I've decided to concentrate on physics for the time being...

Syllabus:

Syllabus of APhO
A. Theoretical Part
1) Mechanics
Foundation of kinematics of a point mass
Vector description of the position of the point mass velocity and acceleration as vectors
Newton's laws, inertial systems
Problems may be set on changing mass
Closed and open systems, momentum and energy, work, power
Conservation of energy, conservation of linear momentum, impulse
Elastic forces, frictional forces, the law of gravitation, potential energy and work in a gravitational field
Hooke's law, coefficient of friction (F/R=const), frictional forces static and kinetic, choice of zero of potential energy
Centripetal acceleration, Kepler's law

2) Mechanics of Rigid Bodies
Statics, center of mass, torque
Couples, conditions of equilibrium of bodies
Motion of rigid bodies, translation, rotation, angular velocity, angular acceleration, conservation of angular momentum
Conservation of angular momentum about fixed axis only
External and internal forces, equation of motion of a rigid body around the fixed axis, moment of inertia, kinetic energy of a rotating body
Parallel axes theorem (Steiner's theorem), additivity of the moment of inertia
Accelerated reference systems, inertial forces
Knowledge of the Coriolis force formula is not required

3) Hydromechanics
No specific questions will be set on this but students would be expected to know the elementary concepts of pressure, buoyancy and the continuity law.

4) Thermodynamics and Molecular Physics
Internal energy, work and heat, first and second laws of thermodynamics
Thermal equilibrium, quantities depending on state and quantities depending on process
Model of a perfect gas, pressure and molecular kinetic energy, Avogadro's number, equation of state of a perfect gas, absolute temperature
Also molecular approach to such simple phenomena in liquids and solids as boiling, melting etc.
Work done by an expanding gas limited to isothermal and adiabatic processes
Proof of the equation of the adiabatic process is not required
The Carnot cycle, thermodynamic efficiency, reversible and irreversible processes, entropy (statistical approach), Boltzmann factor
Entropy as a path independent fiction, entropy changes and reversibility, quasistatic processes

5) Oscillations and Waves
Harmonic oscillations, equation of harmonic oscillation
Solution of the equation for harmonic motion, attenuation and resonance-qualitatively
Harmonic waves, propagation of waves, transverse and longitudinal waves, linear polarisation, the classical Doppler effect, sound waves
Displacement in a progressive wave and understanding of graphical representation of the wave, measurements of velocity of sound and light, Doppler effect in one dimension only, propagation of waves in homogeneous and isotropic media, reflection and refraction, Fermat's principle
Superposition of harmonic waves, coherent waves, interference, beats, standing waves
Realisation that intensity of wave is proportional to the square of its amplitude. Fourier analysis is not required but candidates should have some understanding that complex waves can be made from addition of simple sinusoidal waves of different frequencies. Interference due to thin films and other simple systems (final formulae are not required), superposition of waves from secondary sources (diffraction)

6) Electric Charge and Electric Field
Conservation of charge, Coulomb's law
Electric field, potential, Gauss' Law
Gauss' law confined to simple symmetric systems like sphere, cylinder, plate, etc, electric dipole moment
Capacitors, capacitance, dielectric constant, energy density of electric field

7) Current and Magnetic Field
Current resistance internal , resistance of source Ohm's law, Kirchoff's laws, work and power of direct and alternating currents, Joule's law
Simple cases of circuits containing non-ohmic devices with known V-I characteristics
Magnetic field (B) of a current , current in a magnetic field Lorentz force
Particles in a magnetic field, simple applications like cyclotron, magnetic dipole moment
Ampere's law
Magnetic field of simple symmetric systems like straight wire, circular loop and long solenoid
Law of electromagnetic induction, magnetic flux, Lenz's law, self-induction, inductance, permeability, energy density of magnetic field
Alternating current, resistors, inductors and capacitors in AC-circuits, voltage and current (parallel and series) resonance
Simple AC-circuits, time constants, final formulae for parameters of concrete resonance circuits are not required

8) Electromagnetic Waves
Oscillatory circuit, frequency of oscillations, generation by feedback and resonance
Wave optics, diffraction from one and two slits, diffraction grating, resolving power of a grating Bragg reflection
Dispersion and diffraction spectra, line spectra of gases
Superposition of polarised waves
Electromagnetic waves as transverse waves, polarisation by reflection, polarisers
Resolving power of imaging systems
Black body, Stefan-Boltzmann's law
Planck's formula is not required

9) Quantum Physics
Photoelectric effect, energy and impulse of the photon
Einstein's formula is required
De Broglie wavelength, Heisenberg's uncertainty principle

10) Relativity
Principle of relativity, addition of velocities, relativistic Doppler effect
Relativistic equation of motion, momentum, energy, relation between energy and mass, conservation of energy and momentum

11) Matter
Simple applications of the Bragg equation
Energy levels of atoms and molecules (qualitatively), emission, absorption, spectrum of hydrogen like atoms
Energy levels of nuclei (qualitatively), alpha-, beta- and gamma-decays, absorption of radiation, half-life and exponential decay, components of nuclei, mass defect, nuclear reactions

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