Scientific Computing using Python

ABOUT THE COURSE:Computation has become an essential tool in science and engineering. In this course, we introduce Python programming language, after which we will cover basics of computational methods. The students will be asked to the solution in Python, which the de facto language now. Topics to be discussed include interpolation, integration, differentiation, ODE and PDE solvers, basic linear algebra, and Monte Carlo techniques. These topics form essential computing tools for computational courses in science and engineering.INTENDED AUDIENCE: PG students of Science and Engineering (Specially Physics, Mathematics, Mechanical, Aerospace, Computer science and Chemical Engineering). Advance UG students too can take this course.PREREQUISITES: Basic knowledge of calculus, linear algebra, and ordinary and partial differential equations. Basic knowledge of computation is recommended.INDUSTRY SUPPORT: Companies involved in Computational fluid dynamics, computational electrodynamics, data sciences, finance, etc.

Week 1: Module 1:About ComputersModule 2:Python variablesModule 3:Python arraysWeek 2: Module 1:Python Control StructureModule 2:Python functionsModule 3:Programming styleWeek 3: Module 1:PlottingModule 2:Data input/outputModule 3:Error analysis and nondimensionalizationWeek 4: Module 1:Lagrange InterpolationModule 2:SplinesWeek 5: Module 1:Numerical Integration: Newton CotesModule 2:Gaussian quadratureModule 3:Multidimensional and misc integrationWeek 6: Module 1:DifferentiationModule 2:ODE solvers: Euler methodModule 3:ODEs: Implicit schemesWeek 7: Module 1:ODEs: Higher-order methodModule 2:ODEs: System of eqns, Stiff equationsModule 3:Fourier TransformsWeek 8: Module 1:Spectral method (PDE solvers): Diffusion equationModule 2:Spectral method: Wave and Burger eqn solverModule 3:Spectral: Navier-Stokes eqn solverModule 4:Spectral: Schrodinger eqn solverWeek 9: Module 1:Finite Difference (FD) (PDE solvers): Diffusion equationModule 2:FD method: Wave and Burger eqn solverModule 3:FD Method: Navier-Stokes eqn solverModule 4:FD Method: Schrodinger eqn solverWeek 10: Module 1:Solving Nonlinear Equations (Root finders)Module 2:Boundary value problems (Shooting method)Module 3:Eigenvalue solver for diff equatonsWeek 11: Module 1:Lapace equation solversModule 2:Lapace equation solversModule 3:Poisson equation solversWeek 12: Module 1:Linear algebra: Solution of linear equationsModule 2:Linear algebra: Eigenvalues and eigenvectorsModule 3:Intro to Monte Carlo methodModule 4:Summary