Core03: Modelling, analysis and computation of continuous real world problems - Archived material for the year 2019-2020

2019-2020
Lecturer(s): 
Prof. Colin Please
Course Term: 
Michaelmas
Course Overview: 

Modelling and Analysis of Continuous Real-World Problems will introduce a number of key methods for studying continuum models. Each week we start from real-world problems and show how to derive the corresponding mathematical model. We then use these models as vehicles to demonstrate the relevant analytical and computational methods. At the end of each week, the students will have the complete set of tools needed to set up, analyse and solve a class of mathematical models.

Course Synopsis: 

Diffusion problems arising in heat flow, chemical reactions, pattern formation, and thermal runaway. Conservation laws; well-posedness; separation of variables; transforms; similarity solutions; nonlinear equilibria; linear stability.

Elastic waves; acoustics; Stokes waves; electromagnetism; optics. Method of characteristics; separation of variables; eigenvalue problems; resonance; high-frequency asymptotics.

River flow; porous-medium flow; two-phase flow. Shocks, causality, regularization, weakly nonlinear theory.

Capillary statics; elasticity; buckling; liquid crystals; Calculus of variations; bifurcations; weakly nonlinear analysis.

Reading List: 

J. Nocedal and S.J. Wright, Numerical Optimization, Second edition, Springer, 2006
S.D. Howison, Practical Applied Mathematics: Modelling, Analysis, Approximation, CUP, 2005
M. Holmes, Introduction to the Foundations of Applied Mathematics, Springer, 2009

Please note that e-book versions of many books in the reading lists can be found on SOLO and ORLO.