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MATLAB programming: Data types and structures, arithmetic operations, functions, input and output, interface programming, graphics; implementation of numerical methods.
Introduction: Finite floating point arithmetic, catastrophic cancellation, chopping and rounding errors.
A selection of the following topics will be covered:
Solution of nonlinear equations: Bisection method, secant method, Newton's method, fixed point iteration, Muller's method.
Numerical optimization: Newton's optimization method.
Solutions of linear algebraic equations: Forwarding Gaussian elimination, pivoting, scaling, back substitution, LU-decomposition, norms and errors, condition numbers, iterations, Newton's method for systems, computer implementation.
Interpolation: Lagrange interpolation, Newton interpolation, inverse interpolation.
Numerical Integration: Finite differences, Newton cotes rules, trapezoidal rule, Simpson's rule, extrapolation, Gaussian quadrature.
Numerical solution of ordinary differential equations: Euler's method, Runge-Kutta method, multi-step methods, predictor-corrector methods, rates of convergence, global errors, algebraic and shooting methods for boundary value problems, computer implementation.
NOTE: Students must have a laptop computer.
Introduction: Finite floating point arithmetic, catastrophic cancellation, chopping and rounding errors.
A selection of the following topics will be covered:
Solution of nonlinear equations: Bisection method, secant method, Newton's method, fixed point iteration, Muller's method.
Numerical optimization: Newton's optimization method.
Solutions of linear algebraic equations: Forwarding Gaussian elimination, pivoting, scaling, back substitution, LU-decomposition, norms and errors, condition numbers, iterations, Newton's method for systems, computer implementation.
Interpolation: Lagrange interpolation, Newton interpolation, inverse interpolation.
Numerical Integration: Finite differences, Newton cotes rules, trapezoidal rule, Simpson's rule, extrapolation, Gaussian quadrature.
Numerical solution of ordinary differential equations: Euler's method, Runge-Kutta method, multi-step methods, predictor-corrector methods, rates of convergence, global errors, algebraic and shooting methods for boundary value problems, computer implementation.
NOTE: Students must have a laptop computer.
About this Module
Student Effort Hours:
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Requirements, Exclusions and Recommendations
Not applicable to this module.
Module Requisites and Incompatibles
Not applicable to this module.
Assessment Strategy
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Carry forward of passed components
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| Terminal Exam |
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| Name | Role |
|---|---|
| Dr James Herterich | Lecturer / Co-Lecturer |
| Ms Claire Bergin | Tutor |
| Constantinos Menelaou | Tutor |