Math (Diploma Automobile Engineering 1st-2nd)

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