1. Differential Calculus (30 hrs)
1.1 Definition of function; Concept of limits. Lt x
n
- a
n
, Four standard limits x → a ---------- x - a
Lt Sin x Lt a
x
- 1 Lt (1+x)1/x
x → 0 -------- , x→ 0 --------, x→
0
x x
1.2 Differentiation by definition of xn
, sin x, cos x, tan x, ex
, logax only
1.3 Differentiation of sum, product and quotient of functions. Differentiation of
function of a function.
1.4 Differentiation of inverse trigonometrical functions, Logarithmic
differentiation, Exponential differentiation, Successive differentiation (upto
third order only).
1.5 Applications:
(a) Maxima and minima
(b) Equation of tangent and normal to a curve (for explicit functions only) – Simple problems only
2. Integral Calculus (25 hrs)
2.1 Integration as inverse operation of differentiation
2.2 Simple standard integrals and related problems
2.3 Simple integration by substitution, by parts and by partial fractions (for
45
linear factors only)
2.4 Evaluation of definite integrals (simple problems)- /2 /2 /2
Evaluation of Sinn x dx, Cosn x dx , Sinm
x Cosn x dx
0 0 0
using formulae without proof (m and n being positive integers only)
2.5 Numerical integration by Simpson’s Rule and Trapezoidal Rule
(simple problems only)
3 Ordinary Differential Equations (10 hrs)
3.1. Definition, order, degree, linear and non-linear differential equations
3.2 Formation of differential equations (upto second order)
3.3. Solution of first order differential equations by variable separable method only
4. Statistics (15hrs)
4.1 Measures of Central Tendency: Mean, Median, Mode
4.2 Measures of Dispersion: Mean deviation, Standard deviation
4.3 Co-efficient of rank correlation