2015 Paper 2
- Q1a-i Cyclic groups 5 marks
- Q1a-ii Groups: definition, axioms, examples 5 marks
- Q1b Subrings and ideals 10 marks
- Q1c Absolute and conditional convergence 10 marks
- Q1d Harmonic functions and harmonic conjugate 10 marks
- Q1e Assignment problem (Hungarian method) 10 marks
- Q2a Ring homomorphisms; quotient rings 15 marks
- Q2b Riemann integral 15 marks
- Q2c Laurent's series in an annulus 20 marks
- Q3a Cauchy's residue theorem 15 marks
- Q3b Uniform convergence of series 15 marks
- Q3c-i LPP: standard form; basic, basic feasible, optimal solutions 10 marks
- Q3c-ii LPP: standard form; basic, basic feasible, optimal solutions 10 marks
- Q4a Integral domains; characteristic 15 marks
- Q4b Maxima and minima of single-variable functions 15 marks
- Q4c Simplex method (basic) 20 marks
- Q5a Quasilinear first-order PDEs (Lagrange's method) 10 marks
- Q5b Second-order linear PDEs with constant coefficients (CF, PI) 10 marks
- Q5c Boolean algebra 10 marks
- Q5d Sources, sinks, doublets 10 marks
- Q5e Moment of inertia 10 marks
- Q6a Quasilinear first-order PDEs (Lagrange's method) 15 marks
- Q6b Hamilton's equations 15 marks
- Q6c Lagrange's interpolation 20 marks
- Q7a Heat equation 15 marks
- Q7b Runge-Kutta methods (RK2/RK4) 15 marks
- Q7c-i Hamilton's equations 10 marks
- Q7c-ii Lagrange's equations 10 marks
- Q8a Classification and reduction to canonical form 15 marks
- Q8b Gauss-Seidel iteration 15 marks
- Q8c Two-Dimensional and Axisymmetric Flow 20 marks