- *BOARD OF THE FACULTY OF MEDIEVAL AND MODERN LANGUAGES
- *BOARD OF THE FACULTY SOCIAL STUDIES
- BOARD OF THE FACULTY OF MODERN HISTORY
- CHAIRMEN OF EXAMINERS
- CHANGES IN REGULATIONS
- 1 Boards of the Faculties of English and Literae Humaniores
- 2 Board of the Faculty of Physical Sciences
- 3 Committee on Continuing Education

- EXAMINATIONS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

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A.G. ROSSER, MA, Fellow of St Catherine's

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Politics Qualifying Test: D.B. GOLDEY, MA, D.PHIL., Fellow of Lincoln

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Educational Research Methodology: G. WALFORD, MA, M.PHIL., Fellow of Green College (address: Department of Educational Studies)

Educational Studies: G. WALFORD, MA, M.PHIL., Fellow of Green College (address: Department of Educational Studies)

Mathematical Modelling and Numerical Analysis: J. OCKENDON, MA, D.PHIL., Fellow of St Catherine's (address: Mathematical Institute)

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`Candidates shall take one of the following courses

1. Course I'.

**2** Ibid., p. 43, after l. 34, insert:

(*a*) during their first year of study to have passed
an examination under the auspices of the Board of the Faculty of
Literae Humaniores during the Trinity Term. Candidates who fail
to satisfy the examiners shall be permitted to offer themselves
for re-examination during the following September. Each candidate
shall offer two papers, each of three hours' duration, as
follows:

1. Greek or Latin texts. Candidates must offer either
(*a*) or (*b*):

(*a*) Homer, Odyssey VI; Sophocles, Oedipus Tyrannus
911–1185; Lysias 1.

(*b*) Virgil, Georgics 2.1–176, 362–542;
Horace, Odes III. 5, 7, 9, 13, 14, 18, 21, 26, 30; Seneca,
Epistles 47, 77.

The paper will comprise passages from these texts for translation and comment.

2.Greek or Latin Language. The paper will consist of passages for unseen translation out of Greek or Latin and sentences for translation from English into Latin or Greek.

(*b*) during their second year of study, to offer
papers as for Course I.'

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Mechanics of particles in two dimensions. Vector formation and equations of motion in Cartesian and plane polar co-ordinates. Projectiles moving under gravity, including such motion subject to a damping force proportional to velocity.

Torque and angular momentum. Conservation of angular momentum. Inverse square central forces. Classification of orbits as bound or unbound. Examples of planetary and satellite motion (derivation of equation for u=1/r not required; explicit treatment of hyperbolae and ellipses not required). Rutherford scattering (calculation of the cross- section not required).

Systems of point particles. Centre of mass (or momentum) frame and its uses.

Moment of inertia of a system of particles. Use of perpendicular and parallel-axis theorems. Moment of inertia of simple bodies (the formula for any moment of inertia will be given). Solution of simple dynamical problems involving rotations about a fixed axis.

Vibrations of mechanical systems including vibrations with damping, and including vibrations with a forcing term, but restricted to one variable other than time, resonance and Q-factor. Critical damping. Compound pendulum.

Special theory of relativity restricted throughout to problems in one space dimension. The constancy of the speed of light; simultaneity. The Lorentz transformation

(derivation not required). Time dilation and length contraction. The addition of velocities. Invariance of the space-time interval. Energy, momentum, rest mass and their relationship for a single particle. Conservation of energy and momentum

(transformation not required). Elementary kinematics of the scattering and decay of sub-atomic particles, including the photon. Relativistic Doppler effect is excluded.

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Elementary geometrical optics: reflection and refraction at plane boundary; total internal reflection; deviation by a prism. Reflection and refraction at a spherical boundary. Image formation by concave mirror and by converging and diverging thin lenses. The magnifying lens; simple astronomical telescope consisting of two convex lenses; simple reflecting telescope.

Wave Optics: simple two slit interference (restricted to slits of negligible width). The diffraction grating, its experimental arrangement; conditions for proper illumination. The dispersion of a diffraction grating. (The multiple slit interference pattern and the resolution of a diffraction grating are excluded). Two beam interference by division of amplitude: including simple discussion of the standard Michelson interferometer (and excluding the Michelson stellar interferometer). Fraunhofer diffraction by a single slit: including experimental arrangements. Application to resolution of a single lens.

Limitations of classical physics: qualitative discussion of the problem of the stability of the nuclear atom; photo-electric effect; Franck-Hertz experiment and the existence of energy levels. Experimental evidence for wave-particle duality; X-ray diffraction and Bragg law; Compton scattering (derivation of the Compton formula not required); electron and neutron diffraction. Einstein and de Broglie's relations (E=hv, p=h/[lambda]).

Quantum interference and the two slit experiment. Comparison with
classical optics and classical mechanics. The concept of the
wave-function as a probability amplitude and the probabilistic
interpretation of |[upsilon](x)|^{2}. The one-dimensional
time independent Schrödinger equation and solutions for
plane waves. Heuristic treatment based on position and momentum
operators and energy conservation.

The position-momentum uncertainty relation and simple consequences. Qualitative wave mechanical understanding of the size and stability of the hydrogen atom.

Quantisation as an eigenvalue problem, illustrated by solutions in an infinite square well and by qualitative treatment of the finite well. Analogy with standing waves on a stretched string. Reflection and transmission at potential steps. Qualitative treatment of barrier penetration for simple rectangular barriers. Simple examples and comparison with classical mechanics. [The level of treatment is that to be found in the following books: A.P. French and E.F. Taylor, An Introduction to Quantum Physics, MIT series, Chapman and Hall 1978; K Krane, Introduction to Modern Physics, Wiley 1983; H C Ohanian, Modern Physics, second edition, Prentice Hall 1995.]

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Electrostatics in vacuo: Coulomb's law and its experimental basis. Electric field and potential due to a charge and to a system of charges. The electric dipole; its electric field and potential. The couple and force on, and the energy of, a dipole in an external electric field. Energy of a system of charges; energy stored in an electric field. Gauss' Law in integral form; field and potential due to surface and volume distributions of charge. Force on a conductor. The capacitance of parallel plate, cylindrical and spherical capacitors.

Electrostatics in the presence of dielectric media: Modification to Gauss' Law: polarization, the electric displacement, relative permittivity. Capacitance and energy in the presence of dielectric media.

Magnetic effects in the absence of magnetic media: The B-field. Steady currents: the B-field set up by a current; the Biot-Savart Law. The force on a current and on moving charges in a B-field. The magnetic dipole; its B-field. The force and couple on, and the energy of, a dipole in an external B-field. Energy stored in a B-field . Gauss' Law in integral form. Simple cases of the motion of charged particles in electric and magnetic fields.

Magnetic media: Magnetization, the H-field, magnetic permeability. Ampère's Law in integral form. Energy in the presence of magnetic media. The electromagnet. Questions on magnetic media involving non-uniform fields will not be set.

Electromagnetic induction: The laws of Faraday and Lenz. Self and mutual inductance: calculation for simple circuits. The transformer.

Circuits: Growth and decay of currents in LCR circuits. AC theory; the use of complex impedance in circuit analysis under steady state conditions. The quality factor Q of a circuit.'

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**2** Ibid., delete from p. 104, 1. 37 to p. 105,
1. 21 inclusive and substitute:

Vectors: Vector algebra, scalar and vector products, triple products. Elementary vector geometry of lines and planes. Time dependent vectors and differentiation of vectors, simple applications to mechanics.

Differential calculus of functions of more than one variable: Functions of two variables as surfaces. Partial differentiation, chain rule and differentials and their use to evaluate small changes. Simple transformations of first order coefficients (questions on transformations of higher order coefficients are excluded). Taylor expansion for two variables, maxima, minima and saddle points of functions of two variables. Lagrange multipliers for stationary points of functions of two variables.

Multiple integrals and vector analysis: Double Integrals and their evaluation by repeated integration in Cartesian, plane polar and other specified coordinate systems. Jacobians. Line, surface and volume integrals, evaluation by change of variables

(Cartesian, plane polar, spherical polar coordinates and cylindrical coordinates only unless the transformation to be used is specified). Integrals around closed curves and exact differentials. Green's theorem in the plane. Scalar and vector fields. The operations of grad, div and curl and understanding and use of identities involving these. The statements of the theorems of Gauss, Green and Stokes with simple applications. Conservative fields.

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(polynomial, trigonometric, exponential, hyperbolic, logarithmic) of a complex variable. (Complex transformations and complex differentiation and integration are excluded.)

Matrices: Elementary properties (addition, multiplication, inverse) of two- and three- dimensional matrices. Determinants: minors, cofactors, evaluation by row and column manipulation. Application of matrix methods to the solution of simultaneous linear equations; cases in which solutions are unique, non-unique or do not exist; geometric interpretation of these cases. Linear independence.

Ordinary differential equations: Classification and terminology. Linear homogeneous differential equations and superposition. First order linear differential equations; integrating factors. Second order linear differential equations with constant coefficients; complementary functions and particular integrals; applications to damped and forced vibrations and to complex impedance in AC circuits. Simultaneous linear differential equations: solutions by elimination and by a suitable choice of coordinates.

Normal modes: Coupled undamped oscillations in systems with two degrees of freedom. Normal frequencies, and amplitude ratios in normal modes. General solutions (for two coupled oscillators) as a superposition of modes. Total energy, and individual mode energies.

The one dimensional wave equation: Derivation, and application to transverse waves on a stretched string. Characteristics of wave motion: amplitude, phase, frequency, wavelength, wavenumber, wave vector, phase velocity. (Questions on sound waves in gases will not be set.) Modes of a string with fixed end points (standing waves); general solution as a superposition of modes. Energy in a vibrating string. Travelling waves: energy, power, impedance, reflection and transmission at a boundary.

Fourier series: General series with both sine and cosine functions. Formulae for the Fourier coefficients. Full-range and half-range series, even and odd functions. Discontinuities; summation of series; integration and differentiation of Fourier series.(Questions on Parseval's theorem will not be set.)

Partial differential equations in two independent variables: Method of separation of variables for the one-dimensional wave equation; separation constants; boundary and initial conditions. Method of separation of variables for Laplace's equation in two dimensions, using Cartesian and polar coordinates. Solution of boundary and initial value problems using Fourier series.'

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(*a*) The course will consist of lectures and classes
on architectural history and on site evaluation and survey. The
course may be taken on a part-time basis over a period which
shall normally be of one year's duration and shall not exceed two
years.

(*b*) The course will consist of three taught units,
two of which will be on architectural history and one of which
will be on site evaluation and survey, which will be offered in
three ten-week terms.

2.Every candidate will be required to satisfy the examiners in the following:

(*a*) attendance at the classroom-based courses;

(*b*) submission of the following portfolio of written
work:

(*i*) three essays or projects linked to unit one each
of which shall not exceed 1,500 words in length;

(ii) two essays linked to unit two, each of which shall not exceed 2,500 words in length;

(iii) a workbook linked to unit three;

(iv) a dissertation which shall not exceed 8,000 words in length on a topic agreed by the Board of Studies.

The assignments under (*i*)–(iii) and the
dissertation under (iv) will be forwarded to the examiners c/o
the Registry, Department for Continuing Education, Wellington
Square, Oxford OX1 2JD by such dates as the examiners shall
determine and shall notify to candidates.

3. Candidates will be expected to attend a viva voce examination at the end of the course of studies unless dispensed by the examiners.

4. The examiners may award a distinction to candidates for the certificate.

5. Candidates who fail to satisfy the examiners in the
assignments under 2.(*i*)–(iii), or the dissertation
under 2.(iv), or both, may be permitted to resubmit work in
respect of part or parts of the examination which they have
failed for examination on not more than one occasion which shall
normally be within one year of the initial failure.'

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Department of Plant Sciences, Friday, 9 January, 2 p.m.

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St Hugh's, Monday, 12 January, 2 p.m.

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Examination Schools, Wednesday, 21 January, 10 a.m.

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Examination Schools, Monday, 12 January, 2 p.m.

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Somerville, Monday, 26 January, 9.30 a.m.

S.N. HAIDER, New College: `The monetary system of the Mughal
Empire'.

St Antony's, Friday, 16 January, 2.15 p.m.

*Examiners*: C.A. Bayly, A.D.H. Bivar.

M.C. KILBURN, St John's: `Royalty and public in Britain
1714–89'.

Somerville, Wednesday, 14 January, 2.15 p.m.

*Examiners*: J.M. Innes, F.K. Prochaska.

J. WATSON, Balliol: `The internal dynamics of Gaullism,
1958–69'.

Social Studies
Faculty Centre, Wednesday, 14 January, 2.15 p.m.

*Examiners*: J.E.S. Hayward, J. Jackson.

J. WRIGHT, Magdalen: `Religious dissimulation, conformity, and
compromise in England c.1547–c.1603'.

Jesus, Monday, 5 January, 2 p.m.

*Examiners*: F.M. Heal, E. Duffy.

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Brasenose, Monday, 22 December, 10 a.m.

D.J. LEE, Brasenose: `The effects of damping and of retardation
in models of superconductivity'.

Sub-department of Theoretical Physics, Sunday, 4 January, 9.30
a.m.

*Examiners*: N. Dorey, I. Kogan.

R. SMITH, Christ Church: `Terrain-aided navigation of an
underwater vehicle'.

Department of Engineering Science, Monday, 12 January, 10 a.m.

*Examiners*: M.L.G. Oldfield, D.M. Lane.

T.T. TUCKER, Balliol: `Investigations into the generation and
cycloaddition reactions of chiral carbonyl ylides'.

Dyson Perrins Laboratory, Wednesday, 7 January, 2 p.m.

*Examiners*: C.J. Moody, M.G. Moloney.

R. WILMOUTH, Worcester: `Structural studies on the mechanism and
inhibition of elastase'.

Dyson Perrins Laboratory, Monday, 5 January, 10.30 a.m.

*Examiners*: V. Fulop, R.A. Field.

J.R. WOODWARD, Pembroke: `The effect of magnetic fields in
chemistry and physiology'.

Old Physiology Building, Wednesday, 7 January, 2.15 p.m.

*Examiners*: B. Brocklehurst, D.T. Edmonds.

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Department of Pharmacology, Monday, 19 January, 11.30 a.m.

G. HEINERT, St Hugh's: `Hypoxic and hypercapnic cerebal
vasodilatation'.

University Laboratory of Physiology, Wednesday, 7 January, 10.45
a.m.

*Examiners*: A. Guz, P.A. Robbins.

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Department of Experimental Psychology, Monday, 12 January, 11 a.m.

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Examination Schools, Monday, 5 January, 2 p.m.

G. MAVROTAS, Lincoln: `The effectiveness of foreign aid: a
study using disaggregated data'.

St Hilda's, Tuesday, 20 January, 10 a.m.

*Examiners*: M.B. Gregory, D. Greenaway.