GEM笔试考点,来自法盟官网,自己成中文翻译的~

SYLLABUS FOR THE EXAM
考试大纲
MATHEMATICS
数学
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.
基本逻辑代数
命题演算、数量词。

递归推论。

设置和功能的术语,设置集合如N，Z，Q:算术和组合,
多项式:欧式多项式。

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 ...).
实数集合的性质：
间隔,邻里上界。

序列:有限(柯西准则),收敛速度较快,递归的
f(n+1)=f(n).
关于实数变数的数值函数（极限、连续性、可微性）有限递增公式,单调和逆函数,泰勒公式和不等式,有限扩展，平常功能。

这个领域的复杂的数字,平常的复变函数(指数…)。

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.
线性代数。

向量空间、线性映射、基础和尺寸。

矩阵、行列式、线性系统。

特征
值与特征向量，特征多项式，对角化。

应用微分系统和方程式。

Analysis
Rational functions and their decomposition, Computation of primitives: integral defined on a closed bounded interval, numerical methods. Taylor formula with integral remainder. Vector valued function of the real variable in R2 and R3 (excluding metric properties). Parametric curves in R2 or R3. First and second order linear differential equations Path integral
有理函数及其分解和计算,在一个封闭的定义积分区间,数值方法有界。

泰勒公式与积分的余数。

真正的价值函数向量的变量和R3线(不含度量R2。

属性)参数曲线在R2或R3线。

一阶和二阶变系数线性微分方程的路径积分
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).
数值系列,
实数变量的功能:函数和整个序列的排序和序列，傅里叶序列的应用。

简单的,绝对的,统一和正常的集合。

实数区间的积分，积分参变量积分。

实例应用傅立叶、拉普拉斯,)。

Numerical and vectorial analysis
Differential calculus: multivariable functions. Partial derivatives and linear tangent application. Taylor formula of order 2: application to local extrema. Multiple integrals (functions of 2 or 3 variables). Computation via successive integrations and change of variables formula.
矢量分析与数值解
多元函数微积分:。

偏导数和线性切线应用。

泰勒公式的应用到当地的extrema:。

多重积分(功能),2或3个变量。

通过连续的融合与变化的计算公式的变量。

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.
欧氏空间有限的空间
标量产品、规范、正交基础和orthonormalization。

伴随,米和正常操作,统一。

介绍了空间的外语。

二、依据正交多项式的,依据勒三角函数。

应用傅立叶级数。

傅里叶变换:Plancherel平等。

PHYSICS
International Unit System, Dimensional analysis.
国际单位制，三维分析。

Mechanics
Kinematics: t rajectories, velocity, acceleration, motion of rigid bodies, change of reference frame.
运动学：轨迹，速度，加速度，刚体运动，变化的参照系。

Newtonian dynamics: first, second and third laws, inertial and non-inertial reference frames, conservation laws, forces and potentials, gravitational field, central forces, small oscillations.
牛顿动力学：第一，第二和第三定律，惯性和非惯性参照系，守恒定律，力量和潜力，重力场，向心力，小振荡。

Fluids: pressure, hydrostatics, Euler and Lagrange variables of a continuum, continuity equation, Euler equation of motion.
流体：压力，静水，欧拉和一个统一体，连续性方程，欧拉运动方程拉格朗日变量。

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.
热力学：第一定律，内能，功，热。

可逆和不可逆过程，第二定律，卡诺循环。

状态方程，相变，理想气体，化学势，化学学报
Electricity & Magnetism
Electrostatics: electric charge, Coulomb's law, electric field, potential, Gauss' law, equilibrium of conductors, capacitance.
静电：电荷，库仑定律，电场，电势，高斯定律，平衡的导体，电容。

Magnetostatics: magnetic field, Ampère's laws, Faraday's law of induction. 静磁学：磁场，安培的法律，法拉第感应定律。

Electric currents: electric current, Ohm's law, conductivity, Kirchhoff's laws, time varying currents, free and forced oscillations, condensers, inductance, complex impedance, resonant circuits.
电流:电流、欧姆定律、导电性,基尔霍夫法律、时变电流、自由和强迫振动、冷凝器、电感、复杂的阻抗、共振电路。

Maxwell equations: Lorentz force, plane electromagnetic waves, radiation, light waves, reflexion, refraction, Huyghens principle, diffraction, interference phenomena.
麦克斯韦方程:洛伦兹力、平面电磁波辐射、光、永久性,折
射,Huyghens原理、衍射、干扰现象。

Atomic & molecular physics
Quantum mechanics: Planck's law, Bohr's atom, de Broglie's relation, uncertainty principle, wave function, Schrödinger's equation, stationary states, quantization of energy.
量子力学：普郎克定律、波尔的普朗克的原子,德布罗意的关系、不确定性原理、波函数,薛丁格的方程,稳定状态、量化的能量。

Structure of matter : hydrogen atom, periodic table of the elements, molecules, solid state, elementary statistical physics
物质的结构:氢原子的元素,元素周期表,分子、固态、基本统计物理学。