MATH1 (Diploma Mechanical Engineering 1st-2nd)

1. Algebra 

1.1 Complex Numbers: Definition, real and imaginary parts of a

Complex number, polar and Cartesian, representation of a complex

number and its conversion from one form to other, conjugate of a

complex number, modulus and amplitude of a complex number

Addition, Subtraction, Multiplication and Division of a complex

number. De-movier’s theorem, its application.

1.2 Partial fractions (linear factors, repeated linear factors

1.3 Permutations and Combinations: Value of npr ncr. Simple

problems

1.4 Binomial theorem (without proof) for positive integral index

(expansion and general form); binomial theorem for any index

(expansion without proof) first and second binomial approximation

with applications to engineering problems(25 hrs)

2. Trigonometry (25 hrs)

 2.1 Concept of angles, measurement of angles in degrees, grades and

radians and their conversions.

 2.2 T-Ratios of Allied angles (without proof), Sum, difference formulae

and their applications (without proof). Product formulae

(Transformation of product to sum, difference and vice versa). TRatios

of multiple angles, sub-multiple angles (2A, 3A, A/2).

 2.3 Graphs of

3. Differential Calculus (30 hrs)

3.1 Definition of function; Concept of limits.

 Four standard limits

 3.2 Differentiation by definition of

3.3 Differentiation of sum, product and quotient of functions.

Differentiation of function of a function.

3.4 Differentiation of trigonometric inverse functions. Logarithmic

differentiation. Exponential differentiation Successive differentiation

(excluding nth order).

3.5 Applications:

 (a) Maxima and minima

(b) Equation of tangent and normal to a curve (for explicit

functions only)