2019 Paper 2
- Q1a Cosets and Lagrange's theorem 10 marks
- Q1b Functions of two/three variables: limits, continuity 10 marks
- Q1c Improper integrals (unbounded interval/integrand) 10 marks
- Q1d Cauchy-Riemann equations (necessary and sufficient) 10 marks
- Q1e Graphical method 10 marks
- Q2a Group homomorphisms: kernel, image 10 marks
- Q2b Normal subgroups; quotient groups 10 marks
- Q2c Partial derivatives 15 marks
- Q2d Residues: computation at poles of various orders 15 marks
- Q3a Pointwise vs. Uniform Convergence of Sequences of Functions 15 marks
- Q3b Simplex method (basic) 15 marks
- Q3c Cauchy's theorem (Cauchy-Goursat) 10 marks
- Q3d Euclidean domains 10 marks
- Q4a Lagrange's method of multipliers (constrained extrema) 15 marks
- Q4b Laurent's series in an annulus 10 marks
- Q4c Improper integrals (unbounded interval/integrand) 15 marks
- Q4d Duality 10 marks
- Q5a Family of surfaces 10 marks
- Q5b Newton-Raphson method (convergence, geometric meaning) 10 marks
- Q5c Motion of rigid bodies in two dimensions 10 marks
- Q5d Runge-Kutta methods (RK2/RK4) 10 marks
- Q5e Algorithms and flowcharts for numerical analysis problems 10 marks
- Q6a Quasilinear first-order PDEs (Lagrange's method) 15 marks
- Q6b Number systems 15 marks
- Q6c Motion of rigid bodies in two dimensions 20 marks
- Q7a Hamilton's equations 15 marks
- Q7b Gauss-Seidel iteration 15 marks
- Q7c Classification and reduction to canonical form 20 marks
- Q8a Boolean algebra 15 marks
- Q8b Potential flow 15 marks
- Q8c Sources, sinks, doublets 20 marks