This term I am teaching MATH-40011 Calculus and Applications I at Imperial.

At Cambridge, I taught:

  • Part IA Differential Equations
    linear differential equations, difference equations, non-linear equations, partial derivatives, stationary points, stability of solutions 

  • Part IA Vectors & Matrices
    complex numbers, matrices, determinants, linear maps, systems of linear equations, eigenvectors, diagonalisation, Jordan normal form

  • Part IB Complex Analysis
    analytic functions, conformal mappings, contour integration, Cauchy's theorem, Liouville's theorem, Morera's theorem, the principle of isolated zeros, windings numbers, Jordan's lemma, argument principle, open mapping theorem

  • Part II Fluid Dynamics
    Couette and Poiseuille flows, the Stokes layer, the Rayleigh problem, Stokes flow, lubrication theory, Hele-Shaw cell, vorticity equation, vortex stretching, boundary layers at high Reynolds number

  • Part II Asymptotic Methods
    asymptotic expansions, Watson's lemma, Laplace's method, Riemann-Lebesgue lemma, method of stationary phase, method of steepest descent, WKB method

  • Part II Further Complex Methods
    Cauchy principal value, Hilbert transform, multivalued functions, Gamma function, Beta function, Riemann zeta function, distribution of prime numbers, solution of differential equations by integral representations, second-order ODEs in the complex plane, Riemann P-function, hypergeometric function