# Courses for BSc. Physics

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- are several courses spread out across the various years under department to make learning efficient. These are mostly course related subjects and topics of interest but interlased with a few indirectly related subjects to educate in various aspects in order to produce a versatile graduate.
**YEAR ONE: Semester ONE****PHY 151 INTRODUCTORY MECHANICS 2 Credits**

Average speed and average velocity in one dimension. Instantaneous velocity. Average acceleration. Instantaneous acceleration. Motion with constant acceleration. Acceleration due to gravity. The displacement vector and the general definition of a vector. Addition of vectors. Position vector; components of vectors. Vector multiplication. Vectors and coordinate rotations. Velocity and acceleration vectors. Motion with constant acceleration. Projectiles. Uniform circular motion. Relativity of motion and the Galilean transformations. Newton’s laws of motion. Momentum of a particle. Galilean or Newtonian relativity. Forces; the equation of motion and its solution. Friction. Work in one and three dimensions. Kinetic energy. Potential energy. Conservation of mechanical energy. Newton’s law of universal gravitation. Measurement of G. Circular orbits. Elliptical orbits; Kepler’s laws. Gravitational potential energy. Inertial and gravitational mass; the principle of equivalence. Momentum of a system of particles. Conservation of momentum. Two-body collisions. Centre of mass. Motion of the centre of mass. Energy of a system of particles. Statics of rigid bodies, static equilibrium. Levers and pulleys. Simple harmonic motion. Simple harmonic oscillator : body suspended at the end of a spring simple pendulum . Kinetic and potential energies of a simple harmonic Oscillator. Damped and forced oscillations**CSM 183 INTRODUCTION TO COMPUTERS I 3 Credits**

Definition of computers. Hybrid, analogue and digital computers. Digital computers systems: - mainframe, mini & micro computers. Hardware - memory (RAM, ROM, PROM, EPROM, DRAM, CACHE) auxiliary memory (DRUM, DISK, DISKETTES). Processor - micro processors (arithmetic-logic unit, CPU, control unit) I/O control unit (disk controller, printer controller). Peripheral devices - Keyboards, magnetic tapes, monitors, printers, mouse, plotters, scanners, compact disks. Software - system software, application software. Concepts of an operating system. Files and filenames, wildcards. DOS commands - internal and external. Root directory and directory structure. Command syntax. Using DOS commands - commands such as VER, DIR,. FORMAT, COPY, DATE, TIME, RENAME, TYPE, ERASE, CHKDSK, TREE, CD, MD, RD, DEL, DISKCOPY, XCOPY, SCANDISK, DELTREE. Batch file. What windows is (Graphical user interface). Using a mouse. Starting windows. Shutting down your computer and windows. Basic controls - MENUS, dialog boxes, structure of a window, moving a window, sizing a window, switch between windows, arranging window, arranging icons, scrolling, closing a window. Working with programs - starting and closing programs, starting a program using Run, creating a shortcut, adding start Menu Programs, using the starting folder, starting programs minimized, install and uninstall programs, running DOS applications. Looking at files - using the WINDOWS EXPLORER, changing the display, using the TOOLBAR, file naming, opening and closing documents. Managing files and folders - selecting, copying, moving and deleting files/folders. Printing and printer setup, fonts, printing documents, print management. What is word processing? Starting word processing software. Document cycle (editing existing documents). Cursor movement. Entering text. Editing text. Enhancing the document - underline word/text, bold word/text, delete word/text. Moving text. Definition of computers. Hybrid, analogue and digital computers. Digital computers systems: - mainframe, mini & micro computers. Hardware - memory (RAM, ROM, PROM, EPROM, DRAM, CACHE) auxiliary memory (DRUM,. DISK, DISKETTES). Processor - micro processors (arithmetic-logic unit, CPU, control unit) I/O control unit (disk controller, printer controller). Peripheral devices - Keyboards, magnetic tapes, monitors, printers, mouse,. plotters, scanners, compact disks. Software - system software, application. Software. Concepts of an operating system. Files and filenames, wildcards. DOS commands - internal and external. Root directory and directory structure. Command syntax. Using DOS commands - commands such as VER, DIR, FORMAT, COPY, DATE, TIME, RENAME, TYPE, ERASE, CHKDSK, TREE, CD, MD, RD, DEL, DISKCOPY, XCOPY, SCANDISK, DELTREE. Batch file. What windows is (Graphical user interface). Using a mouse. Starting windows. Shutting down your computer and windows. Basic controls - MENUS, dialog boxes, structure of a window, moving a window, sizing a window, switch between windows, arranging window, arranging icons, scrolling, closing a window. Working with programs - starting and closing programs, starting a. program using Run, creating a shortcut, adding start Menu Programs, using the starting folder, starting programs minimized, install and uninstall programs, running DOS applications. Looking at files - using the WINDOWS EXPLORER, changing the display, using the TOOLBAR, file naming, opening and closing documents. Managing files and folders - selecting, copying, moving and deleting files/folders. Printing and printer setup, fonts, printing documents, print management. What is word processing?. Starting word processing software. Document cycle (editing existing documents). Cursor movement. Entering text. Editing text. Enhancing the document - underline word/text, bold word/text, delete word/text. Moving text. Copying text. Saving document. Retrieving document. Printing document. Merge / mail. Columns. Spell - checking a document. Adding footer. Exiting the word processing software. What is a spreadsheet? Cell and cell pointer. Cell address (Absolute and Relative). Moving the cell pointer. Function key. Starting a Spreadsheet Software. Entering text, numbers and formulae. Using functions. Concept of range. Copying. Moving. Deleting. Formatting - currency, commas. Widening / narrowing columns. Saving a spreadsheet. Changing numbers/text/formula. Printing a spreadsheet. Existing the spreadsheet. Graphing. Printing of graphs. Macro - definition and using macros/DATA commands /FILE commands/GRAPH commands/PRINT commands/RANGE commands/WORKSHEET commands. PRINT GRAPH commands. What is database? Concepts of table or relation, row and columns. What is Database Management System (DBMS)? Starting a database software. Creating a database structure. Adding data to a database. Searching a database. Sorting and indexing a database. Modifying a database's structure. Amending the data in a database. Saving the data in a database. Creating a report. Performing calculations. Selecting records in a database. Using two or more databases. Data base programming Exiting a database software**PHY 153 ELECTRICITY AND MAGNETISM 2 Credits**

Charge and Matter, Conductors. Semiconductors and Insulators. The Electric Field . Gauss's Law. The Electric Potential; Potential due to a Dipole. Electric Potential Energy.. Dielectrics: An Atomic View . Dielectrics and Gauss's Law.. The magnetic Field Circulating Charges. Cyclotrons and synchrotrons . Amp 're's Law. Force between two parallel current carrying conductors .The Biot-Sevart Law.. Energy and the Magnetic field Mutual Inductance . Magnetic Properties of Matter; Diamagnetism, Paramagnetism, Ferromagnetism. Antiferromagnetism, Ferrimagnetism, Electromagnets and Hysteresis. Electromagnetic Oscillations;. Alternating Currents. Power in Alternating Current Circuits. Resonance in Alternating Current Circuits The Transformer.. A.C. and D.C. Measurements**PHY 155 EXPERIMENTAL PHYSICS I 3 Credits**

Explanation and significance of instrumentation as a career in Physics. Design of devices and equipment (for various purposes) as the ultimate aim of instrumentation. Quantities obtained by direct and indirect measurements. General definitions or explanations of

(a) Accuracy and precision

(b) Sensitivity and resolution

(c) Absolute error, relative error and percentage error. A measured Quantity and the associated error

(d) Rounding off values and significant figures

(e) Unit of measure or least count (e.g. Best accuracy obtainable from an instrument)

Causes of error: systematic and random errors. Units of various measurable quantities Standard form The power of a lens "Over accurate" readings (i.e. Recording readings to more decimal places than can actually be obtained with an instrument). Errors Associated with direct measurements (e.g. metre rule, vernier calipers, micrometre screw gauge, multi - range pointer instrument with given limit of error, etc.) Error Associated with quantities obtained by indirect measurements (i.e. combination of errors). The "band diagram" method of determining the "true" value of a quantity measured by different methods (or instruments). Standard deviation and standard error. Correlation efficient and regressional analysis. Least squares method and curve fitting Instrument errors (e.g. voltmeters must have very high resistance etc.) The significance of mechanical properties of matter Tensile force, compressive force and shear force . Tensile strength and young's modulus. Stiffness and toughness . Creep and fatigue Hardness tests The use of Whetstone Bridge to measure both large and small resistance values. The use of analogue and digital multimeters to measure

(a) Voltage (AC and DC)

(b) Current (AC and DC)

(c) Resistance

Use of oscilloscope to measure peak voltages and time periods of various signal waveforms Potential and current divider arrangements. Resonant circuits, Q - Factor, Bandwidth and filters Ammeter and voltmeter calibrations. To learn basic experimental skills in Physics To learn scientific report writing. To consolidate theory. Practical experiment in Mechanics Practical experiments in Heat, Sound, Electricity, Magnetism, Solar Energy, and Nuclear. To learn basic experimental skills in Physics. To learn scientific report writing. To consolidate theory.**PHY 157 MATHEMATICS FOR PHYSICS I 2 Credits**

Elements of logic Some basic notations of set theory concept of functions The real number system R: natural numbers; positive and negative integers; rational and irrational (I) numbers, decimal representation of real numbers Real numbers and length, axioms of arithmetic; axioms of order; fundamental inequalities; completeness property of R; the uncountability of R and I Introduction to axiomatic set theory Elements of point set theory Infinity in the real number system Mathematical induction. Basic concepts: divisibility of integers; the greatest common divisor. Linear Diophantine equations. Number bases. Limits of functions. Continuous functions. Discontinuities. Monotonic functions. Infinite limits and limits at infinity. Derivative of a function of a real variable. Mean value theorem. Continuity of derivatives. L’Hospitals theorem. Derivatives of higher order. Taylor’s theorem. Application of Taylor’s theorem. Relative extrema**CHEM 155 BASIC PHYSICAL CHEMISTRY I 2 Credits**

Chemical electrode equilibrium polarisation and kinetics of electrode processes Mass transfer in electrolytic cells, electroplating Batteries and accumulators, fuel cells Surface tension, basic equations and measurements Thermodynamics of surfaces, surfactants - properties and applications Films and monolayers, wetting agents. Emulsions, emulsifiers, foams, foaming agents.**ENGL 157 COMMUNICATION SKILLS I 2 Credits**

Eight parts of speech:

1. Nouns and pronouns

2. Verbs, voice, tense

3. Adjectives and Adverbs

4. Conjunctions

5. Prepositions

6. Interjections

Use of article. Use of punctuation. Subject – verb agreement (Concord). Skills in reading, comprehension, summary and paragraph writing.**FC 181 FRENCH FOR COMMUNICATION 2 Credits**

La definition et le genre d'un objet

i. Qu' est-ce que c' est? ii. C'est un/une…..

L' identit? d' une personne

i. Qui est-ce? ii C' est …/Est-ce…? iii Qui, c' est… iv Montre-moi ../Voil?/Voici …

L'article defini - Le/La/Les L' emploi de

i. "Est-ce?" ii. "Qui, c' est …" iii. "Non, ce n' est pas …"

Conjugaison

i. Le present de l' indicatif des verbes reguliers et irreguliers

Interrogation

ii. Est-ce que iii. Par inversion iv. Par intonation

L' adjectif

i. Possessif (mon, ton, son, …) ii. Demonstratif ( ce, cette, cet, … )

Les chiffres de zero ? cent ( 0 - 100). L' heure/le temps ( Il fait beau, etc). Localisation (derrire, sous, sur, devant, etc )

L' emploi de

i. Au ii. ? la iii. ? l' iv aux

Les jours de la semaine. Faire connaissance / rencontre. Presentation / salutation. Savoir demander / donner une direction. Au telephone. Au restaurant. Utiliser les formules de politesse. Demander quelque chose / repondre ? une demande. Parler de ses go ets. Identifier quelqu' un. La culture francaise**YEAR ONE: Semester TWO****PHY 152 GEOMETRICAL OPTICS AND WAVES 2 Credits**

Reflection and refraction of plane mirrors. Reflection and refraction of convex and concave mirrors and lenses. Lens defeats and corrections. Simple and compound microscopes, micro-projector, Telescopes, and other optical instruments

General properties of oscillations and waves:

i. Mechanical oscillations : Simple Harmonic Motion (SHM)

ii. Energy in SHM

iii. Electrical oscillations, the general wave equation, planes and spherical solutions, phase angles, amplitude and intensity, frequency and wavelength

iv. Doppler effect in light and sound. Doppler broadening and red shift. Measurement of plasma temperature

i. Damped oscillation, forced oscillations and resonance. Qualitative interference and

diffraction of waves

Superposition of waves:

ii. Linear systems and principle of superposition. Superposition of two wave trains of

the same frequency.

iii. Formation of standing waves. Nodes and antinodes. Superposition of many waves with random phases. Superposition of waves of equal amplitude but slightly different frequency

iv. Amplitude-modulated waves, beats, group and phase velocity, dispersion of waves.

v Addition of SHM’s at right angles plane, circular and elliptical polarization. Lissajous

figures

vi Bandwidth of pulse, range of frequency needed for pulse of given duration.

i. Heisenberg’s uncertainty principle in numbers needed for pulse of given length. Heisenberg uncertainty principle in terms of momentum and position

Acoustic waves:

i. Sound reception, production, recording (The ear, Loudspeaker, Telephone and Earpiece sound recording and reproduction), sound track pitch, musical intervals, intensity and loudness.

ii. The decibel. Calculation of decibels, intensity levels, threshold of hearing, loudness, quality

iii. Helmholtz resonators

iv. Acoustics of rooms. Reverberation

v. Acoustic transducers

vi. Impedance frequency spectra of complex sounds. Distinction between string percussion and wind instruments

vii. Ultrasonic waves (production, properties and applications).

Electromagnetic waves:

i. Gamma and x-radiation, UV, visible, IR

ii. Radio waves sources and general properties

iii. Production and detection of electromagnetic waves.

iv. Measurement of intensity of light; fundamental parameters and units.

Matter waves:

i. Spectrum of blackbody radiation.

ii. Planck’s quantum hypothesis.

iii. Dual nature of light. Wave-particle. Duality of matter

iv. De Broglie’s hypothesis, properties of matter waves.**CSM 184 INTRODUCTION TO COMPUTERS II 3 Credits**

What is a spreadsheet?. Cell and cell pointer. Cell address (Absolute and Relative). Moving the cell pointer. Function key. Starting a Spreadsheet Software. Entering text, numbers and formulae. Using functions. Concept of range. Copying. Moving. Deleting. Formatting - currency, commas. Widening / narrowing columns. Saving a spreadsheet. Changing numbers/text/formula. Printing a spreadsheet. Existing the spreadsheet. Graphing. Printing of graphs. Macro - definition and using macros. /DATA commands /FILE commands/GRAPH commands/PRINT commands/RANGE commands/WORKSHEET commands. PRINT GRAPH commands. What is database?. Concepts of table or relation, row and columns. What is Database Management System (DBMS)?. Starting a database software. Creating a database structure. Adding data to a database. Searching a database

Sorting and indexing a database. Modifying a database's structure. Amending the data in a database. Saving the data in a database. Creating a report. Performing calculations. Selecting records in a database. Using two or more databases. Database programming

Exiting a database software.**PHY 154 PROPERTIES OF MATTER 2 Credits**

pressure: definition and formula for it. Atmosphere 2 pressure, Fortin’s Barometer Variation of atmospheric pressure with height Density, relative density . Archimedes’ principle, Its use in the measurement of density or relative density . Principle of flotation. Hydrometers . Fluids in motion. Streamlines and velocity .Pressure and velocity. Bernoulli's, principle . Applications of Bernoulli’s principle filter pump, aerofoil lift, flow of liquid from wide tank. Torricelli’s theorem. Measurement of fluid velocity. Pitot-static tribe Particle nature of matter. Size and separation of molecules Intermolecular forces. Properties of solids from molecular theory Bonds between atoms and molecules. Proportional and elastic limits . Hooke’s law. Yield point, ductile and brittle substances. breaking stress . Tensile stress and tensile strain. Young’s modulus. Bulk modulus . Modulus of rigidity or shear modulus. torsion wire . Deformation of solid introduction to dislocations. Newton’s formula, co-efficient of viscosity. Steady flow of liquid through a pipe. Poisenille’s formula. Turbulent motion. Stoke’s law, terminal velocity. Molecular theory of viscosity. Energy of gas-liquid, liquid-liquid and solid-solid interfaces. Definition, units, dimensions of surface tension. Some surface tension phenomena: capillarity, angle of contact. Measurement of surface tension Pressure difference in a bubble or curved liquid surface. Emulsions and emulsifiers. Wetting agents and their application. Molecular bonds and surface tension. The ideal gas laws. The ideal-gas temperature scale. Energy of an ideal gas. Equipartition of energy Mean free path. Random walk or Brownian motion. Maxwell’s distribution of velocities. Heat as a form of energy. Thermal expansion of solid and liquids. Thermometers and thermal equilibrium. Conduction of heat. Change of state. Specific heat of a gas .The adiatratic equation**PHY 156 EXPERIMENTAL PHYSICS II 3 Credits**

Small - signal amplifier calculations. Junction diode and veneer diode calculations Uses of thyristors, triacs and diacs (and the circuits in which they are used). The colour - band methods of calculating resistance and capacitance values.. Logic gates and de Morgan’s theorem (Boolean Algebra) Main features of ICS (e.g. Locating Pin 1 and its slot, etc.) ADC and DAC Pulse code modulation (sampling of analogue signals . Noise. The Venin and Norton theorems. Intrinsic and extrinsic semiconductor calculations Fibre - optics Testing the functionality of electronic components (e.g. Transistors, junction diodes, capacitor thyristors, etc.) Magnetomotive force, magnetic field strength (H) and magnetic induction (or magnetic flux density, (B). Magnetic susceptibility (X) reluctance and admittance Magnetization, hysteresis curve and energy dissipated. Hall voltage, measurements.. Photo multipliers, LED, LDR, Photodiodes, Phototransistors, Photovoltaic, etc.. Solid state detectors . Definition of a transducer

(a) Applications of transducers to electronic and other instrumentation systems.

(b) Various forms of energy

(c) Non-electrical quantities that may be measured by transducers (e.g. temperature, using thermistors or Thermo - couples etc.

Cooling laws:

(a) Newton's law of cooling

(b) The five - fourths power law

Different Modes of heat transfer (i.e. Radiation, Convection, etc.). Heat flow along a perfectly lagged bar. Stefan's law. U-values and their significance. Thermal resistance coefficient Ionization chamber, proportional counter, Geiger counter.. Scintillators and scintillation chambers.. Applications of radioisotopes Absorbed dose and dangers of Ionising radiation Single - channel and multi - channel analyzers.. Practical experiments in Mechanics Practical experiments in Heat, Sound, Electricity, Magnetism, Solar Energy, and Nuclear. To learn basic experimental skills in Physic. To learn scientific report writing . To consolidate theory.**PHY 158 MATHEMATICS FOR PHYSICS II 2 Credits**

Riemann integrability. Property of the Riemann integral. The fundamental theorem of integral calculus. Evaluation of integrals.. Connection of the trigonometric functions with the unit circle, the unit equilateral hyperbola and the hyperbolic functions. Properties of the hyperbola and the hyperbolic functions. Inverse hyperbolic functions. Differentiation and integration of the hyperbolic functions. The Riemann sum and the expression of the limit at infinity of certain series in integrals. Cauchy’s fundamental theorem of calculus. Classification and solution of differential equations (DE’s) of the first order. Linear differential equations (LDE’s) of first order. Equations reducible to first – order DE’s. LDE’s of arbitrary order; solution of second-order LDE’s with constant coefficients. Operational calculus and the solution of LDE’s with constant coefficients. Laplace transformations and their application to the solution of second-order LDE’s with constant coefficients. Solution of Euler – type DE’s. Applications to Mechanics. Vectors in Cartesian coordinate systems. Addition and multiplication of such matrix. Change of coordinate axes and the concept of matrices. Matrix algebra. Repeated rotations. Matrix multiplication. Types of matrices: orthogonal, hermitian and unitary matrices. Associated matrices: the transpose, adjoint and inverse of a matrix. The invariants of a matrix: the trace and determinant. Projectiles and evaluation of determinants. Application to the solution of simultaneous linear equations and linear systems of differential equations with constant coefficients**CHEM 156 BASIC PHYSICAL CHEMISTRY II 2 Credits**

Oxidation. Epithaxial growth. Diffusion. Etching. Crystal growth. Lithography. Ion implantation. Plastics. Chemical structure. Physical, mechanical and elastic properties. Processing and uses. Definitions

i. Polymers ii. Plastics iii. Elastomers

Fibres, coatings, adhesives**ENGL 158 COMMUNICATION SKILLS II 2 Credits**

The communication process. Skills in communication. Communication in organisation. How to prepare effective document. The dynamics of oral communication. Business correspondence. Technical report writing. Writing proposals. Memos, briefs, meetings and minutes**FC 182 FRENCH FOR COMMUNICATION II 2 Credits**

L'article partitif ( du, de la, de l' , des, ..). Les pronom

Conjugaison

i. Le futur simple ii. Le passe compose

Pronominalisation ( pronom d'objet direct …). L'expression avec " avoir" / "?tre"

i. Ex - avoir besoin de ii. Ex - avoir envie de, etc

Les chiffres de cent ? l'infinite. Degre de l'adjectif. L'expression avec - "Il y a / Depuis. Le pluriel

Mots interrogatifs

i. Quand ii. combien, etc

Au marche (Acheter et consummer ). Invitation. A la banque. Le voyage ( par avion / par le train ). Remplir une appartement. Correspondance ( lettre non-officielle). La culture fancaise (suite)**YEAR TWO: Semester ONE****PHY 251 ELECTRONICS I 2 Credits**

Work function, space charge, photon emission. General principles and construction of Cathode Ray Oscilloscope. Uses of Oscilloscopes. Rectification and amplification. P-N junction formation and behaviour. Semiconductor diodes characteristics and application. Power supplies and filters. Regulated power supplies. Voltage multipliers. Biasing techniques. AC and DC loadlines. Characteristics of CB, CE, and CC configurations. Introduction to amplifiers : small signal amplifiers, R-C couples amplifiers. Voltage follower configuration.**PHY 253 CLASSICAL MECHANICS I 2 Credits**

Newton’s laws of motion ; equation of motion. Superposition of forces. Solution of the equation of motion for different forces. Dynamics of uniform circular motion. Centripetal force. Law of conservation of linear momentum. Centre of mass (CM), computation of CM’s of solid bodies. Motion of the CM. Energy of a system of particles. Motion of a rocket. Impulsive forces. Collisions in one and two dimensions. The ballistic pendulum. Collisions and reactions of nuclei and of elementary particles. Motion of a rigid body. Rotation about a fixed axis. Angular velocity and angular acceleration. Motion with constant angular acceleration. Kinetic energy of rotation; moment of inertia. Computation of moments of inertia of simple solid bodies. The inertia tenor. Angular momentum of a particle and of a rigid body. The torque; equation of rotational motion; conservation of angular momentum and its applications. Work, Energy and Power in rotational motion. Rolling motion. Precession of a Gyroscope. Classification of constraints: examples. Generalised coordinates. Conservative systems. The one-dimensional calculus of variations. Problems with fixed end points and its solution: the Euler-LaGrange equations. Solution of the Brachistochrone problem and other extremum problems. Hamilton’s principle. Derivative of the LaGrange equations of motion from the Hamilton principle. Application to simple mechanical systems executing small oscillations and to current oscillations in coupled electrical circuits.**PHY 255 THERMODYNAMICS 2 Credits**

Specific heat. Mechanical equivalent of heat. Specific heat of a gas at constant pressure and constant volume. The adiabatic equation. Internal energy. Generalised concept of work. The first law as statement of conservation of energy. Fundamental equation. Internal energy and entropy representation. Extensive and intensive variables. Equation of state. Examples of the Carnot cycle. Carnot’s theorem and corollary. The Kelvin temperature scale. Entropy as a function of state Clausius theorem. Entropy and statement of the second law of thermodynamics. Principle of caratheordory. Entropy and reversibility. Entropy and equilibrium. Principle of increase of entropy. Entropy and unavailability of energy. Entropy and disorder. Entropy and direction of time. Entropy flow and entropy production. Introduction to irreversible thermodynamics. Reversible and irreversible processes. Conditions for thermal and mechanical equilibria. Isentropic, adiabatic and isothermal processes. The Helmholtz and Gibbs free energies; enthalpy. Legendre transformations of the thermodynamic potentials. Physical significance of the potentials. The Maxwell relations. Thermal expansivity. Isothermal and adiabatic compressibilities, heat capacities at constant pressure and volume. Gibbs free energy and phase transitions. First- and second-order phase transitions. Examples. The Clausius-Clapeyron equation. Polymorphic transitions (Ice, carbon, etc) Methods of liquefaction of gases: Joule – Thompson cooling; Adiabatic demagnetization of paramagnetic states. Measurement of low temperatures. Introduction to superfluidity and superconductivity. Heat pumps. Refrigeration. Freeze-drying. Pressure cooking. Thermoelectricity. Solid state refrigerators**PHY 257 EXPERIMENTAL PHYSICS III 3 Credits**

Practical experiments in Solid State Physics and Materials Science. Practical experiments in Optics. Practical experiments in Electronics and design and fabrication of electronic projects . Practical experiments in Nuclear Physics. To learn scientific report writing. To consolidate theory.**PHY 259 MATHEMATICS FOR PHYSICS III 2 Credits**

Directional and partial derivatives. Total derivatives (Differentials). The gradient vector. Differentials of composite functions. Condition for existence of the differential. Partial derivatives of higher order. Applications of partial differentiation: parametric integration; the Jacobian; the inverse and implicit function theorem; extremum problems. Multiple integrals (MI). Surface and volume integrals. Condition for existence of MI. Evaluation of MI: repeated integration; change of variables. Vectors in Cartesian coordinate systems. Change of axes. Scalar and vector fields. Vector fields in a plane. Line integrals; Green’s theorem. Vector fields in space. Gauss’s and Stokes’ theorems. Curvilinear coordinates**PHY 261 PROGRAMMING WITH PASCAL I 3 Credits**

Introduction to computers. Types of high level programming. Languages. Versions of PASCAL. Structure of PASCAL program. Reserved words. Identifiers. Numbers and strings. Constants and variables. Expressions and statements. Integer - type data. Real - type data. Char - type data.. Boolean - type data. Standard constants. Standard functions. Enumerated - type data. Subrange - type data. Utilizing user-defined data. Read and ReadIn statements. Write and WriteIn statements. The EO/n and Eof functions. Formatted output. Declaring string types and variable. String manipulations. The FOR structure. The WHILE - DO structure. The REPEAT - UNTIL structure. Nested control structures. The IF structure. The GOTO statement. Procedures - nested procedures. Parameters - value and reference. Functions. Recursion. The TURBO PASCAL editor. Planning a PASCAL program. Writing a PASCAL program. Entering the program into the computer. Compiling and running.**PHY 263 NUCLEAR PHYSICS 2 Credits**

Properties of nuclei. Labeling, masses and sizes of nuclei. Nuclear spins and dipole moments. Stability curve. Instability of nuclei. Nature of nuclear force. Liquid drop model. Fermi-gas model . Shell model. Infinite square well. Harmonic oscillator. Spin-orbit potential. Predictions of the shell model. Collective model superdeformed nuclei. Alpha decay, barrier penetration. Beta decay. Gamma decay. Fission. Chain reaction. Nuclear fusion. Radioactive decay. Radioactive equilibrium. Natural radioactivity and radioactive dating. Energy loss. Charged particles. Units of energy loss and range. Straggling, multiple scattering, and statistical processes. Energy loss through bremsstrahlung. Interaction of ionizing radiation (?,?,?, n) with matter. Interaction of hadrons at high energies. Ionization detectors. Ionization counters. Proportional counters. Geiger-M?ller counters. Scintillation detectors. Time of flight. Cherenkov detectors. Semiconductor detectors. Calorimeter. Layered detectors. Electrostatic accelerators:. Cockcroft-Walton machines. Van de Graaff accelerators. Resonance Accelerators

i. Cyclotron ii. Linear accelerator

Synchronous accelerators. Phase stability. Strong focusing. Colliding beams. Forces

Elementary particles

i. General ii. Quarks and leptons ii. Quark content of mesons iv. Quark content of baryons

Quantum numbers:

i. Baryon number ii. Lepton number iii. Strangeness iv. Isospin

Gell-Mann - Nishijima relation. Production and decays of resonance. Determining spins. Violation of quantum number:. Weak interactions

(a) Hadronic weak-decays (b) Semileptonic processes

Electromagnetic processes. Parity: ? - meson, ?. Violation of parity. Time reversal. Charge conjugation. CPT theorem. Neutral Kaons CP eigenstates of neutral Kaons. Strangeness oscillation. regeneration. Violation of CP invariance. Time development and analysis of the system. Semileptonic decays.**ENGL 263 LITERATURE IN ENGLISH I 1 Credit****ECON 151 INTRODUCTORY ECONOMICS I 2 Credits**

Fundamental concepts of economics and use of analytical techniques in study of economic problems. Knowledge of principles used in related disciplines. Consumer choice. Determination of prices in different market conditions. Production theory and the theory of distribution**FC 281 FRENCH FOR COMMUNICATION III 2 Credits**

Présentation – se presenter; presenter quelqu’un Remplir une fiche de renseignement

Poser des questions pour se renseigner sur quelqu’un. Saluer. Accueillir des amis chez soi

Dire au revoir / Prendre conge. Inviter / Accepter une invitation. Refuser une invitation

Remercier / répondre aux remerciements. Parler de l’avenir / Faire des projets. Raconter au passé. Exprimer une condition. Chercher une chamber à louer. Verbes: Révision du present de l’indicatif. Le future simple. Le passé compose. L’imparfait. Le conditionnel present.**YEAR TWO: Semester TWO****PHY 252 ELECTRONICS II 2 Credits**

Small signal analysis of common source, gate and drain amplifiers. Qualitative treatment of positive and negative feedback and their applications in amplifier design. Introduction to the applications of linear ICs : timers, operational amplifiers, PLL, etc**PHY 254 CLASSICAL MECHANICS II 2 Credits**

The Lagrangian equation and their application to the solution of more small-oscillation problems. Conservation theorems and symmetry properties: Generalised coordinates and momenta; cyclic or ignorable coordinates; conservation of the generalised momentum conjugate to a cyclic coordinate; conservation of total energy for conservative systems. The concept of the Hamiltonian. The two-body central force problem; reduction to the equivalent one-body problem. The equations of motion and first integrals. The equivalent one-dimensional problem and classification of orbits. The differential equation for the orbit and integrable power-law potentials. The Kepler problem. Scattering in a central force field. Frames of reference; inertial frames; the principle of relativity. The Galilean transformation and its limitations. The Lorentz transformatio. Proper time; time dilation; the Lorentz-Sitzgerald. contraction. Addition of velocities. Covariant four-dimensional formation of STR; 4 – vectors and relativistic invariants. Generalization of Newton’s equations of motion. The Minkorski force. Relativistic momentum, energy and mass. Einstein’s relation. Legendre transformations. Derivation of Hamilton’s canonical equations. Application to simple problems. Cyclic coordinates and Routh’s procedure. Conservation theorems and the physical significance of the Hamiltonian.**PHY 256 E.M. THEORY 2 Credits**

The conservation of charge and the equations of continuity

Maxwell's equations:

i. Maxwell's equations in free space

ii. Maxwell's equations in linear isotropic media

iii. Maxwell's equations for harmonically varying fields

Energy in the electromagnetic field, Poynting theorem. The electromagnetic wave equation. Plane electromagnetic waves in free space. Plane electromagnetic waves in non-conducting isotropic media. Plane electromagnetic waves in conducting media: the "skin depth". Propagation of electromagnetic waves. Polarization of E.M. waves. Boundary conditions of E.M. field vectors at surfaces of discontinuity. Normal and oblique incidence of E.M. waves into a conducting medium. Normal and oblique incidence of E.M. waves into a dielectric medium. Total internal reflection. Tem, TE and TM waves. Transmission lines. Waveguides:. The rectangular waveguides. Time averaged power flow. Cavity resonators.**PHY 258 EXPERIMENTAL PHYSICS IV 3 Credits**

Practical experiments in Solid State Physics and Materials Science. Practical experiments in Optics. Practical experiments in Electronics and design and fabrication of electronic projects . Practical experiments in Nuclear Physics. To learn scientific report writing. To consolidate theory.**PHY 260 MATHEMATICS FOR PHYSICS IV 2 Credits**

Definition and historical background. Basic algebra and geometry of complex numbers. Definition. Transcendental functions; Euler’s formula and its applications. Complex conjugation of FCV. De Moivre’s theorem and calculation of roots. Trigonometric, hyperbolic and logarithmetric functions. Differentiability and analyticity of FCV. The Cauchy-Riemann relations. Integration of FCV. Cauchy’s integral theorem and integral formulae. Power series expansions for analytic functions: Taylor and Laurent expansions. Zeroes and isolated singularities of FCV. Cauchy’s residue theorem and its application to the evaluation of integrals: contour integration. Improper integrals. Conformal mapping by analytical functions. The error functions or integral. Gamma functions; stirling’s formula. The Beta functions. Application of the gamma and beta functions in integration of real functions**PHY 262 PROGRAMING WITH PASCAL II 3 Credits**

One-dimensional array. Multi-dimensional array. Operations with entire arrays. Defining a record. Processing a record. The WITH structure. Variant records. Defining a file. Creating a file. Reading a file. Writing a file. Text and Random Access Files. Updating a file. Defining a set. Constructing a set - numeric, character, user- defined. Operations with sets. Set comparisons. Difference between enumerated types and set. Difference between static and dynamic variables. Type definitions. Variable declarations. Operation with pointer variables and referenced. Variables. Creating and destroying dynamic variables.**PHY 264 OPTICS 2 Credits**

Hughens principle, Applications in Young's Interferometer. Fresnel biprism and other apparatus depending on division of the wave front. Theory of coherence; complete coherence, partial coherence and incomplete coherence. Fringe contrast (visibility).. Division of amplitude. Michelson interferometer Circular fringes localised fringes. Index of refraction by an interference method. .Interference involving multiple reflections; Reflection from a plane - parallel film; the wedge film, Newton's rings, Applications, measurement of film thickness Nonreflecting films, sharpness of fringes.. Fabry - Perot interferometer, Chromatic-resolving power. Study of Hyperfine structure and of line shape.. Interference filters. Fresnel and Franhofer Diffraction by the single slit (elementary consideration). The Fresnel kirchhoff integral and its application in the various apertures. Chromatic resolving power of a microscope. The double slit, derivation of the equation for the intensity. Distinction between interference and diffraction. Maxima and Minima. Missing orders.. The diffraction grating, intensity distribution from an ideal grating. Formation of spectra by a grating. Overlapping orders Resolving power of the grating.. Polarisation by reflection, representation of the vibrations in light. Polarising angle and Brewsters law. Polarisation by a pile of plates.. Polarisation by dichroic crystals.. Polarsiation by double refraction, optic axis The Nicol Prism.. Interference of polarised light, quarter and half - wave plates**ENGL 264 LITERATURE IN ENGLISH II 1 Credit****ECON 152 INTRODUCTORY ECONOMICS II 2 Credits**

National income measurements and determinants. Fluctuations in economic activity and trend in Ghana's national income. Index numbers. International trade and national economy

Role of government.**FC 282 FRENCH FOR COMMUNICATION IV 2 Credits**

Exprimer ses gouts, son opinion sur quelqu’un ou, quelque chose. Parler au téléphone

A la banque (Ouvrir un compte). Dire à quelqu’un de faire quelque chose. Proposer quelque chose à quelqu’un un. Accepter / Refuser. Donner des informations sur son environnement, sur son pays, etc. Exprimer son accord ou son disaccord. Rapporter les paroles de quelqu’un

Rédiger une letter amicable / officielle. Préparer le curriculum vitae, Relations – cause / consequence: Hypothèse. Se situer dans le temps. Quantifier: Lexique de l’opinion : adjectives et adverbs. Verbes exprimant le gout. Verbes d’opinion. Le plus que parfait

Le future antérieur. Le passif. L’infinitif passé. Le subjonctif present. Le conditionnel passé**YEAR THREE: Semester ONE****CORE COURSES****PHY 351 QUANTUM MECHANICS 3 Credits**

Blackbody radiation, Planck's theory. Photoelectric effect, Einstein's quantum theory. Compton effect, dual nature of electromagnetic radiation. Atomic structure: Thompson's and Rutherford's models. Stability of the nuclear atom. Atomic spectra, Bohr's model of the hydrogen atom. Matter waves, De Broglie's hypothesis. Davisson - Germer experiment. Wave Particle Duality. Complimentarity Principle. The Wave Function. Wave Function of a Free Particle.. Principle of Superposition. Wave Packets, Group and Phase Velocities of Matter Waves, Heizenberz's Uncertainty Principle.. The Wave Equation. Operators and Dynamical Variables Position, Momentum and Energy Operators. Interpretation of the Wave function. Probability and Current Densities. Conservation of Probability. Time-Dependent and Time-Independent Coefficient.. Expectation Values of Dynamical Variables and Operators. Ehrenfest's Theorem.. Linear Vector Spaces. Hilbert Space. Operators in Hilbert Space. Commuting and Non-Commuting Operators. Matrix Representation of Operators. Adjoint of an Operator. Hermitian Operators (Observables). Dirac's Bra and Ket Notation. Eigenvalue and Eigenvectors of Hermitian Operators Observables). Simultaneous Measurability of Commuting Observables. Non-Commuting Observables. Heisenberg's Uncertainty Relations.**PHY 353 SOLID STATE PHYSICS I 3 Credits**

Crystals, glasses, polymers. Unit cells - Bravais lattices . Types of symmetry. Some important crystal structures .Miller indices Primary bonding - Covalent, Ionic, Metallic. Seimdary bonding - van der waal. Bragg Formula. Reciprocal lattice. Powder Diffraction. Structure Factor. Experimental Methods - Powder, Lane, rotation. Applications of X-ray diffraction. Types of Defects. Crystal growth.**PHY 355 ENVIRONMENTAL PHYSICS I 2 Credits**

The Homosphere and Heterosphere . The Temperature - Related Regions. The Chemisphere and Ionosphere. Composition of the Homosphere . Physics of Air/Water-Vapour Mixture . Hydrostatic Pressure and "Dry" stability.. Stability of saturated Air: "Wet Lapse Rate". Chemical Dynamic. Expressions of Gaseous Concentrations. Conservation of mass, hydrodynamics. The Euler Equation; Compressible and Incompressible Fluids. The vorticity Equation. The isopycnic Vorticity Theorem. The Navier-Stokes Equation. Bernoulli's Equation for an immiscible Fluid in Steady Motion. Viscous flow around a sphere; stoke's law**PHY 359 MATHEMATICS FOR PHYSICS V 3 Credits**

Definition. Subsequences. Convergent and divergent sequences. Monotonic sequences of real numbers. Definition. Alternating series. Absolute and conditional convergence. Tests for convergence of series with positive terms. Series of non-negative terms. The number e. Tests for convergence: the root and ratio tests; the integral test. Rearrangements of series. Examples of sequences of real-valued functions. Uniform convergence and continuity. The Cauchy condition for uniform convergence. Uniform convergence of infinite series. Uniform convergence and differentiation. Uniform convergence and integration. Bounded convergence. Mean convergence. Integration and differentiation theorems. Taylor series. Orthogonal systems of functions. Linear independence of functions. Fourier series of a function relative to an orthogonal system. Mean-square approximation. The trigonometric Fourier series. Parseval’s formula and its use in the evaluation of some infinite numerical series. Half-range trigonometric Fourier series. Sine and cosine series. The polynomial solutions to the Hermite, Legendre and laguerre polynomials: the Hermite, Legendre and laguerre polynomials. The Bessel equation: the Bessel functions. The modified Bessel functions. The wave and heat equations in one dimension. Solution by separation of variables. The Laplace equation. Solution by separation of variables.**COURSES IN AREA OF SPECIALISATION****1. PHYSICS WITH APPLIED MATHEMATICS****PHY 371 PROGRAMMING WITH C++ I 3 Credits**

C ++ class libraries. C ++ key words. Layout of a typical C ++ Program. Precedence of operators. Variables. Identifiers. Variable declarations. Assignment statements. The types int. and double. Other number types. The type char. Type compatibility Arithmetic operators and expressions. Output using Cout. Input using Cin. Line breaks in I/O. The if selection structure. The if/else selection structure. The while repetition structure. Assignment operators. Increment and decrement operators. The for repetition structure. The switch multiple - selection structure. The do/while repetition structure. The break and continue statements. Declaring arrays. Sorting arrays. Searching arrays. Multidimensional arrays Pointers and strings. Functions as program modules in C ++. The math library functions . Function definitions. Function prototypes Scope rules. Recursion. Inline functions. Function over loading**PHY 357 FLUID DYNAMICS 2 Credits**

Real and ideal fluids. Velocity of a fluid at a point. Streamlines and pathlines; steady and unsteady flows. The velocity potential. The vorticity vectors. Local and particle rates of change; the equation of continuity. Acceleration of a fluid. Pressure at a point in a fluid at rest and in a moving fluid. Conditions at a boundary of two inviscid immiscible fluids. Euler’s equations of motion. Bernoulli’s equation. Steady motion under conservative body forces. Axially symmetric flows. Bessel functions. The wave and heat equations in one dimension. Solution by separation of variables. The Laplace equation. Solution by separation of variables.**PHY 363 COMPUTER ARCHITECTURE 2 Credits**

Logic works. Motorola M68000 assembler (on Unix). B7 numbers: representation and operations. Binary, octal, hex representation. Base conversions. Negative numbers (sign – magnitude, 1’s complement, 2’s complement). Floating point numbers. Addition, subtraction, multiplication (integer, real, carry/borrow, overflow). Character representation (ASCII). B7 Boolean algebra. Boolean logic theorems. Basic functions: NOT, AND, OR, NAND, NOR, XOR. Truth table. Logic symbols. B7 combinational design. Don’t cares, miniterms, maxterms. Sum-of-products, product-of0sums form. NAND, NOR representations. Karnaugh maps. B7 Boolean design and simulation of logic. Using logic works. B7 sequential logic. Latches and flip-flops (SR, D, JK, T). State representation. State representation. Present state, next state, outputs. State diagrams and tables. Finite state machine implementation. B7 computer organization. Block diagram. CPU: ALU, registers, stacks

Memory: DRAM, SRAM**2. PHYSICS WITH BIOMEDICAL PHYSICS****PHY 365 BIOMEDICAL LABORATORY I 3 Credits**

Laboratory experiments involving the use of models of simple nuclear, medical physics and biophysics situations. Use of Medical Physics (Radiation Protection, etc) equipment in Hospitals, and on and near campus to carry out small scale surveys. Field trips to Nuclear and Biomedical institutions and other sites of interest.**PHY 367 MEDICAL PHYSICS I 2 Credits**

Types and sources of ionizing radiations. Interaction types (alpha, beta, photons, and neutrons). Interaction Coefficients. Passage of Charged Particles through Matter. Principles of Measurements. Radiation Quantities and Units. Measurement of Fluence, Energy Fluence and Spectral Distribution. Direct measurement of Absorbed Dose. Exposure and its measurement. Calorimeters. Ionization Chambers. Chemical Dosimetry. Thermoluminescence Dosimetry (TLD). Photographic Dosimetry. Scintillation Detectors. Other Dosimetric Systems. Choice of Dosimetric Systems. Basic human physiology. Cell biology. Interaction of Radiation with cells. Somatic effects of radiation. Hereditary effects of radiation. The X-Ray tube. Electron energy and bremsstrahlung. KVP and characteristics radiation. Efficiency and Efficacy (output). KV production. Rectification. Voltage waveform and x-ray production. Capacitors. MA control. Exposure timing. Heat production. Heat capacity. Focal spot area. Anode body. Tube housing. Contrast types. Effects of Photon Energy (KVP). Area Contrast. Contrast reduction. Collimation. Air gap. Grids. Grid penetration and selection. Screen function. Receptor sensitivity Image blur and noise. Artifacts. Film function. Optical density. Film structure. Photographic process. Sensitivity. Quality control. Contrast transfer. Film latitude and types. Effects of processing. Film fog. X-Ray generator. Receptor sensitivity. Patient. Distance and Area. Automatic exposure control. Intensifier tubes. Video systems. Optical systems and cameras. Receptor sensitivity. Digital image. Image processing. Quantitative data processing and analysis. Display control.**PHY 369 RADIOBIOLOGY I 2 Credits**

Membrane system of the cell. Cell types Initial physical events. Radiolysis of water. Radiation on Aqueous solutions

Radiosensitivity. DNA molecules and their relationship with chromosomes. Radiation lesions in DNA molecules. Repair of DNA lesions. Radiation effects on chromosomes. DNA lesions and cell death. Cell death. Cell survival curves

Cellular radiosensitivity. Cell survival and repair: fractionated irradiation and low dose rate**3. PHYSICS WITH COMPUTING****PHY 371 PROGRAMMING WITH C++ I 3 Credits**

C++ class libraries. C++ key words Layout of a typical C ++ Program. Precedence of operators. Variables. Identifiers. Variable declarations . Assignment statements. The types int. and double. Other number types. The type char. Type compatibility . Arithmetic operators and expressions. Output using Cout . Input using Cin. Line breaks in I/O. The if selection structure . The if/else selection structure . The while repetition structure . Assignment operators . Increment and decrement operators .The for repetition structure , The switch multiple - selection structure . The do/while repetition structure . The break and continue statements. Declaring arrays. Sorting arrays . Searching arrays. Multidimensional arrays . Pointers and strings. Functions as program modules in C ++ . The math library functions . Function definitions . Function prototypes . Scope rules . Recursion Inline functions . Function over loading**PHY 373 MINI-PROJECT WITH APPLICATION PACKAGES I 2 Credits**

Word (Microsoft). Power point. Excel (Microsoft). Access (Microsoft). Works (Microsoft). Coral draw. Paint.**PHY 375 COMPUTER HARDWARE COMPONENTS I 2 Credits**

The system motherboard . The floppy disk drive. The hard disk drive. The CD ROM Drive. The keyboard. The computer monitor. Printers. The power supply unit.**4. PHYSICS WITH ELECTRONICS****PHY 377 ELECTRONIC LABORATORY I 3 Credits****PHY 379 ANALOGUE CIRCUITS 2 Credits**

Small signal transistor models. Basic amplifier structures (CC, CB, CE). Differential amplifiers and current sources. Operational amplifiers, their properties and applications. Biasing and stabilizing circuits. Introduction to integrated circuits the 741 op-amps. Power amplifiers (A class, B class, complementary, Darlington). Frequency response of wide band and narrow band amplifiers. Feedback amplifiers, transients and stability, the error locus concept.**PHY 381 ELECTRONIC MATERIALS AND DDEVICES 2 Credits**

Electron statistics in Semiconductors. Photoconductivity. Non-homogeneous devices. p-n junction. Metal - semiconductor devices . High-field effect in semiconductors The Gunn effect in semiconductors . Magnetic Properties The BCS Theory . High - temperature superconductors Applications. Piezoelectric, pyroelectirc and ferroelectric materials . Classification of ferroelectrics . Applications of ferroelectric thin films and ceramics.**5. PHYSICS WITH GEOPHYSICS****PHY 383 GEOPHYSICS LABORATORY I 3 Credits**

A. Minerals and Rocks Classification and Identification

• Definition: Mineral, Crystal and Rock

• Basic Crystal Systems

• Concepts of Classification and Identification of Minerals and Rocks – Laboratory Work

• Identification of Minerals and Rocks in the Field

• Concepts of Strike and Dip

B. Geophysical Instrumentation Practical

• Electrical Resistivity Model Experiments

• Outdoor Gravity Measurements: Variation of gravity with altitude

• Outdoor Magnetics: Variation of Earth’s magnetic field over a buried magnetised body.**PHY 385 INTRODUCTORY GEOPHYSICS 2 Credits**

Theories of the origin of the Solar System

i. The Nebular hypothesis; Collision hypothesis

ii. The Proloplaner hypothesis

The centrifugal effect of the earth's rotation,

i. the spheroid and geoid

ii. the flattening of the earth

Gravitational potential, Macullagh's formula, g derived from gravitational and rotational potential; IGRF, the Principle of Isostasy [ Pratt and Airy]. Origin of the magnetic and electric fields. The Dynamo theory. Magnetic minerals. Magnetic remanence. Palaeomagnetism. Heat flow. The Heat sources; Rock dating techniques. The internal structure of the earth derived from seismology. Theory of plate tectonics. Types of plate movement.**PHY 387 INTRODUCTORY GEOLOGY 2 Credits**

Origin of igneous rocks. Magmas. Crystallization of magmas. Intrusive and extrusive igneous rocks

Classification of sediments and sedimentary rocks. Diagnosis and lithification. Types of metamorphic rocks. Forces in metamorphism. The geologic time scale

Minerals - general. Economic minerals of Ghana and where they occur.**6. PHYSICS WITH MATERIALS SCIENCE****PHY 389 MATERIALS SCIENCE LABORATORY I 3 Credits****PHY 391 STRUCTURAL DEFECTS IN CRYSTALS AND THEIR CONSEQUENCES**

Geometry and atomic structure of point defects

Line defects ( dislocations) and area defects ( surfaces and interfaces) in materials. Formation of defects and mobility of defects. Energy of defects and its relationship with structure

Mechanisms of diffusion. Diffusion equations. Appli