RELATIONS AND FUNCTIONS

  • REFLEXIVE, SYMMETRIC AND TRANSITIVE
  • TYPES OF FUNCTIONS
  • INVERTIBLE FUNCTIONS
  • BINARY FUNCTIONS

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INVERSE TRIGONOMETRIC FUNCTIONS

  • PRINCIPLE VALUES
  • PROPERTIES OF INVERSE TRIGONOMETRIC FUNCTIONS

MATRICES

  • INTRODUCTION
  • TYPES OF MATRICES, EQUALITY OF MATRICES
  • PROP. OF MATRICES
  • TRANSPOSE OF A MATRIX
  • ELEMENTRY TRANSFORMATION

DETERMINANTS

  • INTRODUCTION
  • PROP. OF DETERMINANTS
  • AREA OF TRIANGLE
  • MINORS AND COFACTORS
  • ADJOINT AND INVERSE OF A MATRIX
  • APPLICATION OF A MATRIX

CONTINUITY AND DIFFERENTIABILITY

  • CONTINUITY
  • CHAIN RULE, PRODUCT RULE, QUOTIENT RULE
  • DIFFERENTIATION OF IMPLICIT FUNCTIONS
  • DIFFERENTIATION OF INVERSE TRIGONOMETRIC FUNCTIONS
  • DIFFERENTIATION OF E FUNCTIONS
  • DIFFERENTIATION OF LOG FUNCTIONS
  • DIFFERENTIATION IN PARAMETRIC FORMS
  • SECOND ORDER DERIVATIVES
  • MEAN VALUE THEOREMS

APPLICATION OF DERIVATIVES

  • RATE OF TRANSFER
  • INCREASING DECREASING FUNCTIONS
  • TANGENTS AND NORMALS
  • APPROXIMATIONS
  • MAXIMA MINIMA

INTEGRATION

  • INTRODUCTION TO INTEGRATION
  • INTEGRATION BY SUBSTITUTION
  • INTEGRATION USING TRIGONOMETRIC IDENTITIES
  • INTEGRATION OF SOME OARTICULAR FUNCTIONS
  • INTEGRATION BY PARTIAL FUNCTIONS
  • INTEGRATION BY PARTS
  • INTEGRATION OF MORE TYPES
  • INTEGRATION AS LIMIT AS A SUM
  • DEFINITE INTEGRALS
  • DEFINITE INTEGRALS USING SUBSTITUTION
  • DEFINITE INTEGRALS USING PROPERTIES

APPLICATIONS OF INTEGRALS

  • AREA UNDER A LINE AND A CURVE
  • AREA BETWEEN TWO CURVES
  • AREA OF A TRIANGULAR SECTION

DIFFERENTIAL EQUATIONS

  • ORDER AND DEGREE OF A DIFFERENTIAL EQUATION
  • GENERAL AND PARTICULAR SOLUTIONS OF A DIFFERENTIAL EQUATION
  • FORMATION OF A DIFFERENTIAL EQUATION
  • DIFFERENTIAL EQUATION BY VARIABLE SEPARATION
  • HOMOGENEOUS DIFFERENTIAL EQUATIONS
  • LINEAR DIFFERENTIAL EQUATION USING INTEGRAL FACTOR

VECTORS

  • INTRODUCTION TO VECTORS
  • ADDITION OF VECTORS
  • SCALAR PRODUCT OF TWO VECTORS
  • VECTOR PRODUCT OF VECTORS

THREE DIMENSIONAL GEOMETRY

  • DIRECTION RATIOS
  • DIRECTION COSINES
  • EQUATION OF A LINE
  • ANGLE BETWEEN TWO LINES
  • SHORTEST DISTANCE BETWEEN TWO LINES
  • DISTANCE BETWEEN TWO SKEW LINES
  • DISTANCE BETWEEN PARALLEL LINES
  • EQUATION OF A PLANE IN NORMAL FORM
  • EQUATION OF A PLANE PERPENDICULAR TO GIVEN VECTOR AND PASSING THROUGH A POINT
  • EQUATION OF A PLANE PASSING THROUGH 3 NON COLLINEAR POINTS
  • EQUATION OF A PLANE PASSING THROUGH INTERSECTION OF TWO PLANES
  • INTERCEPT OF A PLANE
  • COPLANARITY OF TWO LINES
  • ANGLE BETWEEN TWO PLANES
  • DISTANCE OF A POINT FROM A PLANE
  • ANGLE BETWEEN A LINE AND A PLANE

LINEAR PROGRAMMING

  • GRAPHICAL PROBLEMS
  • WORD PROBLEMS
  • MISCELLINIOUS PROBLEMS

PROBABILITY

  • CONDITIONAL PROBABILITY
  • MULTIPLICATION THEOREM
  • INDEPENDENT EVENTS
  • BAYE’S THEOREM
  • PROBABILITY DISTRIBUTION
  • MEAN AND VARIANCE
  • BINOMIAL DISTRIBUTION