2024 Paper 2
- Q1a Cosets and Lagrange's theorem 10 marks
- Q1b Harmonic functions and harmonic conjugate 10 marks
- Q1c Improper integrals (analysis perspective) 10 marks
- Q1d Cauchy-Riemann equations (necessary and sufficient) 10 marks
- Q1e Big-M / two-phase method (artificial variables) 10 marks
- Q2a Cauchy sequences; completeness of R 15 marks
- Q2b Group homomorphisms: kernel, image 15 marks
- Q2c Analytic Functions: Complex Differentiability 20 marks
- Q3a Residues: computation at poles of various orders 15 marks
- Q3b Uniform Convergence: Term-by-Term Differentiation 20 marks
- Q3c Duality 15 marks
- Q4a Subrings and ideals 15 marks
- Q4b Riemann integral 15 marks
- Q4c Assignment problem (Hungarian method) 20 marks
- Q5a Second-order linear PDEs with constant coefficients (CF, PI) 10 marks
- Q5b Gauss-Jordan method 10 marks
- Q5c-i Representation of Integers, Signed Integers, and Reals (incl. Double Precision) 5 marks
- Q5c-ii Number systems 5 marks
- Q5d Motion of rigid bodies in two dimensions 10 marks
- Q5e Potential flow 10 marks
- Q6a Laplace equation: Dirichlet/Neumann, separation of variables 20 marks
- Q6b Boolean algebra 15 marks
- Q6c Moment of inertia 15 marks
- Q7a Quasilinear first-order PDEs (Lagrange's method) 15 marks
- Q7b-i Simpson's 1/3 and 3/8 rules 7.5 marks
- Q7b-ii Trapezoidal rule (composite; error) 7.5 marks
- Q7c Euler's equation of motion for inviscid flow 20 marks
- Q8a Classification and reduction to canonical form 15 marks
- Q8b Newton's forward difference interpolation 15 marks
- Q8c Vortex motion; circulation 20 marks