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UNIT:1(Algebra) Complex Numbers

  • Algebra of complex numbers, addition, multiplication, conjugation.
  • Polar representation, properties of modulus and principal argument.
  • Triangle inequality, cube roots of unity.
  • Geometric interpretations.

UNIT:1 Quadratic Equations

  • Quadratic equations with real coefficients.
  • Relations between roots and coefficients.
  • Formation of quadratic equations with given roots.
  • Symmetric functions of roots.

UNIT:1 Sequence & Series

  • Arithmetic, geometric & harmonic progressions.
  • Arithmetic, geometric & harmonic means.
  • Sums of finite arithmetic and geometric progressions, infinite geometric series.
  • Sums of squares and cubes of the first n natural numbers.

UNIT:1 Logarithms and their properties.

  • Logarithms and their properties.

UNIT:1 Permutation & Combination

  • Problems on permutations & combinations.

UNIT:1 Binomial Theorem

  • Binomial theorem for a positive integral index.
  • Properties of binomial coefficients.

UNIT:1 Matrices & Determinants

  • Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix.
  • Determinant of a square matrix of order up to three, the inverse of a square matrix of order up to three.
  • Properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties
  • Solutions of simultaneous linear equations in two or three variables.

UNIT:1 Probability

  • Addition and multiplication rules of probability, conditional probability.
  • Bayes Theorem, independence of events.
  • Computation of probability of events using permutations & combinations.

UNIT:2(Trigonometry) Trigonometric Functions

  • Trigonometric functions, their periodicity and graphs, addition and subtraction formulae.
  • Formulae involving multiple and sub-multiple angles.
  • The general solution of trigonometric equations.

UNIT:2(Trigonometry) Inverse Trigonometric Functions

  • Real valued functions of a real variable, into, onto and one-to-one functions.
  • Sum, difference, product, and quotient of two functions
  • Composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.
  • Even and odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions.

(Unit-3 : Vectors) Properties of Vectors

  • The addition of vectors, scalar multiplication.
  • Dot and cross products
  • Scalar triple products & their geometrical interpretations.

Unit-4 : Differential Calculus -Functions

  • Vectors and scalars, the addition of vectors.
  • Components of a vector in two dimensions and three-dimensional space.
  • Scalar and vector products, scalar and vector triple product.

Unit-4 : Differential Calculus-Limits & Continuity

  • Limit and continuity of a function
  • Limit and continuity of the sum, difference, product and quotient of two functions.
  • L'Hospital rule of evaluation of limits of functions.

Unit-4 : Differential Calculus: Derivatives

  • The derivative of a function, the derivative of the sum, difference, product and quotient of two functions.
  • Chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.
  • Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative.
  • Tangents and normals, increasing and decreasing functions, maximum and minimum values of a function.
  • Rolle's Theorem and Lagrange's Mean Value Theorem..

Unit-5 : Integral calculus: Integration

  • Integration as the inverse process of differentiation.
  • Indefinite integrals of standard functions, definite integrals, and their properties..
  • Fundamental Theorem of Integral Calculus.
  • Integration by parts, integration by the methods of substitution and partial fractions.

Unit-5 :Integral calculus:Application of Integration

  • Application of definite integrals to the determination of Areas involving simple curves.

Unit-5 :Integral calculus:Differential Equations

  • Formation of ordinary differential equations.
  • The solution of homogeneous differential equations, separation of variables method.
  • Linear first order differential equations.