their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions;. one- one, into and onto functions, composition of functions. Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a +ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots. UNIT 3 Matrices and Determinants Integral as an anti - derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. UNIT 5 Mathematical Induction Principle of Mathematical Induction and its simple applications. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic exponential, composite and implicit functions derivatives of order upto two. Rolle's and Lagrange's Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals. Real valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Evaluation of simple integrals of the type UNIT 8 Limit, Continuity and Differentiability UNIT 4 Permutations and Combinations Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special 2 3 series: ∑ n, ∑ n , ∑ n . Arithmetico - Geometric progression. UNIT 9 Integral Calculus UNIT 6 Binomial Theorem and its Simple Applications Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications. Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications. UNIT 7 Sequences and Se