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)