Quick Facts

Medium Of Instructions	Mode Of Learning	Mode Of Delivery
English	Self Study	Video and Text Based

Courses and Certificate Fees

Fees Informations	Certificate Availability	Certificate Providing Authority
INR 1000	yes	IIT Kharagpur

Differentiability
Lagrange’s mean value theorem
Cauchy’s mean value theorem
Taylor’s and Maclaurin’s theorem
Functions of several variables: Limit, continuity, partial derivatives and their geometrical interpretation, total differential and differentiability
Derivatives of composite and implicit functions, implicit function theorem, derivatives of higher order and their commutativity
Euler’s theorem on homogeneous functions, Taylor’s expansion of functions, maxima and minima, constrained maxima/minima problems using Lagrange’s method of multipliers

Convergence of improper integral, test of convergence, Gamma and Beta functions, their properties, differentiation under the integral sign
Leibnitz rule of differentiation Double and triple integral, change of order of integration, change of variables, Jacobian transformation, Fubini theorem, surface, area and volume integrals, integral dependent on parameters applications
Surface and Volume of revolution. Calculation of center of gravity and center of mass.

Numerical analysis: Iterative method for solution of system of linear equations
Jacobi and Gauss-Seidal method, solution of transcendental equations: Bisection, Fixed point iteration, Newton-Raphson method.

Vector spaces, basis and dimension, Linear transformation, linear dependence and independence of vectors
Gauss elimination method for system of linear equations for homogeneous and nonhomogeneous equations

Rank of a matrix, its properties, solution of system of equations using rank concepts
Row and Column reduced matrices, Echelon Matrix, properties

Hermitian, Skew Hermitian and Unitary matrices, eigenvalues, eigenvectors, its properties, Similarity of matrices, Diagonalization of matrices

Scalar and vector fields, level surface, limit, continuity and differentiability of vector functions, Curve and arc length, unit vectors, directional derivatives

Divergence, Gradient and Curl, Some application to Mechanics, tangent, normal, binormal, Serret-Frenet Formulae, Application to mechanics

Line integral, parametric representations, surface integral, volume integral, Gauss divergence theorem, Stokes theorem, Green’s theorem

Limit, continuity, differentiability and analyticity of functions
Cauchy-Riemann equations, line integrals in complex plane Cauchy’s integral formula, derivatives of analytic functions, Cauchy’s integral theorem
Taylor’s series, Laurent series, zeros and singularities, residue theorem, evaluation of real integrals