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Flipkart Book Index
- Introduction to Different Types of Expansions
- Factorial
- Fundamental principle of multiplication
- Permutation
- Number of permutations of n different objects taken r at a time
- Permutitious when all the objects are not distinct objects
- Combination
- Number of combination of n different things taken r at a time
- Properties of “cr
- Binomial theorem
- Properties of binomial coefficients
- Binomial theorem for any index
- Definition of ‘e’ and its expansion
- Exponential series
- Exponential theorem
- Logarithm
- Properties of logarithm
- Logarithmic series
- Complex Number
- Introduction
- Integral power of iota ‘I’
- Complex number
- Geometrical representation of complex number
- Equality of complex numbers
- Fundamental operations on complex numbers
- Properties of addition and multiplication operations
- Conjugate complex numbers
- Properties of complex conjugate
- Modulus of complex number
- Properties of modulus
- Polar form of complex number
- Working rule for finding amplitude
- Trigonometrical Ratio of Allied Angles
- Sign convention of trigonometric ratios
- Square relation of trigonometric ratios
- Trigonometric ratios of standard angle
- Allied angles
- Represent of trigonometric ratios of angle (-θ) in terms of angle θ
- Representation of trigonometric ratios of angle (90°-θ) in terms of angle θ
- Representation of trigonometric ratios of angle (90°+θ) in terms of angle θ
- Representation of trigonometric ratios of angle (180°-θ) in terms of angle θ
- Representation of trigonometric ratios of angle (180°+θ) in terms of angle θ
- Trigonometrical ratios of compound angles
- Other important formulae
- Expansion of tan (A+B) and tan (A-B)
- Transformation of product into sum or difference
- Transformation of sum or difference into product
- Trigonometric ratios of multiple and sub multiple angles
- To find the trigonometrical ratios of an angle a in terms of angle A/2
- To find the value of tan A/2 in terms of tan A
- Trigonometrical ratio of an angle of 18°
- Trigonometric ratio of an angle of 36°
- Trigonometric equations
- General and principle values of the roots of a trigonometric equation
- To find general the general value of different trigonometric ratios
- Equation involving squares of trigonometric function
- Matrices, Determinants and Their Applications
- Determinants of matrix
- Order of matrix
- General from of a matrix
- Various types of matrix
- Operations on matrix
- Transpose of a matrix
- Symmetric and skew symmetric matrix
- Conjugate matrix
- Conjugate transpose matrix or tranjugate matrix
- Harmitian and skew hermitian matrix
- Orthogonal matrix
- Definition of determinant
- Value of determinant
- Minors and cofactors of a determinant
- Properties of determinant
- Product of determinants
- Non singular matrix
- Singular matrix
- Adjoint of a matrix
- Inverse of a matrix
- Solution of system of linear equations by cramer’s rule
- Solution of system of linear equation by the inverse of a matrix
- Characteristics equation of a matrix
- Eigen values and Eigen vectors
- Cayley – Hamilton theorem
- Numerical Integration
- Introduction
- General quadrature formula for equidistant values of independent variable
- Some important approximate quadrature formulae
- Newton – raphson method
- Point
- Co – ordinate axis
- Co – ordinates
- Distance between two points
- Division or section formula
- Centroid of a triangle
- Incentre of the triangle
- Ex – centres of a triangle
- Area of triangle
- Locus
- Straight Line
- Introduction
- Equation of co – ordinate areas
- Equation of lines parallel to coordinate axes
- Slope of a straight line
- Slope of the line passing through the points (X1, Y1) and (X2, Y2)
- Condition for parallelism of two lines
- Condition for perpendicularity of two lines
- General form of the equation of straight line
- Different forms of Ax + By + C = 0
- Angle between two lines
- Angle between two lines when one line is parallel to y – axis
- Point of intersection of two lines
- Perpendicular distance of a point from a line
- Distance between two parallel lines
- Condition for the equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 represent the same line
- Conic Section
- Definition
- Different forms of equation of circle
- Equation of circle in different cases
- Intercept on the axes
- Parametric equation of the circle
- Intersection of a circle and line
- Tangent
- Equation of tangent
- Normal
- Equation of normal
- Definition
- Standard equation of the parabola
- Important definitions
- Different types of parabola
- Intersection of a parabola and a line
- Equation of tangent
- Equation of normal
- Foot of the normal
- Parametric equations
- Definition
- Standard equation of the ellipse
- Some important definitions
- Second form of ellipse
- Focal property of an ellipse
- Parametric coordinates of an ellipse
- Intersection of an ellipse and a line
- Equation of the tangent
- Equation of normal
- Definition
- Standard equation of the hyperbola
- Some important definitions
- Focal property of hyperbola
- Parametric equations and coordinates
- Conjugate hyperbola
- Rectangular hyperbola
- Functions
- Introduction
- Function
- Value of a function
- Types of function
- Limit, Continuity and Differentiability
- Introduction
- Definition of limit
- Theorems on limits
- Some standard limits
- Methods to calculate limit
- Continuity
- Differentiability
- Differentiation
- Differentiation by first principle
- Properties of differentiation of function
- Derivative of function of function – chain rule
- Logarithmic differentiation
- Differentiation of implicit functions
- Differentiation of parametric functions
- Differentiation by trigonometric substitution
- Differentiation of a function with respect to another function
- Second order derivatives
- Application of Derivatives
- Geometrical meaning of derivative
- Tangent and normal
- Angle of intersection of curves
- Rate of change of quantities
- Errors and approximations
- Maximum and minima
- Necessary conditions for the extreme value
- Sufficient condition for extreme value
- Working rule for finding maximum and minimum by second derivative test
- Maximum and minimum value of the function in closed interval [a, b]
- Indefinite Integral
- Introduction
- Integration of a function
- Indefinite integral and constant of integration
- Standard formulae of integration
- Fundamental theorems on integration
- Integration by simplification
- Integration by substitution
- Rule of substitution
- Integration by parts
- Rule of integration by parts
- Some important integrals by the help of integration by parts
- Partial fraction
- Integration of rational algebraic functions
- Some standard integrals
- Integration of some special rational functions
- Integration of some special irrational functions
- Integration of trigonometric functions
- Definite Integral
- Definition
- Solution definite integral
- Substitution in definite integral
- Properties of definite integral
- Some special definite integrals
- Differential Equations
- Definition of differential equation
- Order of a differential equation
- Degree of a differential equation
- Formation of differential equations
- Solution of differential equation
- General and particular solution of differential equation
- Differential equations of the first order and first degree
- Equations in which variables are separable
- Homogeneous differential equations
- Differential equations reducible to homogeneous from
- Bernoulli’s equation
- Exact differential equation
- Method of finding out the general solution of an exact differential equation
- Method of substitution
- Liner Differential Equations with Constant Co – Efficients
- Definition
- Complete solution of differential equation f (D) y=X) f (D) y=Xd
- Auxiliary equation (A.E.) for finding C.F.
- Rules for finding C.F.
- Solution of electrical circuits L-R, L-C, L-C-R
- Rules for finding P.L.
- Easy methods of finding P.I.
- Vectors
- Introduction
- Types of vectors
- Addition of vectors
- Subtraction of two vectors
- Expression of a vector in terms of the position vectors of its end points
- Product of two vectors
- Vector or cross product
- Product of three vectors
- Applications of vector in engineering problems
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