IIT Kgp 1st year syllabus

I want to get information about the Syllabus for I year subjects and Basic Electronics (3rd semester course). So here can you provide me information about it?

[Shaleen]

I would like to tell you about the Syllabus for I year subjects and Basic Electronics (3rd semester course), as you want.

Syllabus for I year subjects and Basic Electronics (3rd semester course)
MA 10001 Mathematics-I (3-1- 0 4)

Differential Calculus:
Rolle's theorem, Cauchy's mean value theorem (Lagrange's mean value theorem as a special case), Taylor's and Maclaurin's theorems with remainders, indeterminate forms, concavity and convexity of a curve, points of inflexion, asymptotes and curvature. Limit, continuity and differentiability of functions of several variables, partial derivatives and their geometrical interpretation, differentials, derivatives of composite and implicit functions, derivatives of higher order and their commutativity, Euler's theorem on homogeneous functions, harmonic functions, Taylor's expansion of functions of several variables, maxima and minima of functions of several variables - Lagrange's method of
multipliers.


Ordinary Differential Equations:
First order differential equations - exact, linear and Bernoulli's form, second order differential equations with constant coefficients, method of variation of parameters, general linear differential equations with constant coefficients, Euler's equations, system of differential equations.


Complex Variables:
Limit, continuity, differentiability and analyticity of functions, Cauchy-Riemann equations, line integrals in complex plane, Cauchy-Goursat theorem, independence of path, existence of indefinite integral, Cauchy's integral formula, derivatives of analytic functions, Power series, Taylor's series, Laurent's series, Zeros and singularities, Residue theorem, evaluation of real integrals.


Integral Calculus:
Fundamental theorem of integral calculus, mean value theorems, evaluation of definite integrals - reduction formulae.


MA 10002 Mathematics-II (3-1-0 4)


Linear Algebra:
Algebra of matrices. Vector spaces - linear dependence of vectors, basis, linear transformations, rank and inverse of a matrix, solution of algebraic equations - consistency conditions, Hermitian, skew Hermitian and unitary matrices, bilinear forms, eigenvalues and eigenvectors.



Integral Calculus:
Convergence of improper integrals, tests of convergence, Beta and Gamma functions - elementary properties. Differentiation under integral sign, differentiation of integrals with variable limits - Leibnitz rule. Rectification, double and triple integrals, computations of area, surfaces and volumes, change of variables in double integrals - Jacobians of transformations, integrals dependent on parameters - applications.


Vector Calculus:
Scalar and vector fields, level surfaces, directional derivative, Gradient, Curl, Divergence, Laplacian, line and surface integrals, theorems of Green, Gauss and Stokes, line integrals independent of path.


Numerical Analysis:
Finite differences, Newton's forward and backward interpolation formulae, central difference interpolation formulae. Trapezoidal and Simpson's 1/3rd rules for numerical integration. Solution of polynomial and transcendental equations - bisection, Newton-Raphson and regula falsi methods. Numerical solution of system of linear equations – Gauss, Gauss-Jordan elimination and Gauss-Seidel iteration methods.


For more information, please contact;

Address:
Indian Institute of Technology Kharagpur  
University
Kharagpur, West Bengal 721302
Phone: 03222 255 221