## SOEE2250 Numerical Methods and Statistics

### 10 creditsClass Size: 38

Module manager: Dr Stephen Stackhouse
Email: S.Stackhouse@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2021/22

### Pre-requisites

 SOEE1160 Comp & Prog in Geosciences

This module is not approved as a discovery module

### Module summary

Numerical methods and statistics play a fundamental role in all aspects of geophysical research. This module teaches students the basic techniques needed for careful analysis of experimental data and solving numerical problems.The students will be introduced to the mathematical methods in the lectures and translate these into Python programs in the practical sessions.

### Objectives

The objective of the first part of the module is to introduce students to the most common numerical methods, both theory and implementation in Python. The objective of the second part is for students to learn how to handle and report data with uncertainties in an appropriate manner.

Learning outcomes
Learning outcomes
On completion of this module students should be able to:

1. Derive expressions for simple numerical methods.

2. Solve mathematical problems via recall or use of the appropriate numerical method for finding the roots or optima of functions, solving linear systems of equations, interpolating values, performing numerical integration and differentiation, and solving initial-value and boundary-value problems.

3. State the advantage and disadvantages of different numerical methods and, where appropriate, conditions required for convergence.

4. Handle and report data with uncertainties in an appropriate manner.

### Syllabus

Numerical methods
1. Errors in Numerical Methods
2. Finding Roots
3. One-Dimensional Optimisation
4. Linear Systems - Direct Methods
5. Linear Systems - Iterative Methods
6. Interpolation
7. Numerical Integration
8. Numerical Differentiation
9. Initial-Value Problems
10. Boundary-Value Problems.
Statistics
1. Error Representation
2. Error Propagation
3. Statistical Analysis
4. Normal Distribution
5. Least-Squares Fitting.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 20 1.00 20.00 Practical 10 2.00 20.00 Private study hours 60.00 Total Contact hours 40.00 Total hours (100hr per 10 credits) 100.00

### Private study

Students will be expected to spend time reviewing course material, completing the problems sets and practicals, and practising computer programming.

### Opportunities for Formative Feedback

Students get formative feedback on their weekly computer programming practicals.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Computer programming assessment 30.00 Total percentage (Assessment Coursework) 30.00

The resit for this module will comprise a single unseen examination paper which will form 100% of the resit mark.

Exams
 Exam type Exam duration % of formal assessment Online Time-Limited assessment 1 hr 30 mins 70.00 Total percentage (Assessment Exams) 70.00