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Basic Details:

  • Course Code: EM 2050
  • Credits: 3
  • Pre-requisites: EM216, EM 217
  • Compulsory/Optional: Compulsory for Mechanical Engineering Specialization

Aim :

The aim of the course is to introduce computational methods with emphasis on numerical methods and Fourier methods, providing students with necessary background on its theoretical, implementation and application aspects.

Intended Learning Outcomes:

On successful completion of the course, the students should be able to;

  • Solve nonlinear equations, linear systems, interpolate, initial-value problems and boundary value problems numerically; perform interpolation and integration
  • Describe the principles of Fourier analysis; apply Fourier methods to solve boundary value problems
  • Analyze convergence and computational cost of computational methods
  • Implement computational methods on a programming language
  • Apply computational methods to solve some practical engineering problems

Couse Content:

Floating point arithmetic, Big O notation, matrix norms, review of programming (e.g. MATLAB / GNU Octave / Python)

Bisection method, Newton's methods, convergence

LU factorization, iterative methods (Jacobi, Gauss-Seidel), convergence, computational cost

Lagrange, trigonometric interpolation

mid-point rule, trapezoidal rule

Euler methods, stability, consistency, convergence, applications

Finite Difference Methods, Finite Element Methods, convergence, applications

Fourier series, Fourier transform, Discrete Fourier Transform, Fourier methods to solve BVP, applications

Time Allocation (Hours):

Lectures
0
Assignments
0
Practicals
0

Recommended Texts:

  • Ackleh et al. Classical and Modern Numerical Analysis,1st Edition(2009) Chapman and Hall/CRC.
  • Quarteroni et al. Scientific Computing with MATLAB and Octave,2nd Edition(2014) Springer.
  • Strang. Computational Science and Engineering,1st Edition(2007), Wellesley Cambridge Press
  • Gockenbach. Partial Differential Equations: Analytical and Numerical Methods,2nd Edition
    (2002)SIAM.

Assessment:

In - course:

Tutorials/Assignments/Quizzes
40%

End-semester:

60%