Description:
| Aims: To teach those aspects of Numerical Analysis which are most relevant to a general mathematical training, and to lay the foundations for the more advanced courses in later years.
Learning Outcomes: After taking this unit, students should be able to:
* Demonstrate knowledge of simple methods for the approximation of functions and integrals, solution of initial value problems for ordinary differential equations and the solution of linear systems
* Use basic methods for the analysis of the errors made in these methods.
* Show awareness of some of the relevant practical issues involved in their implementation, including coding of algorithms using MATLAB.
* Write the relevant mathematical arguments in a precise and lucid fashion.
Skills: Numeracy T/F A
Problem Solving T/F A
Computation skills T/F A
Written and Spoken Communication F (in tutorials).
Content: MATLAB Programming for Numerical Analysis: Floating point numbers and rounding error.
Concepts of Convergence and Accuracy: Order of convergence, extrapolation and error estimation.
Approximation of Functions: Polynomial interpolation, error analysis.
Numerical Integration: Newton-Cotes formulae. Gauss quadrature. Composite formulae. Error analysis.
Numerical Solution of ODEs: Euler, Backward Euler, Trapezoidal and explicit Runge-Kutta methods. Stability. Consistency and convergence for one step methods. Error estimation and control.
Linear Algebraic Equations: Gaussian elimination, LU decomposition, pivoting, Matrix norms, conditioning, backward error analysis, iterative refinement.
Coding of algorithms: in MATLAB.
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