## GEOG3020 Numerical Methods and Statistics

### 10 creditsClass Size: 40

Module manager: Prof Andy Baird
Email: a.j.baird@leeds.ac.uk

Taught: Semester 1 View Timetable

Year running 2019/20

### Pre-requisites

 SOEE1160 Comp & Prog in Geosciences

### This module is mutually exclusive with

 SOEE2250 Numerical Methods & Statistics

This module is not approved as a discovery module

### Objectives

Students are introduced to the most common numerical methods and their implementation in Python. They also learn how to handle and report data with uncertainties in an appropriate manner. They are required to think and write about the role of simulation in physical geography.

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

1. Design and implement computer programs to solve numerical problems that would be impossible or time-consuming to complete by hand, and understand their limitations.

2. Derive expressions for simple numerical methods.

3. 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.

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

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

6. Evaluate the role of numerical methods in environmental models and the need to consider data uncertainty when setting up and testing such models.

### 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.
The wider context: the use of simulation in physical geography.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 11 2.00 22.00 Practical 10 2.00 20.00 Private study hours 58.00 Total Contact hours 42.00 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. They will also spend time reading on the role of simulation in physical geography.

### Opportunities for Formative Feedback

Problems sets will be given out in the lectures and reviewed in subsequent lectures. Students will receive oral and written feedback on their computer programs.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment In-class computer programming assignment coupled with a short report on the role of simulation in physical geography (1000 words, short-answer format) 40.00 Total percentage (Assessment Coursework) 40.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 1 hr 30 mins 60.00 Total percentage (Assessment Exams) 60.00

Students who fail the module will be required to resit any failed component.