MSccSM List of topics - please indicate Y for topics you have studied - N for those
you have not - and return the completed list
(Multivariate) Calculus
1 [y/n] Differentiation and chain rule [Y]
2 [y/n] Partial differentiation [Y]
3 [y/n] Qualitative and asymptotic analysis of functions (including trigonometric and hyperbolic functions)
[Y]
4 [y/n] Taylor expansion [Y]
5 [y/n] Integration (by substitution, parts and partial fraction); multivariate integrals [Y]
6 [y/n] Gaussian integrals [Y]
7 [y/n] Integration by steepest descent method [N]
Complex analysis:
8 [y/n] Fourier transforms [N]
9 [y/n] Fourier representations of delta functions [N]
10 [y/n] Contour integration [N]
11 [y/n] Residue theorem [N]
Probability
12 [y/n] Probability distributions [Y]
13 [y/n] Joint distributions [Y]
14 [y/n] Conditional distributions [Y]
15 [y/n] Marginalisation [Y]
16 [y/n] Moments and correlations [Y]
17 [y/n] Moment generating functions [Y]
18 [y/n] Gaussian distributions [Y]
19 [y/n] Bayes relations [Y]
20 [y/n] Prior and posterior distributions [Y]
Linear algebra
21 [y/n] Determinant, traces [Y]
22 [y/n] Eigenvalues and (left and right) eigenvectors [Y]
Partial Differential equations:
23 [y/n] Heat equation and solution by Fourier transform [Y]
24 [y/n] Methods of characteristics [N]
ODE and Dynamical Systems:
25 [y/n] First order linear differential equations; [Y]
26 [y/n] First order dynamical system: phase portrait, linear stability and asymptotic analysis; [Y]
27 [y/n] Second order linear dynamical systems: solution by diagonalization [Y]
28 [y/n] Second order dynamical systems:linear stability analysis [Y]
Classical and statistical mechanics
29 [y/n] Newtonian dynamics [N]
30 [y/n] Hamiltonian mechanics [Y]
31 [y/n] Free-energy, partition function, Boltzmann distribution [N]
Introductory quantum mechanics
32 [y/n] Bra and Ket notation [N]
33 [y/n] Creation and annihilation operators [N]
34 [y/n] Quantum harmonic oscillator [N]