Lecture notes and course material for M3M6 Applied Complex Analysis at Imperial College
Office Hours: 11:00-12:00 Tuesdays during term, Huxley 6M40
- M.J. Ablowitz & A.S. Fokas, Complex Variables: Introduction and Applications, Second Edition, Cambridge University Press, 2003
- R. Earl, Metric Spaces and Complex Analysis, 2015
See also previous lecture notes for previous course M3M6 Methods of Mathematical Physics
- Problem Sheet 1 (Solutions)
- Problem Sheet 2 (Solutions)
- Problem Sheet 3 (Solutions)
- Problem Sheet 4 (Solutions)
- Mastery material (Solutions)
- Mastery Sheet
- Project proposal due 19 Feb 2020
- Project due 19 March 2020
Examples of previous projects:
- Wasim Rehman, Quantum Mechanics and Matrix Functions via Trapezium Rule
- Tianyi Pu, 2D Ideal Fluid Flow Around an Obstacle
- Review of complex analysis
- Cauchy's integral formula and Taylor series
- Laurent series and residue calculus
- Analyticity at infinity
- Applications to real integrals
- Convergence rate of the trapezium rule
- Matrix norms and matrix functions
- Matrix functions via Cauchy's integral formula
- Computing matrix functions via the trapezium rule
- Branch cuts
- Representing analytic functions by their behaviour near singularities
- Cauchy transforms and Plemelj's theorem
- Hilbert transforms
- Inverting the Hilbert transform and ideal fluid flow
- Electrostatic charges in a potential well
- Logarithmic singular integrals
- Logarithmic singular integral examples
- Inverting logarithmic singular integrals
- Orthogonal polynomials
- Classical orthogonal polynomials
- Orthogonal polynomials and differential equations
- Orthogonal polynomials and singular integrals
- Hermite polynomials
- Riemann–Hilbert problems
- Laurent and Toeplitz operators
- Half-Fourier and Laplace transforms
- The Wiener–Hopf method