╨╧рб▒с>■  .0■   -                                                                                                                                                                                                                                                                                                                                                                                                                                                ье┴q` ЁR┐ bjbjqPqP."::       д2╓ ╓ ╓ ╓ т 2lЄ ыээээээ$^h╞jЕ Е Е  &   Е   ы Е ы    ■ АZv▄g╬╓ ЧB ы<0l 0┘0  ╝0╗0 Zd @ д 4╪ н ї lЕ Е Е Е 222д╓ 222╓ 222     TEST SYLLABUS MATHEMATICS Elementary logic and Algebra Propositional calculus, quantifiers. Arguments ad absurdo, by recursion. Set and function terminology, sets N, Z and Q: arithmetic and combinatorics, Polynomials: Euclidian division. а Properties of the set R Interval, neighbourhood, upper bound. Sequences: limit (Cauchy criterion), rate of convergence, recursion un+1 = f(un). Numerical functions of the real variable: limits and continuity, differentiability, finite increments formula, monotony and inverse functions, Taylor formulas and inequalities, finite expansions, usual functions. The field of complex numbers, usual complex functions (exponentials ...). а Linear algebra Vector spaces, linear maps, basis and dimension. Matrices, determinants, linear systems. Eigenvalues and eigenvectors, characteristic polynomial, diagonalization. Application to differential systems and equations. а Analysis Rational functions and their decomposition, Computation of primitives: integral defined on a closed bounded interval, numerical methods. Taylor formula with integral remainder. Vector valuedа function of the real variable in R2 and R3 (excluding metric properties). Parametric curves in R2 or R3. First and second order linear differential equationsа Path integral а Numerical series Functions of the real variable: sequences and series of functions, entire series, applications to Fourier series. Simple, absolute, uniform and normal convergences. Integrals over a real interval, integrals depending on a parameter. Examples and applications (Fourier, Laplace). а Numerical and vectorial analysis Differential calculus: multivariableа functions. Partial derivatives and linear tangent application. Taylor formula of order 2: application to local extrema. Multiple integrals (functions ofа 2 or 3 variables). Computation via successive integrations and change of variables formula. а Finite dimensional euclidean spaces Scalar products, norms, orthonormal basis and orthonormalization. Adjoint, hermitian, unitary and normal operators. Introduction to the space L2. Orthonormal basis in L2, Legendre polynomials, basis of trigonometric functions. Applications to Fourier series. Fourier transformation : Plancherel equality.а а а PHYSICS International Unit System, Dimensional analysis. а Mechanics Kinematics: trajectories, velocity, acceleration, motion of rigid bodies, change of reference frame. а Newtonian dynamics: first, second and third laws, inertial and non-inertial reference frames, conservation laws, forces and potentials, gravitational field, central forces, small oscillations. а Fluids: pressure, hydrostatics, Euler and Lagrange variables of a continuum, continuity equation, Euler equation of motion. а Thermodynamics: first law, internal energy, work, heat. Reversible and irreversible processes, second law, Carnot cycles. Equations of state, change of phase, ideal gases, chemical potentials, chemical reactions, equilibrium equations, affinity. а Electricity & Magnetism а Electrostatics: electric charge, Coulomb's law, electric field, potential, Gauss' law, equilibrium of conductors, capacitance. а Magnetostatics: magnetic field, Ampшre's laws, Faraday's law of induction. а Electric currents: electric current, Ohm's law, conductivity, Kirchhoff's laws, time varying currents, free and forced oscillations, condensers, inductance, complex impedance, resonant circuits. а Maxwell equations: Lorentz force, plane electromagnetic waves, radiation, light waves, reflexion, refraction, Huyghens principle, diffraction, interference phenomena. а  ;Ў и ╢ П Ч   1QpУ╚╩╨╪  #}П@F╛╠╢═╨▐Q_Юпct  э█╤─╣лалалалалалалаТЗТалаz─аzаzалалаzаzаzаzаvhv4hv4hv40JmH sH hv45Б\БmH sH hv4hv45Б\БmH sH hv4hv4mH sH hv4hv40J>*mH sH hv40J>*mH sH hv4hv40JmH sH h°4%0JmH sH #h7uHhv40J>*CJ(aJ(mH sH #h7uHh°4%0J>*CJ(aJ(mH sH -<Е╙ЇЎ \ ж и ╖ Н П Ш    /яррр╨рр╨рррр╨ррр╨рр╨рр╨р$дд@&[$\$a$gdв╔$дд[$\$a$gdv4$дд@&[$\$a$gdв╔ ¤/1RnpФ╞╚╩╦╠═╬╧╨╪┘  {}ЁрЁЁрЁ╘╧╧╧╧╧╧╧╔╧╝╘╝╘╘ дд@&[$\$gdв╔@&gdв╔gdv4 дд[$\$gdv4$дд@&[$\$a$gdв╔$дд[$\$a$gdv4}>@╝╛┤╢╬╨OQЬЮac  єєєєєєцєєєцєєєє┌ дд[$\$gd▒Nw дд@&[$\$gdв╔ дд[$\$gdv4,1Рh░В. ░╞A!░Й"░Й#РЙ$РЙ%░░─░─ Р─ЖЬ8@ё 8 ckЗeCJ_HaJmH sH tH $A@Є б$ ╪ЮдЛ╡k=ДW[SOBiє │B nfРhИ @ ╝ ╛ ┤ ╢ ╬ ╨ O Q Ь Ю a c 0ААШ0ААШ0ААШ0АА0АААШ0ААШ0АА0АААШ0ААШ0ААШ0ААШ0АА0АААШ0АЎАШ0АЎАШ0АЎА0АААШ0АиАШ0АиА0АААШ0АПАШ0АПА0АААШ0ААШ0АА0АААШ0А1АШ0А1А0АААШ0АpАШ0АpАШ0АpАШ0АpАШ0АpАШ0АpАШ0АpАШ0АpАШ0АpА0АААШ0А╨А0АААШ0А┘А0АААШ0А АШ0А АШ0А АШ0А АШ0А АШ0А АШ0А АШ0А А0АААШ0А╢ АШ0А╢ АШ0А╢ А0АААШ0АQ АШ0АQ АШ0АQ АШ0АQ АШ0АQ А  /}     a╗D]е b╗KНc╗─JНd╗T>╜ e╗>╜ f╗^е !!╖╖''╜╜8*Аurn:schemas-microsoft-com:office:smarttagsАCityА9*Аurn:schemas-microsoft-com:office:smarttagsАplaceА t╚z nu├╨IX%,?HчюГМм╖┬╘╓▌▀ш&1?G░║) / Q _ q y ▄ ч v } ║ ├ ╤ ┘ <`aД3Б╖чшYZМ!HV`ї√К╝╜.vБГ╢%mФ╒╓%&vwЦЯпЎ 7 E K 33333333333333333333333333╨┘ аk╘4qu╛╨y`HшU¤клS╘ O(╛╨Ї∙7AKr╤ >╘4quфc╨FклSy`HAKr∙WRклSклS╠>┘cy`HAKrшU¤╘4quy`Hх°4%v47uH▒Nwв╔/gє @А,Ц ┬ Ё@  Unknown            GРЗz А Times New Roman5РАSymbol3&Р Зz А Arial;РЖЛ[SOSimSun"qМЁ─йУjЗУjЗЇ Ї !ЁЙЙ┤┤ББ242ГЁHX)Ё ?ф                     v42   MATHEMATICSEmmanuel DEQUEKERо_oП(u7b■ рЕЯЄ∙OhлС+'│┘0ДРШм╕╘рь   @ L Xdlt|и MATHEMATICSEmmanuel DEQUEKER Normal.dot ╬в╚э╙├╗з2Microsoft Office Word@@BИ]▄g╬@BИ]▄g╬Ї ■ ╒═╒Ь.УЧ+,∙о0─ X`ДМФЬ дм┤╝иEcole des Mines de douaiц  ■   ■    !"#$■   &'()*+,■   ¤   /■   ■   ■                                                                                                                                                                                                                                                                                                                           Root Entry         └FPmv▄g╬1А1Table        0WordDocument        ."SummaryInformation(    DocumentSummaryInformation8            %CompObj            m                        ■                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           ■       └FMicrosoft Office Word ╬─╡╡ MSWordDocWord.Document.8Ї9▓q