Careers360 Logo
Browse by Stream
Search Colleges, Exams, Schools & more
Interested in this College?
Get updates on Eligibility, Admission, Placements Fees Structure
Compare

Quick Facts

Medium Of InstructionsMode Of LearningMode Of Delivery
EnglishSelf StudyVideo and Text Based

Important dates

Course Commencement Date

Start Date : 20 Jan, 2025

End Date : 11 Apr, 2025

Enrollment Date

End Date : 27 Jan, 2025

Certificate Exam Date

Start Date : 03 May, 2025

Other

End Date : 14 Feb, 2025

Courses and Certificate Fees

Fees InformationsCertificate AvailabilityCertificate Providing Authority
INR 1000yesIIT Kharagpur

The Syllabus

  • 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.

  • Differential Equations – first order, solution of first order ODEs
  • Integrating factor, exact forms, second order ODEs, auxiliary solutions

  • 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.

  • Finite differences, interpolation, error in interpolation polynomials
  • Newton’s forward and backward interpolation formulae
  • Lagrange’s interpolation 
  • Numerical integration: Trapezoidal and Simpson’s 1/3rd and 3/8th rule.

  • 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

Instructors

Articles

Similar College

Similar Courses

Conduction and Convection Heat Transfer

Indian Institute of Technology Kharagpur via  SwayamNPTEL

Years 1Free

Computational Fluid Dynamics for Incompressible Flows

Indian Institute of Technology Guwahati via  SwayamNPTEL

Years 1Free

Computational Fluid Dynamics

Indian Institute of Technology Madras via  SwayamNPTEL

Years 1Free
View All Courses

More Courses by IIT Kharagpur

Comprehensive Molecular Diagnostics and Advanced Gene Expression Analysis

Indian Institute of Technology Kharagpur via  SwayamNPTEL

Years 1Free

Combustion of Solid Fuels and Propellants

Indian Institute of Technology Kharagpur 

Months 8Free

Constrained And Unconstrained Optimization

Indian Institute of Technology Kharagpur via  SwayamNPTEL

Years 1Free
View All Courses

Explore on Careers360

Download Careers360 App
All this at the convenience of your phone

  • Regular Exam Updates

  • Best College Recommendations

  • College & Rank predictors

  • Detailed Books and Sample Papers

  • Question and Answers

Scan and download the app

OR

Back to top