Semester-I(HONS): DC01
Deeper properties of Limit, Continuity, Hyperbolic Function, Successive Differentiation etc.
Application of Differential Calculus e.g. Tangent & Normal, Curvature, Asymptotes, Evolute, Envelope etc.
Application of Integral Calculus e.g. Definite Integral as limit of a sum, Arc length, Area under a plane curve, Surface of revolution.
Semester-I(GENS): DC01 UNIT 4
Three dimensional coordinate system, Direction Cosine
Straight Line, Problems
Equation of Plane and elementary properties
Sphere and its tangent plane
Right circular cone
Semester-II(HONS): DC04 UNIT -3 & 4
Ring, Subring, Examples on ring
Divisor of zero, Integral Domain, Characteristic of an Ring
Skew-Field, Field
Ring Homomorphism, Isomorphism
Ideal, Prime and Maximal Ideal
Semester-II(GENS): DC02 UNIT 3
Definite Integral as limit of a sum
Reduction formula and related problems
Improper Integral
Use of Beta and Gama function
Semester-III(HONS): DC05 UNIT -4
Sequence of functions
Continuity, differentiability and integrability of the limit function of a sequence of functions
Sum function of a series of functions
Cauchy criteria for uniform convergence and Weierstrass M-test
Semester-III(HONS): DC06 UNIT -4
Inner Product, Norms
Orthogonal and orthonormal vectors, Gram-Schmidt Orthogonalization process
Adjoint of a linear operator
Semester-III(HONS): DC07 UNIT -3
Triple product of vector
Continuity and Differentiability of vector function
Line and volume integration of vector function
Semester-III(GENS): DC03 UNIT -1
Vector, Linear dependence and independence of vectors
Scalar and vector products
Linear transformation on Euclidean space
Vector equation of plane, straight line and volume of Tetrahedron
Part II:
Linear Programming Problem: Solution of an LPP by Graphical Method, Simplex Method, Charnies Big-M Method, Two Phase Method, Duality, Assignment Problem, Transportation Problem, Travelling Salseman Problem, Game Theory.
Part III:
Metric Space
Tensor Analysis
Rigid Dynamics
Semester-IV(HONS):
DC08 UNIT -3
Power series solution
DC 10 UNIT 01
Probability Theory
UNIT 02
Distribution Function
Semester-V(HONS):
DC 12 :
UNIT 01
Error, Relative error, Absolute Error, Round-off, Bisection method, Newton's method, Secant method, Regula-falsi method, fixed point iteration, Newton-Raphson method.
UNIT 02
Interpolation: Newton's forward & backward interpolation, Stirling and Bessel's interpolation, Gauss Elimination method, Gauss-Seidel method, Gauss-Jacobi method of solution of system of linear equations
UNIT 03
Numerical Integration: Newton Cotes formula, Trapezoidal rule, Simpson's 1/3 rule, Gauss quadrature formula, Solution of ordinary differential equation: Euler's method, Runga-Kutta method
UNIT 04
C programming Language: Data type, if-else Statement, switch statement, while loop, do-while loop, for loop, break and continue, functions, array, simple problems