NPTEL : NOC:Computational Science in Engineering (Aerospace Engineering)

Co-ordinators : Prof. Ashoke De


Lecture 1 - Linear Algebra: Introduction

Lecture 2 - Linear Algebra: Introduction (Continued...)

Lecture 3 - Linear Algebra: Permutation Matrix, Existence of Solution

Lecture 4 - Linear Algebra: Permutation Matrix, Existence of Solution (Continued...)

Lecture 5 - Linear Algebra: Linear Independence, Basis Vector and Dimensions

Lecture 6 - Linear Algebra: Null Space, Column Space, Row Space, Introduction to Orthogonal System

Lecture 7 - Linear Algebra: Orthogonal System, Projection, Determinant

Lecture 8 - Linear Algebra: Orthogonal System, Projection, Determinant (Continued...)

Lecture 9 - Linear Algebra: Properties of Determinant, Cramer's Rule, Introduction to Eigen Values

Lecture 10 - Linear Algebra: Eigen Values, Eigen Vectors, SVD

Lecture 11 - Linear Algebra: Eigen Values, Eigen Vectors, SVD (Continued...)

Lecture 12 - ODE: Introduction to ODEs, Initial Value Problem, Separation of Variables

Lecture 13 - ODE: Solution of Exact ODEs, First Order Linear Systems

Lecture 14 - ODE: Solution of Second Order Linear ODEs

Lecture 15 - ODE: Existence and Uniqueness of Solution, Non-Homogeneous System

Lecture 16 - ODE: Higher Order Linear ODEs, Variation of Parameters, System of ODEs

Lecture 17 - ODE: Linear Systems, Superposition for Homogeneous Systems

Lecture 18 - Fourier Analysis, Orthogonality of Trigonometric Systems, Euler's Formula

Lecture 19 - Parseval's Theorem, Fourier Integrals, Laplace Transforms

Lecture 20 - PDE: Introduction to PDEs, Solution of PDEs using Characteristics Curve

Lecture 21 - PDE: First Order PDEs, Dilation Invariant Solution of Differential Equations

Lecture 22 - PDE: Solution of Linear PDEs

Lecture 23 - PDE: Separation of Variables, Eigenvalue Problem, Poisson Integral Representation

Lecture 24 - PDE: Boundary Conditions, Solution of 2D systems

Lecture 25 - Introduction to Numerical Methods, Mathematical Models, Errors

Lecture 26 - Errors, Numerical Differentiation, Stability

Lecture 27 - Roots of Equations: Graphical Method, Bi-Section Mehtod, False-Position Method

Lecture 28 - Secant Method, Brent's Method, Multipoint Iteration Method, Derative Free Method

Lecture 29 - Complex Roots, Birge-Vieta Method, Bairstow's method

Lecture 30 - Solution of Linear Algebric Equations, Gauss Elimination Method

Lecture 31 - Direct Methods: Gauss Elimination, Gauss-Jordan, Crout's Method, Cholesky Method, Iterative Methods: Jacobi Iteration Method, Gauss-Seidel

Lecture 32 - Extrapolation Method, Eigenvalue Problem, Jacobi Method, Householder's Method for Symmetric Matrices, Power Method, Inverse Power Method

Lecture 33 - Interpolation: Taylor's Series, Lagrange and Newton Interpolation, Iterated Interpolation, Hermite Interpolation, Finite Difference Operations

Lecture 34 - Piecewise and Spline Interpolation, Bivariate Interpolation, Least Square Approximation, Uniform Polynomial Approximation

Lecture 35 - Numerical Differentiation and Intergration, Methods Based on Finite Differences, Methods based on Undetermined Coefficients, Extrapolation Methods, Partial Differentiation

Lecture 36 - Numerical Integration: Newton-Cotes Method, Gaussian Integration Methods, Lobatto Integration Method, Radau Integration Method, Composite Integration Methods

Lecture 37 - Double Integration: Trapezoidal Rule, Simpson's Rule, Solution of ODEs: Difference Equation, Single Step Methods, Explicit Methods

Lecture 38 - Runge-Kutta Methods, Euler-Cauchy Method, Multi-step Methods, Predictor-Corrector Methods

Lecture 39 - System of Differential Equations, Stability Analysis, Solution of Boundary Value Problem: Shooting Method

Lecture 40 - Numerical Approach to Solution of PDEs: Heat Conduction Equation, Convergence and Stability