**
UNIT-1 : SETS, RELATIONS AND FUNCTIONS:**

Sets and 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.

**
UNIT-2 : COMPLEX NUMBERS AND QUADRATIC EQUATIONS:**

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:**

Matrices, algebra of matrices, types of matrices,
determinants and matrices of order two and three.
Properties of determinants, evaluation of determinants,
area of triangles using determinants. Adjoint and
evaluation of inverse of a square matrix using
determinants and elementary transformations, Test of
consistency and solution of simultaneous linear
equations in two or three variables using determinants
and matrices.

**UNIT-4 : PERMUTATIONS AND COMBINATIONS:**

Fundamental principle of counting, permutation as an
arrangement and combination as selection, Meaning of P (n,r)
and C (n,r), simple applications.

** UNIT-5 : MATHEMATICAL INDUCTION:**

Principle of Mathematical Induction and its simple
applications.

**UNIT-6 : BINOMIAL THEOREM AND ITS 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 SERIES:**

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 series: **∑** n, **∑** **n**^{2},
**∑**n^{3}. Arithmetico - Geometric
progression.

**UNIT-8 : LIMIT, CONTINUITY AND DIFFERENTIABILITY:**

Real - valued functions, algebra of functions,
polynomials, rational, trigonometric, logarithmic and
exponential functions, inverse functions. Graphs of
simple functions. Limits, continuity and
differentiability. 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.

**UNIT-9 : INTEGRAL CALCULUS:**

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.

**Evaluation of simple integrals of the type**

⌠__dx_____,
⌠__dx_______, ⌠__dx_______,
⌠__dx_______, ⌠__dx_______

x^{2}±a^{2
} √ x^{2}±a^{2 }
a^{2 }- x^{2
}√ a^{2 }- x^{2 }
ax^{2}+bx+c

⌠__dx_________
, ⌠__(px+q)dx___, ⌠__(px+q)dx___

√ ax^{2}+bx+c
ax^{2}+bx+c √ ax^{2}+bx+c

**and**

^{dx}