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# ACM40290

#### Numerical Algorithms (ACM40290)

Subject:
Applied & Computational Maths
College:
Science
School:
Mathematics & Statistics
Level:
4 (Masters)
Credits:
5
Module Coordinator:
Dr James Herterich
Trimester:
Autumn
Mode of Delivery:
On Campus
Internship Module:
No

Curricular information is subject to change.

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.

###### 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

70

Total

100

###### 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 Invalid Option
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Assignment(Including Essay): Individual exercises - 4 sets each worth 10% Week 4, Week 6, Week 8, Week 11 Alternative linear conversion grade scale 40% No
40
No
Exam (In-person): Final written exam End of trimester
Duration:
2 hr(s)
Alternative linear conversion grade scale 40% No
60
No

###### Carry forward of passed components Invalid Option
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
Constantinos Menelaou 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) - Autumn: All Weeks Mon 11:00 - 11:50
Autumn Tutorial Offering 1 Week(s) - Autumn: Weeks 2-12 Thurs 12:00 - 12:50
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Wed 12:00 - 12:50