1、ECOLE POLYTECHNIQUE INGENIEUR POLYTECHNICIENPROGRAMINTERNATIONAL ADMISSIONSRecomme nded kno wledge in Physical Scie ncesThe recomme nded kno wledge in Physical Scie nces for the applica nts to the“ Traci-International admissions ” is detailed below.This docume nt is meant to give the applica nts dir

2、ect ions on the kno wledge they arelikely to be in terviewed upon .It is give n for in formati on purposes only and cannot becon sidered as a basis of the programme for the sec ond track exam in ati ons.Ecole Polytechnique reserves the right to test an applicant s knowledge on otherfields of Physica

3、l Sciences than those listed in this document.Besides, Ecole Polytech nique expects the applica nts to know the nu merical values of the basic con sta nts of physics, as well as the orders of magn itude of the physical phe nomena of n ature.The applica nts should be able to show excelle nt sta ndard

4、 mathematical skills.An excelle nt level in mathematics and in physical scie nces is a key to successful studies at Ecole Polytech niq ue.I. MECHANICS?Newt onian mecha nics?Mecha nics of solids?Statics and mecha nics of fluids?Applicati ons of mecha nicsII. ELECTRIC CIRCUITSIII. ELECTRICITY AND MAGN

5、ETISM?Electrostatics?Mag netostatics?Electromag netic wavesIV. OPTICS?Geometrical optics?Wave opticsV. THERMODYNAMICS?Perfect gas?First and sec ond prin ciples of thermod yn amicsPhysical con sta ntsThe values of Pla nek, Boltzma nn and Avogadro con sta nts, the charge and the mass of the electron,

6、the speed of light in vacuum, the electric permittivity and the magnetic permeability of free space, in SI system of units (at least two significant digits are required.Orders of magn itudeThe orders of magnitude of quantities such as the magnetic field of the Earth, thes surface, the concen tratio

7、n ofradius of the Earth, the accelertion of free fall at the Earth electro ns in a typical metal, the wavele ngths of the electromag netic waves of the visible spectrum, the distance between two atoms in a solid or liquid, the Bohr radius of the fun dame ntal state of the hydroge n atom, the size of

8、 the nu cleus.Compulsory mi ni mal requireme nts of calculati on skillsMasteri ng a certa in nu mber of calculati on skills such as is compulsoryExpa nsionsBe able to study the behaviour of a physical qua ntity A (x in the n eighbourhood of agive n value of its argume nt x . The com mon expa nsions

9、about x 0(22111;1l n( ; 22131cot ; 33ta n ; 221cos ; 63s in x x x x x x x x e x x x g x x x x x x x x-+ + + - + - - = aaaa Derivatives and primitives of the functions of a single variableDerivatives of the eleme ntary functions (x g x tg x x x e x n x cot , ,cos ,sin , ,ln , as well as of the compos

10、iti on function f (g (x .Rules for the derivative of the product and the quotient of two functions of a real variable. Primitives of the eleme ntary functions above.In tegrati on by parts.Conditions for the convergence of an integral in the cases of an infinite integrationin terval or the prese nce

11、of points of disc on ti nu ity.Functions of several variables. Com mon differe ntial operators.Total differe ntial.Partial derivatives with respect to an independent variable in the case of a function of several variables. Nabla operato? . Gradient of a function f (r . r r ? f Curl of a vector field

12、 A (r . Diverge nee A ? r A .?t . Circulation j(.C d l A .Laplacia n and vector Laplacia n .f 2? A 2? Multiple integrals. Stokes, Gauss-Ostrogradski theorems.Reduct ion of multiple in tegrals to simple in tegrals by using the symmetry properties (cyli ndrical, spherical of the in tegra nts and surfa

13、ces (volumes invo IvedStokes theorem.Gauss-Ostrogradski theorem.Differential equationsSolution of first order differential equations with separable variables.Soluti on of sec ond order lin ear and homoge neous differe ntial equati ons with con sta nt coefficie nts. Characteristic polyno mial, nu mbe

14、r and n ature of solutio ns, critical damp ing.Soluti on of sec ond order lin ear in homoge neous equati ons with con sta nt coefficie nts. Con cepts of forced oscillati ons and res onan ce.Equati ons with partial derivativesD Alembert s solutiorthefwave equation.Progressive mono chromatic pla ne wa

15、ves. Con cepts of wave vector, wavele ngth,freque ncy and period.Principal phenomenological laws (Fick, Fourier and diffusion equations. Energy, mass, etc. bala nee with in an eleme ntary volume.Lin ear algebraCalculati on of a determ inant, diago nalizati on of a matrix, con cepts of eige nv alues

16、and eige nvectors of a lin ear operator.Trigo no metryDefinitions and properties of the basic trigonometric functions (sine, cosine, tangent, cota ngent.B / 2 cos (Com mon trigo no metric formulas (cos 2x = cos 2x - sin 2x ; sin 2x = 2 sin x cos x ; sin a + sin B = 2 sin ( a + -舉 22co3D& a + cos B =

17、 2 cos ( a + B / 2, etc.Fourier series of a regular eno ugh periodic function.I. MECHANICSNewt onian mecha nicsNewt on s laws: the prin ciple of in ertia, the prin ciple of actio n and reactio n, the fun dame ntal equati on of dyn amics.Galilea n relativity. Con cept of non-i nertial refere nee fram

18、es and forces referred to as ? in ertia ? forces (in particular, i n the case of lin ear accelerati on and uniform rotati on frames An gular mome ntum theorem. Kin etic en ergy theorem. Mome ntum theorem.A two particle system. Cen tral force moti on, bound states, scatteri ng states.Expressions for

19、the velocity and the acceleration of a material point in cylindricaland spherical co-ord in ates.Con cept of pote ntial en ergy .In depe ndence on the path of the work done by a pote ntial-derived force.Con servati on of mecha ni cal en ergy of an isolated material system in the case of con servativ

20、e forces.Con servati on of an gular mome ntum in the case of cen tral forces. First and sec ond Kepler s laws (the law of coni cal sect ions and the law of areas.Con servati on of mome ntum in the case of an isolated system. Elastic and in elastic collisio n problems. Con cept of a centre of mass of

21、 a system.Expressions for the potential, kinetic and total energy of a particle in the case of a circular trajectory.Mecha nics of solidsRigid bodies (non-deformable solids. Solids rotating about a fixed axis. Moment ofin ertia of a rigid body. Expressi on for the kin etic en ergy of a rigid body as

22、 a sum of atran slatio nal term of its centre of mass and of a rotatio nal term referred to the cen tre-of- mass referenee frame (Koenig s theorem. The problem of the compound pendulum.Statics and mecha nics of fluidsEuler s description (the concept of a velocity field of a fluid. Concepts of flowde

23、n sity, mass flow rate and volume flow rate. Mass bala nee. Equati on of the con servati on of mass in its local form.Defin iti ons of a statio nary flow, of an in compressible flow, of a non-rotati onal flow.Perfect flows: Euler s equati on, Berno ulli s relatio nship on in compressible andhomoge n

24、eous flows.Calculatio n of the result ing force of the pressure forces exerted upon an object, in fluid statics. The Archimedes principle (the buoyancy force applied to an object immersed in a fluid.Applicati ons of mecha nicsLore ntz force (force exerted on a charged particle in con sta nt electric

25、 and magn etic fields. Trajectory of a charged particle in a static and uniform magnetic field.Lin ear oscillatio ns; damped harm onic oscillati ons. Forced oscillati ons, res onan ce.II. ELECTRIC CIRCUITSElectric voltage. Kirchoff s laws of knots and meshes. Electric current. OhmSuperpositi on theo

26、rem.Basic circuit components: resistor, capacitor, coil. Their impedances in sinusoidal regime. Transient regime of charging and discharging a capacitor.Sinu soidal curre nts and voltages. Maximum value, rms (root mea n square value. Impeda nces in series and in parallel.Study of resonances in circu

27、its in sinusoidal regime. RLC circuit. Relation to resonance in mecha ni cs.III. ELECTRICITY AND MAGNETISMElectrostaticsCoulomb s law. The concept of electric field. Electrostatic field E. Circulation and flow of E. Gauss theorem. Stymmoperties of E.Electrostatic pote ntial and Poisson s equation.Ca

28、lculati on of E and for a simple charge distributionp . Electrostatic potentialbetwee n the plates of a pla nar capacitor.Con cept of electric dipole, field created by a dipole at large dista nces, in teracti onenergy of a permanent dipole with the electric field. Definition of the electric polariza

29、tion vector. Electric field in a con ductor at equilibrium. Equipote ntial surfaces.Electric field in the vic inity of a metal surface.Coulomb s law betwee n two charges immersed in a homoge nous lin ear and isotropic dielectric medium.Mag netostaticsMagn etic field B. Symmetry properties of B.Magn

30、etic field created by a th in wire carry ing a curre nt (Biot-Savart law, the twoMaxwell equati ons (the diverge nee of B and Amp e re s law, vector pote ntial A.Non-uni city of the electrostatic pote ntial and the vector pote ntial A, uni city of theelectric field E and the magnetic field B.Circula

31、ti on of B. Relati on ship betwee n the circulati on of B and the en circledcurre nts (theorem of the total curre nt.Calculation of B created by straight wires and circular loops. Field along the axis ofa circular loop and of a coil (sole noid hav ing a circular cross-secti on.Magn etic dipole and m

32、agn etic mome nt M. Expressi on for the in teracti on en ergy between a magnetic moment and a magnetic field B.Flux of B. Electromagnetic induction phenomenon, Faraday s law, Lenz rule.Electromag netic wavesElectromag netic waves in vacuum.Maxwell s equations in vacuum. Progressive hanric plane wave

33、s as solutions ofthe Maxwell s equations in vacuum. Frequency, wavelength, wave vector. The concept of phase velocity.Tran sversality of the electric and mag netic fields.The state of polarizati on state an electromag netic wave. Lin ear and circularpolarizati ons. Volume den sity of the electromag

34、netic en ergy, Poynting vector.Con cept of wave packet. Group velocity.Electromag netic waves in matter (li near and isotropic medium.Macroscopic E and B fields. Con stitutive relati on ships compleme ntin gMaxwell sequations. Frequencydependent complex dielectric constant ( 3.Con cepts of complex r

35、efract ion in dex, dispersi on and absorpti on.Microscopic models describ ing the material polarizati on of the medium: Drudemodel, model of the elastically bound electron (Lorentz model.IV. OPTICS Geometric optics Con cept of light ray. Reflect ion and refractio n by aplane mirror. Snell-Descartes

36、laws. Limit angle. The total reflection phenomenon.Spherical mirrors, le nses, con jugati on and magn ificatio n relati ons. Wave opticsReflecti on and refractio n of a harm onic progressive polarized pla ne wave at the in terfacebetwee n two dielectric media. Proof of Sn ell-Descartes laws. Con cep

37、t of optical path.In terfere nee betwee n two totally cohere nt waves. Michels onromete.Thinteir&fos.Fabry-P rot cavity. Diffraction at infinity. Huyghens-Fresnel principle. Diffraction by arectangular slit. Diffraction at infinity by two slits (Young s slits, by a row of slits. VTHERMODYNAMICS Thermody namic state fun ctio ns: in ternal en ergy, en tropy,en thalpy, free en ergy, free en thalpy, as well as their differe ntials. Exte nsive and in ten sive variables, thermodynamic equilibrium. Heat capacities at a const