Autumn 2021: MATH100 Differential Calculus with Applications to Physical Sciences and Engineering
Spring 2022: MATH522 Numerical Analysis (Graduate course)
A 30 hour module for 2nd year undergraduate students at Warwick (2013, 2014). The focus of this module is on analytical ideas. Main topics are Picard, maximal solutions, Gronwall, first order regular perturbation theory, Euler method, stability in autonomous systems (linearised and Lyapunov). [ notes | exercises ]
A 16 hour introduction for 4th year undergraduates in Oxford. Topics covered are optimality conditions, Newton's method, Steepest descent, quasi-Newtion methods, trust region methods, some constrained optimisation. [ notes | exercises ]
A 16 hour introduction for 4th year undergraduates in Oxford. Examples of topics covered are Kinematics, stress, constitutive models, symmetries, incompressible materials, linearised elasticity, brittle fracture. I am not making my lecture notes available online as they are are heavily derived from John Ball's, but I will be happy to provide them upon request.
A 5 hour summer school course on the numerical analysis of a/c coupling taught at the NSF PIRE Summer School for Graduate Students New frontiers in multiscale analysis and computing for materials, June 21-29, 2012. The website contains the course material and recordings of the lectures.
A 3 hour summer school course on far-field modelling and computing crystalline defects in an infinite lattice at the Berlin Mathematical School Summer School on Applied Analysis for Materials, 25 Aug - 5 Sept 2015. The course covers
analysis for defects embedded in infinite lattices
boundary conditions for their numerical simulations
analysis of a coarse-graining scheme (a/c coupling)
Disclaimer: these are slides and as such contain some errors and several deliberate inaccuracies. They should not be used as a reference, but only as a study guide for the literature on a/c multiscale methods. The three main references from which the material for this shortcourse is drawn are , , and .