MAS6446 Mathematical methods and modelling of natural systems

Semester 2, 2021/22 20 Credits
Lecturer: Dr Nils Mole Timetable Reading List
Aims Outcomes Assessment

Mathematical modelling enables insight in to a wide range of scientific problems. This module combines Mathematical Methods (MAS325), where there is an emphasis on solving problems that involve small parameters, which may be difficult to solve analytically or computationally, and Modelling of Natural systems (MAS414), where there is an emphasis on the practical application of methods, combining analytical and computational approaches.

There are no prerequisites for this module.
No other modules have this module as a prerequisite.


Outline syllabus

  • Integral methods and differential equations: Dirac δ-function, Fourier and Laplace transforms, applications to differential equations, Green functions.
  • Asymptotic expansions: algebraic equations with small parameter, asymptotic expansion of functions defined by integrals.
  • An introduction to chaotic dynamics.
  • Machine learning methods to retrieve forest biophysical parameters.
  • A stochastic approach to modelling disease spread.

Office hours

Please see Blackboard.



Aims

  • To develop methods for solving differential equations using integral transforms and representations.
  • To introduce asymptotic methods for solving algebraic equations.
  • To introduce asymptotic methods for evaluating integrals.
  • develop students’ skills in comprehending problems, formulating them mathematically and obtaining solutions by appropriate methods.
  • provide practical demonstrations of how mathematical modelling may be used to gain insight in to the dynamics of natural systems.
  • build on mathematical methods (ordinary/partial differential equations, linear stability analysis, scientific computing in Python), and expose students to how they can be used to model natural systems.

Learning outcomes

By the end of the unit, a candidate will 1. be familiar with the ideas of mathematical modelling and understand the utility of mathematical modelling to understand natural phenomena (QAA benchmark for mathematics, 5.4v); 2. be able to formulate a mathematical model that represents the dynamics of a natural system and apply appropriate methods to obtain solutions (QAA benchmark for mathematics, 5.4v); 3. be able to gain insight in to a natural system through the application of mathematical modelling techniques; 4. recognise how mathematical methods may be used to model natural systems.

32 lectures, no tutorials, 9 practicals

Assessment

MAS325: Exam 50%
MAS414: Three pieces of coursework 3 x 15%, one oral presentation 5%.

Reading list

Type Author(s) Title Library Blackwells Amazon
C Bender and Orszag Advanced Mathematical Methods For Scientists And Engineers I: Asymptotic Methods and Perturbation Theory 515.350245 (B) Blackwells Amazon
C Hastie T, Tibshirani R, Friedman JH The Elements of Statistical Learning: Data Mining, Inference, and Prediction 006.31 (H) Blackwells Amazon
C Murray JD Mathematical Biology I and II 570.15118 (M) Blackwells Amazon
C Strogatz SH Nonlinear dynamics and chaos: with applications to physics, physics, biology, chemistry, and engineering 531.3 (S) Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.