Computational Science in Engineering
Indian Institute of Technology Kanpur and NPTEL via Swayam
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Overview
INTENDED AUDIENCE :Freshman/Sophomore undergraduate students and postgraduate students of Aerospace/Mechanical/Chemical/Civil EngineeringPREREQUISITES : Basics of Mathematics and programmingINDUSTRIES SUPPORT :Aerospace, Automobile, Chemical and Power Generation and Defense Industries
Syllabus
COURSE LAYOUT
Week 1:Linear Algebra: Introduction to Vectors, Vector spaces and subspaces, Solving Linear systemsWeek 2:Linear Algebra: Orthogonality, Determinants, Eigenvalues & Eigen vectors, SVDWeek 3:Ordinary Differential Equations: ODE, homogeneous and non-homogeneous ODEs, second order linear ODE, higher order ODEsWeek 4:Solution of Higher Order ODEs, Fourier Analysis, Fourier Integrals, Laplace TransformsWeek 5:Partial Differential Equations: Classification, 1D & 2D equations, BC, 2nd order PDEsWeek 6:Basis of numerical analysis, errors, stability, Interpolation and extrapolationWeek 7:System of linear algebraic equations and eigenvalue problems: Direct methods, Iterative methods, convergence analysis, Eigenvalues and Eigenvectors, bounds on eigenvalues, Methods for symmetric matrices and arbitrary matricesWeek 8:Solution of ODEs: Difference equation, Numerical methods, convergence, stability, Single step and multistep methods, Predictor-corrector methods, stability analysis of multistep methods, IVP (shooting methods), BVP (methods and solutions)
Taught by
Prof. Ashoke De
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