The Computational Science in Engineering is a rapidly evolving field that exploits the power of computation as an approach to major challenges on the frontiers of natural and social science and all engineering fields. The primary focus lies on developing problem-solving methodologies and robust tools for numerical simulation. The goal is to present the fundamentals of scientific computing, with short codes to implement the key concepts. This includes a framework for applied mathematics such as Linear Algebra, ODEs and PDEs. To understand phenomena and processes from science and engineering, these simulations require advanced skills in mathematical modelling, numerical analysis, efficient algorithms, computer architecture, software design and implementation, validation, and visualization of results. 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
Overview
Syllabus
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 Transforms
Week 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)
Week 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
