Computational Science in Engineering free videos and free material uploaded by IIT Kanpur Staff .
Week 1:Linear Algebra: Introduction to Vectors, Vector spaces and subspaces, Solving Linear systems
Week 2:Linear Algebra: Orthogonality, Determinants, Eigenvalues & Eigen vectors, SVD
Week 3:Ordinary Differential Equations: ODE, homogeneous and non-homogeneous ODEs, second order linear ODE, higher order ODEs
Week 4:Solution of Higher Order ODEs, Fourier Analysis, Fourier Integrals, Laplace Transforms
Week 5:Partial Differential Equations: Classification, 1D & 2D equations, BC, 2nd order PDEs
Week 6:Basis of numerical analysis, errors, stability, Interpolation and extrapolation
Week 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 matrices
Week 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)
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 Engineering
PREREQUISITES : Basics of Mathematics and programming
INDUSTRIES SUPPORT :Aerospace, Automobile, Chemical and Power Generation and Defense Industries
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