A sketch of students (or, perhaps, fellows) in a manuscript of William of Ockham's commentary on Aristotle's Physics (MS293 from the Merton College library, image courtesy of J. Walwarth). 
Michaelmas
Term
2018 LECTURES (28 hours) Lindemann LT Monday 10:0011:30 (weeks 1,2,4,5,7,8) Monday 10:0011:00 (week 6) Monday 16:0018:00 (weeks 1,2,3,4,5,6,7,8) Tuesdays 14:0016:00 (week 8) CLASSES Seminar Room (501 DWB) Tuesday 14:0016:00 (weeks 4, 7, 9) EXAM in week 0 of Hilary Term Course materials, reading suggestions, scheduling notices, problem sets to appear below. 
A sketch of students (or, perhaps, fellows) in a manuscript of William of Ockham's commentary on Aristotle's Physics (MS293 from the Merton College library, image courtesy of J. Walwarth). 

PART I: KINETIC THEORY OF GASES 
9 hours (Mon 8.10.18  Mon 22.10.18) Dr Paul Dellar
Timescales
and length scales. Hamiltonian mechanics of N particles. Liouville’s
Theorem. Reduced distributions. BBGKY hierarchy. BoltzmannGrad limit
and truncation of BBGKY equation for the 2particle distribution
assuming a shortrange potential. Boltzmann's collision operator and
its conservation properties. Boltzmann's entropy and the Htheorem.
MaxwellBoltzmann distribution. Linearised collision operator. Model
collision operators: the BGK operator, FokkerPlanck operator.
Derivation of hydrodynamics via ChapmanEnskog expansion. Viscosity and
thermal conductivity.
The objective of this part of the course is to introduce the basic language of kinetic theory and show how, starting from a kinetic description, one can construct fluid equations for a collisional system close to Maxwellian equilibrium. Lecture 1+ (10:0011:30; Mon 8.10.18) Lectures 23 (16:0018:00; Mon 8.10.18) Lecture 4+ (10:0011:30; Mon 15.10.18) Lectures 56 (16:0018:00; Mon 15.10.18) Lecture 78 (16:0018:00; Mon 22.10.18) 
Problem Class 1 14:0016:00 on Tue 30.10.18 (week 4) Homework due 23:59 Sun 28.10.18 to Ching Chong (in Maths) Lecture Notes Paul Dellar's webpage for this part of the course, including lecture notes, problem set, and reading suggestions 

PART II: KINETIC THEORY OF PLASMAS & QUASIPARTICLES 
10 hours (Mon 29.10.18  Mon
12.11.18) Prof Alexander
Schekochihin Kinetic
description of a plasma: Debye shielding, micro vs. macroscopic
fields, VlasovMaxwell equations. Klimontovich’s version of BBGKY
(nonexaminable). Plasma frequency. Partition of the dynamics into
equilibrium and fluctuations. Linear theory: initialvalue problem for
the VlasovPoisson system, Laplacetranform solution, the dielectric
function, Landau prescription for calculating velocity integrals,
Langmuir waves, Landau damping and kinetic instabilities (driven by
beams, streams and bumps on tail), Weibel instability, sound waves,
their damping, ionacoustic instability, ionLangmuir oscillations.
Energy conservation. Heating. Entropy and free energy. Ballistic
response and phase mixing. Role of collisions; coarsegraining.
Elements of kinetic stability theory. Quasilinear theory: general
scheme. QLT for bumpontail instability in 1D. Introduction to
quasiparticle kinetics.
The main new set of concepts in this part of the course, compared to Part I, is about the behaviour of a system that has not only particles but also fields: how do they exchange energy? how do they interact? 
Problem Set 2: you will
find it in the Lecture Notes Problem Class 2 14:0016:00 on Tue 20.11.18 (week 7) Homework due 23:59 Sun 18.11.18 to Ching Chong (in Maths) The latest version (12.11.18) of the typed notes is available here. Check back for upadtes! Reading: 

Lecture 9+ (10:0011:30; Mon 29.10.18) Kinetic
description of a plasma: Debye shielding, micro vs. macroscopic
fields, VlasovLandauMaxwell equations. Basic properties of the Landau
collision integral. Plasma frequency. Slow equilibrium and fast
fluctuations. Lecture
Notes sec 1.11.7, 1.9, 2.12.2

Klimontovich sec 4, 5, 11 (his version of BBGKY etc.) Helander sec 3 (coll. operator) Helander sec 4 (fluid eqns) Braginskii (ChapmanEnskog for plasma, original derivation) 

Lectures
1011 (16:0018:00; Mon 29.10.18) Outline of
the hierarchy of approximations: linear, quasilinear, weak turbulence,
strong turbulence. Linear theory: initialvalue problem for the VlasovPoisson system, Laplacetransform solution, the dielectric function, Landau prescription for calculating velocity integrals. Solving the plasma dispersion relation in the slow damping/growth limit. Langmuir waves. Lecture
Notes sec 2.33.4

Zakharov et al.; Nazarenko (general scheme of weak turbulence theory) Kadomtsev; Sagdeev & Galeev (from linear to QL to WT for plasma) Landau's paper (original derivation) Hazeltine & Waelbroeck sec 6.3, 6.4 Alexandrov et al. sec 2, 4 (all the waves catalogued, with an emphasis on plasma as a dielectric) 

Lecture 12+ (10:0011:30; Mon 5.11.18) Landau damping and
kinetic
instabilities. Sound waves, their damping, ionacoustic instability,
ionLangmuir oscillations. Energy conservation. You are ready to do Q13 of the Problem Set (+Q4 if you read the optional sec 5) Lecture
Notes sec 3.5, 3.83.10, 4.1


Lectures 1314 (16:0018:00; Mon 5.11.18) Heating.
Entropy and free energy. Perturbed
distribution function: ballistic
response and phase mixing. Phase
mixing: role of collisions; coarsegraining. Structure of the perturbed
distribution near a resonance: the Casevan Kampen mode. Beam instabilities. Lecture
Notes sec 4.14.6, 3.7

Hazeltine & Waelbroeck sec
6.2 (Landau damping and phase mixing without Laplace transforms) 

Lecture 15 (10:0011:00; Mon 12.11.18) Quasilinear
theory: general scheme. You are ready to do Q57 of the Problem Set Lecture
Notes sec 7.1


Lectures 1617 (16:0018:00; Mon 12.11.18) QLT
for bumpontail instability in 1D. Quasiparticles. You are ready to do Q89 of the Problem Set Lecture
Notes sec 7.37.6, 7.9

Krall
& Trivelpiece sec 10 Kadomtsev sec I.3 Sagdeev & Galeev sec II2 (...and read on for more advanced topics) Tsytovich sec 3, 5, 7 (on plasmon kinetics and beyond) Peierls's and Ziman's books (on electrons and phonons in metals) 

PART III: KINETIC THEORY OF SELFGRAVITATING SYSTEMS 
9 hours (Mon
19.11.18  Tue 27.11.18) Prof
James Binney
Unshielded
nature of gravity and implications for selfgravitating systems.
Meanfield approximation with simple examples. Negative specific heat
and impossibility of thermal equilibrium. Relaxation driven by
fluctuations in mean field. Evaporation. Angleaction variables.
Potentialdensity pairs. Longtime response to initial perturbation.
FokkerPlanck equation. Computation of the diffusion coefficients in
terms of resonant interactions. Application to a tepid disc.
Here again there are particles (stars) and fields (gravitational). The key feature is that there are no collisions at all and one must understand the behaviour of a kinetic system that is not close to a Maxwellian equilibrium. Lecture 18+ (10:0011:30; Mon 19.11.18) Lectures 1920 (16:0018:00; Mon 19.11.18) Lecture 21+ (10:0011:30; Mon 26.11.18) Lectures 2223 (16:0018:00; Mon 26.11.18) Lectures 2425 (14:0016:00; Tue 27.11.18) 
Problem Set 3: you will
find it in the typed Lecture Notes Problem Class 3 14:0016:00 on Tue 4.12.18 (week 9) Homework due 23:59 on Sun 2.12.18 to Ching Chong (in Maths) Lecture Notes 