Physics with a Foundation Year - BSc (Hons)

Introduction to Special Relativity:

Inadequacy of Galilean Transformation; Postulates of Relativity; Lorentz transformation; Time dilation, length contraction and simultaneity; Special relativity paradoxes; Invariant intervals; Momentum and energy in special relativity; Equivalence of mass and energy.

Introduction to Astronomy:

Astronomical coordinate systems and conversions; Positions and motions of stars; Timekeeping systems; Introduction to the distance scale.

Introduction to Astrophysics and Cosmology:

Stellar luminosity and magnitudes; Magnitude systems; Colour of stars; Stellar spectral classification; Evolution of stars, Hertzsprung-Russell diagram; Cosmological principle; Redshift; Hubble constant; Space expansion.

Derivatives and Integrals: Derivatives of elementary functions, chain rule, product rule, Integrals of elementary functions, Evaluation by substitution, Integration by parts, Area under the graph of a function.

Vectors: Basic properties, linear dependence, scalar and vector products, triple products, vector identities.

Matrices: Matrix representation, systems of equations, products, inverses, determinants, solution of linear systems, eigenvalues and eigenvectors, transformations.

Elementary Functions: Binomial coefficients, expansions and series, Maclaurin series, Taylor series, Exponential functions, Hyperbolic functions, Inverse functions.

Functions of a single variable: Linear and quadratic functions, polynomials, rational functions, limits, infinite series, approximation of functions.

Complex numbers: Quadratic equations, Argand diagram, modulus, Argument, complex exponential, de Moivre's theorem, roots of polynomials.

Differential Equations: Solving differential equations, separable equations, linearity, homogeneity, first and second order equations, particular integrals. Boundary and initial values, auxiliary equations with complex roots, coefficients and terms, examples from physics.

Partial Derivatives: functions of two variables , partial derivatives, directional derivatives, functions many variables, higher derivatives, function of a function, implicit differentiation, differentiation of an integral w.r.t a parameter, Taylor expansions, stationary points.

Elementary multivariate Calculus: the chain rule, Multiple integrals, integrals over rectangles/irregular areas in the plane, change of order of integration.

Polar Coordinates: Cylindrical polar coordinates in two and three dimensions, integrals, spherical coordinates, solid angle.

Introduction to Vector Calculus : Gradients, Divergence, Gauss's theorem, Curl, Stokes' theorem.

Measurement and motion; Dimensional analysis, Motion in one dimension: velocity, acceleration, motion with constant acceleration, Motion in a plane with constant acceleration, projectile motion, uniform circular motion, and Newton's laws of motion.

Work, Energy and Momentum; Work, kinetic energy, power, potential energy, relation between force and potential energy, conservation of energy, application to gravitation and simple pendulum, momentum, conservation of linear momentum, elastic and inelastic collisions.

Rotational Motion; Rotational motion: angular velocity, angular acceleration, rotation with constant angular acceleration, rotational kinetic energy, moment of inertia, calculation of moment of inertia of a rod, disc or plate, torque, angular momentum, relation between torque and angular momentum, conservation of angular momentum.

Concept of field; 1/r2 fields; Gravitational Field; Kepler's Laws, Newton's law of gravitation, Gravitational potential, the gravitational field of a spherical shell by integration.

Oscillations and Mechanical Waves; Vibrations of an elastic spring, simple harmonic motion, energy in SHM, simple pendulum, physical pendulum, damped and driven oscillations, resonance, mechanical waves, periodic waves, their mathematical representation using wave vectors and wave functions, derivation of a wave equation, transverse and longitudinal waves, elastic waves on a string, principle of superposition, interference and formation of standing waves, normal modes and harmonics, sound waves with examples of interference to form beats, and the Doppler Effect. Phase velocity and group velocity.

Properties of Light and Optical Images; Wave nature of light. Reflection, refraction, Snell’s law, total internal reflection, refractive index and dispersion, polarisation. Huygens' principle, geometrical optics including reflection at plane and spherical surfaces, refraction at thin lenses, image formation, ray diagrams, calculation of linear and angular magnification, magnifying glass, telescopes and the microscope.

Electric Field; Discrete charge distributions, charge, conductors, insulators, Coulomb’s law, electric field, electric fields lines, action of electric field on charges, electric field due to a continuous charge distribution, electric potential, computing the electric field from the potential, calculation of potential for continuous charge distribution.

Magnetic Field; Force on a point charge in a magnetic field, motion of a point charge in a magnetic field, mass spectrometer and cyclotron.

Electric current and Direct current circuits, electric current, resistivity, resistance and Ohm’s Law, electromotive force, ideal voltage and current sources, energy and power in electric circuits, theory of metallic conduction, resistors in series and in parallel, Kirchhoff’s rules and their application to mesh analysis, electrical measuring instruments for potential difference and current, potential divider and Wheatstone’s bridge circuits, power transfer theorem, transient current analysis in RC, RL, LC and LRC circuits using differential equations.

Alternating Current Circuits; Phasor and complex number notation introduced for alternating current circuit analysis, reactance and complex impedance for Capacitance and Inductance, application to LRC series and parallel circuits. Series and parallel resonance, AC potential dividers and filter circuits, Thevenin's theorem, AC bridge circuits to measure inductance and capacitance, mutual inductance, the transformer and its simple applications.

Static Equilibrium, Elasticity and fluids; Elasticity: stress, strain, Hooke's law, Young's modulus, shear modulus, forces between atoms or molecules, intermolecular potential energy curve, equilibrium separation, Morse and 6-12 potentials, microscopic interpretation of elasticity, relation between Young's modulus and parameters of the interatomic potential energy curve, the nature of interatomic forces, the ionic bond, calculation of the energy to separate the ions in an ionic crystal, viscosity of fluids, Poiseuille's law, Stokes' law.

Thermodynamics; Thermal equilibrium, temperature scales, thermal expansion of solids, relation between thermal expansion and the interatomic potential energy curve, the transfer of thermal energy: conduction, convection, radiation, the ideal-gas law, Boltzmann's constant, Avogadro's number, the universal gas constant. The kinetic theory of gases, pressure of a gas, molecular interpretation of temperature, molecular speeds, mean free path, specific heat, molar specific heat. The equipartition theorem, degrees of freedom. Heat capacities of monatomic and diatomic gases and of solids. Internal energy of a thermodynamic system, the first law of thermodynamics, work and the PV diagram of a gas., work done in an isothermal expansion of an ideal gas. Molar heat capacities of gases at constant pressure and at constant volume and the relation between them. Adiabatic processes for an ideal gas. Heat engines and the Kelvin statement of the second law of thermodynamics, efficiency of a heat engine. Refrigerators and the Clausius statement of the second law of thermodynamics. Equivalence of the Kelvin and Clausius statements. The Carnot cycle, the Kelvin temperature scale.

Atoms; The nuclear atom, Rutherford scattering and the nucleus, Bohr model of the atom, energy level calculation and atom spectra, spectral series for H atom. Limitation of Bohr theory. Photoelectric Effect. Blackbody Radiation. Compton scattering. X-ray diffraction. De Broglie hypothesis. Electron diffraction. Introduction to wavefunctions, Heisenberg's Uncertainty Principle.

Standard Lectures:

How Physical Sciences are taught at Kent.

Library use. Bibliographic database searches.

Error analysis and data presentation. Types of errors; combining errors; Normal distribution; Poisson distribution; graphs – linear and logarithmic.

Probability and Statistics. Probability distributions, laws of probability, permutations and combinations, mean and variance.

Academic integrity and report writing skills.

Laboratory experiments:

A number of experiments in weekly sessions; some of the experiments require two consecutive weeks to complete.

Experiments introduce students to test equipment, data processing and interpretation and cover subjects found in the Physics degree program which include the following topics:

Mechanics, Astronomy/Astrophysics, statistical and probability analysis, numerical simulations, electric circuits and Thermodynamics.

Computing Skills:

Introduction to the concept of programming/scripting languages. Introduction to operating systems: including text editors, the directory system, basic utilities and the edit-compile-run cycle.

Introduction to the use of variables, constants, arrays and different data types; iteration and conditional branching.

Modular design: Use of programming subroutines and functions. Simple input/output, such as the use of format statements for reading and writing, File handling, including practical read/write of data files.

Producing graphical representation of data, including histograms. Interpolating data and fitting functions.

Programming to solve physical problems.

Introduction to typesetting formal scientific documents.