interest for a certain principal is added to the principal and from that moment the interest is calculated on the new principal. Thus, the interest is not only calculated on the original balance but the balance or principal obtained after adding the interest.
Concave
Concave is a shape of a figure or a solid that has a surface curving inwards or bulging inwards. It is also known as non – convex. Concave down or concave up are the other forms of concave shapes.
Concentric
The geometrical figures that are similar in shape and share a common center. Usually, the term concentric is used for concentric circles.
Concurrent
If two or more than two lines or curves intersect at the same point then they are said to be concurrent at that point.
Conditional Equation
A equation that is true for some values of the variables and is false for other values of the variables. The equation has certain conditions imposed on it that are only satisfied by certain values of the variables.
Cos-1x
The inverse of cos function is read as 'cos inverse x'. For example, cos-1½ = 60º.
Cot-1x
By cot-1x we mean the angle whose cotangent is equal to x. For example, when we are asked to find the smallest angle whose cotangent is equal to 1? The answer is 45º. Thus, cot-11 = 45º.
Cube
Cube is a three dimensional figure bounded by six equal sides. The volume of cube is given by l3, where l is the side of a cube.
Cube Root
A cube root is a number denoted as x⅓ such that b3 = x For example, (64)⅓ = 4.
Cubic Polynomial
A polynomial of degree 3 is known as the cubic polynomial. For example, x3 + 2x2 + x.
Cuboid
Cuboid is a three dimensional box that has length, width and height. Rectangular Parallelepiped is the other name for a cuboid.
Calculus
The branch of mathematics that deals with integration, differentiation and various other forms of derivatives.
Cardinal Numbers
Cardinal numbers are used to indicate the number of elements in an infinite or finite sets.
Cardinality
It is same as cardinal numbers. It is to be noted that cardinality of every infinite set is same.
Cartesian Coordinates
The Cartesian coordinates are the axes that are used to represent the coordinates of a point. (x,y) and (x,y,z) are the Cartesian coordinates.
Cartesian Plane
The planes formed by horizontal and vertical axes like the x and y axis is called the Cartesian plane.
Catenary
The curve formed by a hanging a wire or a ring is called as catenary. Generally, a catenary is confused with a parabola. However, though the looks are similar, it is not same as the parabola. The graph of a hyperbolic cosine function is called the catenary.
Cavalieri’s Principle
A method to find the volume of solids by using the formula V = bh, where b = area of cross section of the base (cylinder/prism) and h = height of the solid.
Central Angle
An angle in a circle with vertex at the circle's center.
Centroid
The intersection point of the three medians of a triangle.
Centroid Formula
The centroid of the points (x1, y1, x2, y2,....xn, yn) is given by:
(x1 + x2 + x3+......xn)/n , (y1 + y2 + y3+ …..yn)/n
Ceva’s Theorem
Ceva's theorem is a way that relates the ratio in which three concurrent cevian divides a triangle. If AB, BC and CA are the three sides of a triangle and and AE, BF and CD are the three cevian of the triangle, then according to Ceva's theorem,
(AD/DB)(BE/EC)(CF/FA) = 1.
Cevian
A line that extends from the vertex of a triangle to the opposite side like altitudes and medians.
Chain Rule
A method used in differential calculus to find the derivative of a composite function.
(d/dx)f(g(x)) = f'((g(x))g'(x) or (dy/dx) = (dy/du)(du/dx)
Change of Base Formula
A very useful formula in logarithm that is used to express a certain logarithmic function in a different base. That's why it is called as base change formula.
Base Change Formula: logax = (logbx/logba)
Check a Solution
Checking a solution means putting the value of corresponding variables in the equation and verify if the equations satisfy the given equation or systems of equation.
Chord
A chord is a line segment that joins the two points on a curve. In a circle, the largest chord is the diameter that joins the two ends of the circle.
Circle
The locus of all points that is always at a fixed distance from a fixed point.
Circular Cone
A cone with a circular base.
The volume of circular cone is given by V = 1/3πr2
Circular Cylinder
A cylinder with circle as bases.
Circumcenter
The center of a circumcircle is called as circumcenter.
Circumcircle
A circle that passes through all the vertices of a regular polygon and triangles is called as circumcircle.
Circumference
The perimeter of a circular figure.
Circumscribable
A plan figure that has a circumcircle.
Circumscribed
A figure circumscribed by a circle.
Circumscribed Circle
The circle that touches the vertices of a triangle or a regular polygon.
Clockwise
The direction of the moving hands of a clock.
Closed Interval
A closed interval is the one in which, both the first and last terms are included while considering the entire set. For example, [3,4].
Coefficient
The constant number that is multiplied with the variables and powers in an algebraic expression. For example, in 234x2yz, 243 is the coefficient.
Coefficient Matrix
The matrix formed by the coefficients of a linear system of equations is called the coefficient matrix
Cofactor
When a determinant is obtained by deleting the rows and columns of a matrix in order to solve the equation, it is called as the cofactors.
Cofactor Matrix
A matrix with the elements of the cofactors, term by term, in a square matrix is called as the cofactor matrix.
Cofunction Identities
Cofunction identities are the identities that show the relation between the trigonometrical functions like the sine, cosine, cotangent,
Coincident
If two figures are superimposed on each other, then they are said to be coincident. In other words, a figure is coincident when all points are coincident.
Collinear
Two points are said to be collinear if they lie on the same line.
Column of a Matrix
The vertical set of numbers in a matrix is called the column of the matrix.
Combination
A selection of objects from a group of objects. The order is irrelevant in the selection of the object.
Combination Formula
A formula that is used to determine the number of possible combinations of r objects from a set of n objects. The formula involves the binomial coefficients and is given as:
nCr. It is read as 'n choose r'
Combinatorics
The branch of mathematics that studies the permutations and combinations of objects and materials.
Common Logarithm
The logarithm to the base 10 is called as common logarithm.
Commutative
An operation is said to be commutative if x ø y = y ø x, for all values of x and y. Addition and multiplication are commutative operations. For example, 4 + 5 = 5 + 4 or 6 X 5 = 5 X 6. Division and subtraction are not commutative.
Compatible Matrices
Two matrices are said to be compatible for multiplication if the number of columns of 1st matrix equals to the number of rows of the other.
Complement of an Angle
The complement of angle say 75º is 90º – 75º = 15º.
Complement of an Event
The set of all outcomes of an event that are not included in the event. The complement of set A is written as Ac. The formula is given as: P(Ac) = 1 – P(A) or P (not A) = 1- P(A).
Complement of a Set
The elements of a given set that are not contained in the given set.
Complementary Angles
If the sum of two angles is 90º, then they are said to be complementary angles. For example, 30º and 60º are complementary to each other as their sum equals 90º.
Composite Number
A positive integer whose factors are the numbers other than 1 and the number itself. For example, 4, 6, 9, 12 etc. 1 is not a composite number.
Compound Fraction
A compound fraction is a fraction that has at least one fraction term in the numerator and denominator.
Compound Inequality
When two or more than two inequalities are solved together it is known as compound inequality.
Compound Interest
While calculating compound interest, the amount that is earned as an interest for a certain principal is added to the principal and from that moment the interest is calculated on the new principal. Thus, the interest is not only calculated on the original balance but the balance or principal obtained after adding the interest.
Concave
Concave is a shape of a figure or a solid that has a surface curving inwards or bulging inwards. It is also known as non – convex. Concave down or concave up are the other forms of concave shapes.
Concentric
The geometrical figures that are similar in shape and share a common center. Usually, the term concentric is used for concentric circles.
Concurrent
If two or more than two lines or curves intersect at the same point then they are said to be concurrent at that point.
Conditional Equation
A equation that is true for some values of the variables and is false for other values of the variables. The equation has certain conditions imposed on it that are only satisfied by certain values of the variables.
Cos-1x
The inverse of cos function is read as 'cos inverse x'. For example, cos-1½ = 60º.
Cot-1x
By cot-1x we mean the angle whose cotangent is equal to x. For example, when we are asked to find the smallest angle whose cotangent is equal to 1? The answer is 45º. Thus, cot-11 = 45º.
Cube
Cube is a three dimensional figure bounded by six equal sides. The volume of cube is given by l3, where l is the side of a cube.
Cube Root
A cube root is a number denoted as x⅓ such that b3 = x For example, (64)⅓ = 4.
Cubic Polynomial
A polynomial of degree 3 is known as the cubic polynomial. For example, x3 + 2x2 + x.
Cuboid
Cuboid is a three dimensional box that has length, width and height. Rectangular Parallelepiped is the other name for a cuboid.
D
De Moivre’s Theorem
De Moiver's Theorem is a formula that is widely used in complex number system in order to calculate the powers and roots of complex numbers. Mathematically, it is given by:
[r(cosθ + isinθ)]n = rn(cosnθ + isinnθ).
Decagon
A 10 sided polygon is called as decagon.
Deciles
In statistics, deciles are any of the nine values that divide the data into 10 equal parts. The first decile cuts off at the lowest 10% of the data that is called as the 10th percentile. The 5th decile cuts off the at the lowest 50% of the data that is called as 50th percentile or 2nd quartile or median. The 9th decile cuts off lowest 90% of the data that is the 90th percentile.
Decreasing Function
A function whose value decreases continuously as we move from left to right of its graph is called decreasing function. A line with negative slope is a perfect example of a decreasing function where the value of the function decreases as we proceed on the x-axis. If the decreasing function is differentiable then its derivative at all points (where the function is decreasing) will be negative.
Definite Integral
An integral that is evaluated over an interval. It is given by aʃbf(x)dx. Here the interval is [a, b].
Degenerate Conic Sections
If a double cone is cut with a plane passing through the apex of the plane, it is called as the degenerate conic sections. It has the general equations of the form:
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
Degree (angle measure)
Degree is the measure of the slope or the angle that a line or a plane subtends. Degree is represented by the symbol °.
Degree of a Polynomial
The power of a highest term in an algebraic expression is called as the degree of the polynomial. In the expression 2x5 + 3y4 + 5x3, the degree of the polynomial is 5.
Degree of a Term
In 5y7, degree of term is 7, in 5x24y3, the degree of the term is the sum of the exponents of 5x and 4y, that means 5.
Del Operator
Del operator is denoted by symbol ∂(x, y, z)/∂x. The del operator ∇ = (∂/∂x, ∂/∂y) or ( ∂/∂x, ∂/∂y, ∂/∂z )
Deleted Neighborhood
Deleted neighborhood of a set is defined as a set {x: 0 < |x – a| < δ}. For example, one deleted neighborhood of 2 is the set {x: 0 < |x – 2| < 0.1}, which is the same as (1.9, 2) ∪ (2, 2.1).
Delta (Δ δ)
A Greek letter representing the basic discriminant of a quadratic equation.
Denominator
The lower part of a fraction is called denominator. In fraction (4/5), 5 is the denominator.
Dependent Variable
Consider an expression y = 2x + 3, here, x is the independent variable and y is the dependent variable. It is a general notion to plot the graph by taking independent variable on x axis and dependent variable on Y-axis.
Derivative
The slope of a line tangent to a function is called as the derivative of the function. This is the graphical interpretation of the derivative. As a differentiation operation, consider f(x) = x2 then it's derivative is f'(x) = 2x.
Descartes' Rule of Signs
A method for determining the maximum number of positive zeros of a polynomial. According to this rule, the number of changes in the sign of the algebraic expression gives the number of roots of the expression.
Determinant
Determinants are the mathematical objects that are very useful in determining the solution of a set of system of linear equations.
Diagonal Matrix
A square matrix that has zeroes everywhere except the main diagonal.
Diagonal of a Polygon
A line segment joining non-adjacent vertices of a diagonal. If a polygon is of n-sides then the number of diagonals is given by the formula:
n(n-3)/2 diagonals.
Diameter
The longest chord of a circle is called diameter. It can be also defined as the line segment that passes through the center of the circle and touches both the ends of the circumference of the circle.
Diametrically Opposed
Two points directly opposite to each other on a circle.
Difference
The result of subtracting two numbers is called as difference.
Differentiable
A curve that is continuous at all points of its domain is called as a differentiable function. In other words if a derivative exists for a curve at all points of the domains variable, it is said to be differentiable.
Differential
A tiny or infinitesimal change in the value of a variable.
Differential Equation
A mathematical equation involving the functions and derivatives. For example, (dy/dx)2 = y
Differentiation
Performing the process of finding a derivative.
Digit
Any of the numbers among the nine digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Dihedral Angle
The angle formed by the intersection of two planes.
Dilation
Dilation refers to the enlargement of a geometrical figure by transformation method.
Dilation of a Geometric Figure
A transformation in which all distances are increased by some common factor. The points are stretched from a common fixed point P.
Dilation of a Graph
In graphical dilation, the x-coordinates and y-coordinates are enlarged by some common factor. The factor by which the transformation of the graph is done must be greater than 1. If the factor is less than 1, it is called compression.
Dimensions
The sides of a geometrical figure are often referred to as dimensions.
Dimensions of a Matrix
The number of rows and columns of matrix is called as the dimensions of the matrix. For example if a matrix has 2 rows and 3 columns, its dimensions will be 2X3 (read as two cross three).
Direct Proportion
When one of the variables is a constant multiple of the other, it is called as direct variation. For example, y = kx (here y and x are the variables and k is a constant factor).
Directrices of an Ellipse
Two parallel lines on the exterior of an ellipse that are perpendicular to the major axis.
De Moivre’s Theorem
De Moiver's Theorem is a formula that is widely used in complex number system in order to calculate the powers and roots of complex numbers. Mathematically, it is given by:
[r(cosθ + isinθ)]n = rn(cosnθ + isinnθ).
Decagon
A 10 sided polygon is called as decagon.
Deciles
In statistics, deciles are any of the nine values that divide the data into 10 equal parts. The first decile cuts off at the lowest 10% of the data that is called as the 10th percentile. The 5th decile cuts off the at the lowest 50% of the data that is called as 50th percentile or 2nd quartile or median. The 9th decile cuts off lowest 90% of the data that is the 90th percentile.
Decreasing Function
A function whose value decreases continuously as we move from left to right of its graph is called decreasing function. A line with negative slope is a perfect example of a decreasing function where the value of the function decreases as we proceed on the x-axis. If the decreasing function is differentiable then its derivative at all points (where the function is decreasing) will be negative.
Definite Integral
An integral that is evaluated over an interval. It is given by aʃbf(x)dx. Here the interval is [a, b].
Degenerate Conic Sections
If a double cone is cut with a plane passing through the apex of the plane, it is called as the degenerate conic sections. It has the general equations of the form:
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
Degree (angle measure)
Degree is the measure of the slope or the angle that a line or a plane subtends. Degree is represented by the symbol °.
Degree of a Polynomial
The power of a highest term in an algebraic expression is called as the degree of the polynomial. In the expression 2x5 + 3y4 + 5x3, the degree of the polynomial is 5.
Degree of a Term
In 5y7, degree of term is 7, in 5x24y3, the degree of the term is the sum of the exponents of 5x and 4y, that means 5.
Del Operator
Del operator is denoted by symbol ∂(x, y, z)/∂x. The del operator ∇ = (∂/∂x, ∂/∂y) or ( ∂/∂x, ∂/∂y, ∂/∂z )
Deleted Neighborhood
Deleted neighborhood of a set is defined as a set {x: 0 < |x – a| < δ}. For example, one deleted neighborhood of 2 is the set {x: 0 < |x – 2| < 0.1}, which is the same as (1.9, 2) ∪ (2, 2.1).
Delta (Δ δ)
A Greek letter representing the basic discriminant of a quadratic equation.
Denominator
The lower part of a fraction is called denominator. In fraction (4/5), 5 is the denominator.
Dependent Variable
Consider an expression y = 2x + 3, here, x is the independent variable and y is the dependent variable. It is a general notion to plot the graph by taking independent variable on x axis and dependent variable on Y-axis.
Derivative
The slope of a line tangent to a function is called as the derivative of the function. This is the graphical interpretation of the derivative. As a differentiation operation, consider f(x) = x2 then it's derivative is f'(x) = 2x.
Descartes' Rule of Signs
A method for determining the maximum number of positive zeros of a polynomial. According to this rule, the number of changes in the sign of the algebraic expression gives the number of roots of the expression.
Determinant
Determinants are the mathematical objects that are very useful in determining the solution of a set of system of linear equations.
Diagonal Matrix
A square matrix that has zeroes everywhere except the main diagonal.
Diagonal of a Polygon
A line segment joining non-adjacent vertices of a diagonal. If a polygon is of n-sides then the number of diagonals is given by the formula:
n(n-3)/2 diagonals.
Diameter
The longest chord of a circle is called diameter. It can be also defined as the line segment that passes through the center of the circle and touches both the ends of the circumference of the circle.
Diametrically Opposed
Two points directly opposite to each other on a circle.
Difference
The result of subtracting two numbers is called as difference.
Differentiable
A curve that is continuous at all points of its domain is called as a differentiable function. In other words if a derivative exists for a curve at all points of the domains variable, it is said to be differentiable.
Differential
A tiny or infinitesimal change in the value of a variable.
Differential Equation
A mathematical equation involving the functions and derivatives. For example, (dy/dx)2 = y
Differentiation
Performing the process of finding a derivative.
Digit
Any of the numbers among the nine digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Dihedral Angle
The angle formed by the intersection of two planes.
Dilation
Dilation refers to the enlargement of a geometrical figure by transformation method.
Dilation of a Geometric Figure
A transformation in which all distances are increased by some common factor. The points are stretched from a common fixed point P.
Dilation of a Graph
In graphical dilation, the x-coordinates and y-coordinates are enlarged by some common factor. The factor by which the transformation of the graph is done must be greater than 1. If the factor is less than 1, it is called compression.
Dimensions
The sides of a geometrical figure are often referred to as dimensions.
Dimensions of a Matrix
The number of rows and columns of matrix is called as the dimensions of the matrix. For example if a matrix has 2 rows and 3 columns, its dimensions will be 2X3 (read as two cross three).
Direct Proportion
When one of the variables is a constant multiple of the other, it is called as direct variation. For example, y = kx (here y and x are the variables and k is a constant factor).
Directrices of an Ellipse
Two parallel lines on the exterior of an ellipse that are perpendicular to the major axis.
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