MA14710 Mathematical Methods and Modelling 1
Introductory description
The module introduces the fundamentals of mathematical modelling and scaling analysis, before discussing and analysing difference and differential equation models in the context of physics, chemistry, engineering as well as the life and social sciences.
Module aims
To introduce the basic concepts of ODEs and difference equations and their solutions.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
 Introduction to mathematical modelling: Mathematical modelling cycle, types of models (stochastic, deterministic, discrete, continuous, ….).
 Scaling and dimensional analysis: Buckingham’s Pi Theorem, examples from chemical reactions and projectile motion, perturbation methods (timepermitting).
 First order linear equations: first order linear equations, examples of existence and uniqueness, integration techniques (integrating factors, ..).
 Second order equations: general homogeneous equations and linear second order equations with constant coefficients, reduction to 2x2 systems, sketching the flow under a vector field (2d only, phase diagrams).
 Nonlinear equations and 2x2 systems: linear stability such as predator and prey models.
 Difference equation: discrete population models such as the logistic model/fishery management, stability and instability of solutions (6+7 could be moved before 4).
 Discretisation techniques: explicit and implicit Euler, connection to difference equations, stability.
Learning outcomes
By the end of the module, students should be able to:
 understand the modelling cycle and be able to formulate and analyse simple models themselves
 use scaling, nondimensionalisation and linear stability techniques to reveal and understand the main underlying dynamics/driving factors
 solve simple ODEs (first order and second order) and interpret their qualitative behavior
 solve simple difference equations and understand their connection to continuous ODEs
 understand the basic concepts of numerical approximation
Indicative reading list
Logan, David. A first course in differential equations. Springer, 2006.
Robinson, James C. An introduction to ordinary differential equations. Cambridge University Press, 2004.
Holmes, Mark H. Introduction to the foundations of applied mathematics. Springer, 2009.
Hermann, Martin, and Masoud Saravi. Nonlinear ordinary differential equations. Springer India, 2016.
Witelski, B. and Bowen, M., Methods of Mathematical Modelling: Continuous Systems and Differential Equations, Springer, 2015
Subject specific skills
The module introduces the fundamentals of mathematical modelling and scaling analysis, before discussing and analysing difference and differential equation models in the context of physics, chemistry, engineering as well as the life and social sciences.
Transferable skills
Students will acquire key modelling and problem solving skills which will empower them to address problems in a large range of scientific fields with confidence.
Study time
Type  Required 

Lectures  20 sessions of 1 hour (48%) 
Online learning (scheduled sessions)  9 sessions of 1 hour (21%) 
Private study  13 hours (31%) 
Total  42 hours 
Private study description
Working on assignments, going over lecture notes, text books, exam revision.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D
Weighting  Study time  

Assignments  15%  20 hours 
Inperson Examination  85%  38 hours 

Assessment group R
Weighting  Study time  

Inperson Examination  Resit  100%  

Feedback on assessment
Marked homework (both assessed and formative) is returned and discussed in smaller classes. Exam feedback is given.
Courses
This module is Core for:

UMAAGV17 Undergraduate Mathematics and Philosophy
 Year 1 of GV17 Mathematics and Philosophy
 Year 1 of GV17 Mathematics and Philosophy
 Year 1 of GV17 Mathematics and Philosophy

UPXAGF13 Undergraduate Mathematics and Physics (BSc)
 Year 1 of GF13 Mathematics and Physics
 Year 1 of GF13 Mathematics and Physics

UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
 Year 1 of FG31 Mathematics and Physics (MMathPhys)
 Year 1 of FG31 Mathematics and Physics (MMathPhys)
This module is Optional for:
 Year 1 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 1 of USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)

USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 1 of GG14 Mathematics and Statistics
 Year 1 of GG14 Mathematics and Statistics

USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
 Year 1 of Y602 Mathematics,Operational Research,Stats,Economics
 Year 1 of Y602 Mathematics,Operational Research,Stats,Economics
This module is Option list B for:

UCSAG4G1 Undergraduate Discrete Mathematics
 Year 1 of G4G1 Discrete Mathematics
 Year 1 of G4G1 Discrete Mathematics
 Year 1 of UCSAG4G3 Undergraduate Discrete Mathematics