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ACM20030

Academic Year 2024/2025

Computational Science (ACM20030)

Subject:
Applied & Computational Maths
College:
Science
School:
Mathematics & Statistics
Level:
2 (Intermediate)
Credits:
5
Module Coordinator:
Dr Niels Warburton
Trimester:
Autumn
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

Most problems in Applied Mathematics are modelled using a set of equations that can be written down but cannot be solved analytically. In this module we examine numerical methods that can be used to solve such problems with a computer. Practical computer lab sessions will cover the implementation of these methods using mathematical software (Python). No previous knowledge of computing is assumed.

Topics and techniques discussed include but are not limited to the following list:

- The programming environment: installing and running Python, version control with Git
- Introduction to programming: functions, loops, logical statements, arrays, floating-point arithmetic, data storage, debugging code, documentation
- Visualising results and datasets: plotting using Matplotlib and other visualisation software
- Interpolation: Lagrange polynomials, Newton's divided-difference. Linear least squares
- Root-finding for single-variable functions: Bracketing and Bisection, Newton–Raphson method. Error and reliability analyses for the Newton–Raphson method.
- Solving ordinary differential equations (ODEs): Euler Method, Runge–Kutta method. Shooting methods. Error analysis.
- Numerical integration: Midpoint, Trapezoidal and Simpson methods. Error analysis.
- Matrices: condition numbers, inversion

About this Module

Learning Outcomes:

On completion of this module students should be able to

- Run Python code via interactive Jupyter notebooks
- Use version control software
- Write simple programs involving input/output, plotting, loops, conditionals and functions
- Describe and implement different methods for interpolation.
- Describe and implement elementary root-finding procedures.
- Solve ODEs numerically using standard algorithms, analyse their accuracy and stability, and implement them numerically.
- Describe elementary numerical integration integration schemes, analyse their accuracy, and implement them.
- Describe elementary numerical algorithms for computing properties of matrices

Student Effort Hours:
Student Effort Type Hours
Lectures

18
Computer Aided Lab

24
Specified Learning Activities

40
Autonomous Student Learning

24
Total

106

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning

Requirements, Exclusions and Recommendations
Learning Recommendations:

Students are recommended to have successfully completed level one courses in calculus and algebra, along the lines of the following module pairs:

1. MATH10300 - Calculus in the Mathematical Sciences and MATH10270 - Linear Algebra in the Mathematical Sciences

2. MATH10330 - Calculus in the Phy Sciences and MATH10280 - Linear Algebra in the Physical Sciences


Module Requisites and Incompatibles
Not applicable to this module.
 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Assignment(Including Essay): A combination of written and coding-based assignments and in class practical exercises Week 1, Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10, Week 11, Week 12 Alternative linear conversion grade scale 40% No
20
 No
Exam (In-person): Written exam End of trimester
Duration:
2 hr(s)
 Alternative linear conversion grade scale 40% No
50
 No
Exam (In-person): Coding-based in-class tests Week 8, Week 10 Alternative linear conversion grade scale 40% No
30
 No

Carry forward of passed components
No
 

Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Name Role
Mr Kevin Cunningham Tutor
Mr Daire O'Donovan Tutor
Mr Brian Skelly 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 17:00 - 17:50
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Wed 13:00 - 13:50
Autumn Computer Aided Lab Offering 1 Week(s) - Autumn: All Weeks Fri 15:00 - 15:50
Autumn Computer Aided Lab Offering 1 Week(s) - Autumn: All Weeks Mon 11:00 - 11:50
Autumn Computer Aided Lab Offering 2 Week(s) - Autumn: All Weeks Fri 10:00 - 10:50
Autumn Computer Aided Lab Offering 2 Week(s) - Autumn: All Weeks Tues 13:00 - 13:50
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