CHAPTER I: MATHEMATICAL LOGIC
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Statements - Introduction
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quantifier and quantified statements
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logical connectives : conjunction
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truth tables of compound statements
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examples related to real life and mathematics
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statement patterns and logical equivalence - tautology
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negation of compound statement
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algebra of statements-idempotent law
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difference between converse
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application-introduction to switching circuits (simple examples)
CHAPTER III: TRIGONOMETRIC FUNCTIONS
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Trigonometric equations-general solution of trigonometric equation of the type : sinθ = 0 cosθ = 0 tanθ = 0 sinθ = sinα cosθ = cosα tanθ = tanα sin2 θ = sin2 α cos2 θ = cos2 α tan2 θ = tan2 α acosθ + bsinθ = C
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solution of a triangle : polar coordinates
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inverse trigonometric functions-definitions
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graphs of inverse trigonometric function
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properties of inverse functions
CHAPTER IV: PAIR OF STRAIGHT LINES
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Pair of lines passing through origincombined equation
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theorem-the joint equation of a pair of lines passing through origin and its converse
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acute angle between the lines represented by ax2 +2hxy+by2 =0
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condition for parallel lines
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condition for perpendicular lines
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pair of lines not passing through origin-combined equation of any two lines
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condition that the equation ax2 +2hxy+by2 +2gx+2fy+c=0 should represent a pair of lines (without proof)
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acute angle between the lines (without proof)
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condition of parallel and perpendicular lines
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point of intersection of two lines
CHAPTER VIII: THREE DIMENSIONAL GEOMETRY
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Direction cosines and direction ratios: direction angles
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relation between direction ratio and direction cosines
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condition of perpendicular lines
CHAPTER XI: LINEAR PROGRAMMING PROBLEMS
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Introduction of L.P.P. definition of constraints
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nonnegativity restrictions
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feasible and infeasible region
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Mathematical formulation-mathematical formulation of L.P.P. different types of L.P.P. problems
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graphical solutions for problem in two variables
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optimum feasible solution
PART - II
CHAPTER I: CONTINUITY
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Continuity of a function at a point : left hand limit
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definition of continuity of a function at a point
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discontinuity of a function
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algebra of continuous functions
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continuity in interval-definition
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continuity of some standard functionspolynomial
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exponential and logarithmic function
CHAPTER II: DIFFERENTIATION
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Revision- revision of derivative
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relationship between continuity and differentiability-left hand derivative and right hand derivative (need and concept)
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every differentiable function is continuous but converse is not true
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Derivative of composite function-chain rule
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derivative of inverse function
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derivative of inverse trigonometric function : Derivative of implicit function definition and examples
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derivative of parametric function – definition of parametric function
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exponential and logarithmic functionderivative of functions which are expressed in one of the following form a) product of functions b) quotient of functions c) higher order derivative second order derivative d)
CHAPTER III: APPLICATIONS OF DERIVATIVE
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Geometrical application-tangent and normal at a point
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and Mean value theorem and their geometrical interpretation (without proof)
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derivative as a rate measure-introduction
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increasing and decreasing function
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approximation (without proof)
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Maxima and minimaintroduction of extrema and extreme values
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maxima and minima in a closed interval
CHAPTER V: APPLICATIONS OF DEFINITE INTEGRAL
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Area under the curve : area bounded by curve and axis (simple problems)
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area bounded by two curves
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volume of solid of revolution-volume of solid obtained by revolving the area under the curve about the axis (simple problems)
CHAPTER VI: DIFFERENTIAL EQUATION
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Definition-differential equation
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particular solution of differential equation
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formation of differential equation-formation of differential equation by eliminating arbitary constants (at most two constants)
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solution of first order and first degree differential equation-variable separable method
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homogeneous differential equation (equation reducible to homogeneous form are not expected)
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Linear differential equation
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applications: population growth
CHAPTER VIII: PROBABILITY DISTRIBUTION
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discrete and continuous random variable
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probability mass function (p.m.f.)
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probability distribution of a discrete random variable
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cumulative probability distribution of a discrete random variable
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variance and standard deviation of a discrete random variable
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probability density function (p.d.f.)
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distribution function of a continuous random variable
CHAPTER IX: BERNOULLI TRIALS AND BINOMIAL DISTRIBUTION
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Definition of Bernoulli trial
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conditions for Binomial distribution
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binomial distribution (p.m.f.) mean
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variance and standard deviation
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calculation of probabilities (without proof)
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Normal distribution : p.d.f. mean
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variance and standard deviation
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simple problems (without proof)
BETA
