B.E in ENGINEERING MATHEMATICS

1. Differential Calculus :
Unit - I: Successive differentiation. Taylor's and Machauria's series for one variable.Tangents and
Normals, subtangent and subnormal (Cartesian form). Curvature and radius of curvature
(Cartesian, parametric and polar term), center of curvature (cartesian form only), L'Hospital's rule.
Maximum and Minimum function of one variable.
Unit - II: Partial differential function of several variables, first and higher order derivative. Euler's
theorem, chain rules and total differentia co-efficient,Jaco bians Taylor's and Maclaurin's series of
two variables, Maxima & Minima of function of two variables, Lagrange's method of undetermined
multipliers.
2. Analytical Trigonometry :
Unit - III: Cartesian and polar terms of complex numbers, De-moilver's theorem.,hyperbolic
functions and there inverse, Logarithm of complex quantities. Sum mation of series (C+ is
Method)
Section -B
3. Theory of Equations :
Unit-IV: General properties of polynomial equations, between root & coefficients transformation
of equations. Horner's method of synthetic division
4. Integral Calculus :
Unit-V : Beta and Gamma functions. Differentiation of definite Integral, Tracing of curves
(Cartesian & Polar curves) rectification of simple curves, quadrature, volumes and surface of
solids of revolutions (Cartesian, Polar & root mean square values.
5. Analytical Solid Geometry :
Unit-VI : Cartesian, Cylindrical and spherical system of co-ordinates and their transformations.
Details study of lines and planes in Cartesian system. Shift of origin, projection of segment,
projection of Plane, closed curves, projection of lines and planes. Shortest distance between two
lines, Equations of sphere. Right circular cylinder and right circular cone.