1. Differential Calculus:
a. Successive differentiation, Leibnitz theorem, Taylor & Maclaurin's expansions, In determinant forms,.
b. Tracing of curves- asymptotes (parallel to axis & oblique), Tracing of Cartesian, Parametric & Polar curves.
c. Partial Diff. - Partial & Total Differential co-efficient, Euler's theorem, Transformations, Geometrical interpretation of partial derivatives, Tangent plane & normal plane, Jacobians, Taylor's expansion for two variables, Errors and approximations, Maxima And Minima of function of two variables, Lagrange's method of undetermined multipliers to determine stationary values.
2. Integral Calculus :
a. Reduction formulae for the type f p/4 sinn x dx, f p/2 cosn x dx, f p/2 sinm x cosn x dx. f p/4 tann x dx, f p/4 cotn x dx (m,n are positive integers), Beta Gamma & Error functions, Elliptical functions, fř..........o < k < 1, fř ........... (1-k2 sin2x)˝ do, 0 < k < 1 (1-k2 sin2x)˝ also at ř = f p/2
b. Application of integration-area of bounded region, length of a curve, volume & surface area of solid of revolution for Cartesian, Parametric & Polar Curves.
c. Multiple integrals - Double integral, Change of order of integration, Transformation of variables by Jacobian only for double integration, Change to polar co-ordinates in double integration only, Triple integral, Application multiple integration to find Areas, Volumes, C.G., M.I. & Mean values.
3. Complex Numbers : De Moivre's theorem and its application, function of complex variables - exponentials, Hyperbolic, Inverse hyperbolic, Trigonometric & Logarithmic.
4. Infinite Series : Definition, Comparison test, Cauchey's integral test, Ratio test, Root test, Leibnitz's rule for alternating series, Power series, Range of convergence, Uniform convergence.
5. Matrix Algebra : Elementary transformations & rank, inverse by elementary transformation, Normal form of a matrix, Consistency of system of linear equation, solution of system of equations, linearly dependant vectors in R3, Linear and orthogonal transformations, Eigen values and eigen vectors.
6. Differential Equation and Modeling : Modeling of engg. systems (leading to ODE of 1st order, 1st degree, including orthogonal trajectories), exact differential equation & integrating factors, Unified approach to solve first order equations, Linear, Reducible to linear, Applications including modeling, Solution of 1st order and higher degree differential equations (Clairut's equation only).
Books for Study :
(1) Applied Mathematics vol-I by P.N. Wartikar & J.N. Wartikar
(2) Higher Engg. Mathematics by Dr. B.S. Grewal
(3) Engineering Mathematics by Shrivastva
Books for Reference :
(1) Engineering Mathematics Part I & II by Shantinarayan
(2) Text Book of Engineering Mathematics by Mathur & Jaggi
(3) A First Course in Mathematics for Engineers by Chandrika Prasad
