Courses
EGN3454 Numerical Methods For Engineers
Major topic areas covered:
Linear algebra - Matrix properties, LU decomposition, exact inversion, iterative inversion, eigenvalues, spectral radius, banded matrices
Root finding – E.g., bisection, Newton-Raphson
Interpolation - Curve fitting, e.g., linear regression, Lagrangian polynomial, least squares
Integration – E.g., trapezoidal, Simpsons rule, Gaussian quadrature
Differentiation - Finite difference, Taylor series, high-order difference schemes, error in differencing
PDEs - Classification, integration using RK methods
Numerical solutions for PDEs - E.g., Jacobi iteration, Point Gauss-Seidel, Line Gauss-Seidel, ADI
Fundamentals of error analysis in computing
EML5725 Computational Fluid Dynamics
Major topic areas covered:
Governing equations of fluids and their classification
Basics of finite volume and finite difference techniques in CFD (code development)
Fundamentals of discretization
Concepts in numerical diffusion, stability, and Von Neumann stability/error analysis
Solution of convection-diffusion problem (code development)
Solution of elliptic equations - heat conduction problem (code development)
A basic algorithm to solve incompressible flows (code development)
A basic algorithm to solve compressible flows - subsonic scenarios (code development)
A basic algorithm to solve compressible flows - supersonic scenarios (code development)
EML5060 Mathematical Analysis For Mechanical Engineering 1
Major topic areas covered:
Calculus: Properties of functions (slopes, intercepts, asymptotes, etc.), maxima/minima, Optimization, Lagrangian Multipliers, Taylor series, Fourier series, Vectors, planes
Ordinary Differential equations: First order ODEs - solution techniques, Homogenous/inhomogeneous, linear/nonlinear, Laplace transform based solutions, discontinuous functions, Higher-order ODEs, Some applied problems in mechanical systems
Linear algebra: Vector spaces, Matrix operations/manipulations, linear dependence, Solutions techniques for linear systems, row/column spaces, Eigenvalue concepts, orthonormalization, special matrices