2020 Paper 2
- Q1a Group homomorphisms: kernel, image 10 marks
- Q1b Principal Ideal Domains (PID) 10 marks
- Q1c Cauchy sequences; completeness of R 10 marks
- Q1d Cauchy's theorem (Cauchy-Goursat) 10 marks
- Q1e LPP: standard form; basic, basic feasible, optimal solutions 10 marks
- Q2a Cyclic groups 15 marks
- Q2b Uniform continuity 15 marks
- Q2c Contour integration of real integrals using residues 20 marks
- Q3a Fields and finite fields 15 marks
- Q3b Simplex method (basic) 15 marks
- Q3c Partial derivatives; equality of mixed partials (Schwarz) 20 marks
- Q4a Cauchy-Riemann equations (necessary and sufficient) 15 marks
- Q4b Fundamental theorems of integral calculus 15 marks
- Q4c Transportation problem 20 marks
- Q5a Family of surfaces 10 marks
- Q5b Newton-Raphson method (convergence, geometric meaning) 10 marks
- Q5c Boolean algebra 10 marks
- Q5d Second-order linear PDEs with constant coefficients (CF, PI) 10 marks
- Q5e Moment of inertia 10 marks
- Q6a Quasilinear first-order PDEs (Lagrange's method) 15 marks
- Q6b Gauss-Seidel iteration 15 marks
- Q6c Hamilton's equations 20 marks
- Q7a Cauchy's method of characteristics 15 marks
- Q7b Gaussian quadrature 20 marks
- Q7c Potential flow 15 marks
- Q8a Wave equation 20 marks
- Q8b Lagrange's interpolation 15 marks
- Q8c Sources, sinks, doublets 15 marks