# ACM40290 Numerical Algorithms

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.

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Curricular information is subject to change

Learning Outcomes:

(1) Knowledge and Understanding. Having successfully completed the module, you will be able to demonstrate knowledge and understanding from a selection of:

Numerical methods to solve systems of linear equations.
Numerical methods to solve nonlinear equations.
Numerical methods to solve optimisation problems.
Numerical methods to solve interpolation problems.
Numerical methods to solve simple differential equations.

(2) Intellectual Skills. Having successfully completed the module, you will be able to:

Analyse a mathematical problem and determine which numerical technique to use to solve it.
Show logical thinking in coding a mathematical problem in algorithmic form.

(3) Practical Skills. Having successfully completed the module, you will be able to:

Use Matlab, its instructions and its programming language.
Use your knowledge of Matlab to learn more easily any other programming language you will need to use in future.

Student Effort Hours:
Student Effort Type Hours
Lectures

18

Computer Aided Lab

12

Autonomous Student Learning

64

Total

94

Approaches to Teaching and Learning:
Lectures, computer-based tutorials, enquiry and problem-based learning.
Requirements, Exclusions and Recommendations
Learning Recommendations:

Students are recommended to have previous knowledge of Linear Algebra, Calculus (Taylor series) and Computational Methods (ACM20030 or equivalent).

Module Requisites and Incompatibles
Equivalents:
Numerical Algorithms (MAPH40290)

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Assignment: Individual take-home assignments Throughout the Trimester n/a Standard conversion grade scale 40% No

40

Examination: End of Trimester Exam 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

60

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour
Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Name Role
Dr James Herterich Lecturer / Co-Lecturer
Ms Claire Bergin Tutor
Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.

Autumn

Lecture Offering 1 Week(s) - 1, 2, 3, 6, 7, 8, 10, 11, 12 Mon 11:00 - 11:50
Lecture Offering 1 Week(s) - 4, 5 Mon 11:00 - 11:50
Lecture Offering 1 Week(s) - 9 Mon 11:00 - 11:50
Tutorial Offering 1 Week(s) - Autumn: All Weeks Thurs 12:00 - 12:50
Lecture Offering 1 Week(s) - Autumn: All Weeks Wed 12:00 - 12:50
Autumn