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2020 Stanford Pre-Collegiate University-Level Online Math & Physics

Category: 高端夏校 Date: 2017年12月15日下午4:29

2020 Stanford Pre-Collegiate University-Level Online Math & Physics

2020 斯坦福在線大學(xué)預(yù)修數(shù)學(xué)與物理項(xiàng)目

項(xiàng)目介紹

Stanford Pre-Collegiate University-Level Online Math & Physics斯坦福在線大學(xué)預(yù)修數(shù)學(xué)與物理項(xiàng)目為學(xué)生提供大學(xué)水平的9門數(shù)學(xué)課程和4門物理課程。對(duì)現(xiàn)中學(xué)階段學(xué)習(xí)學(xué)有余力的學(xué)生即可報(bào)名，不僅上課時(shí)間靈活，且每門課程提供3個(gè)學(xué)分和成績(jī)單。不僅提前讓學(xué)生體驗(yàn)了本科學(xué)習(xí)的難度，更是節(jié)約大學(xué)學(xué)費(fèi)和時(shí)間的好方法之一呢。

數(shù)學(xué)類課程分類：

Multivariable Differential Calculus：學(xué)習(xí)兩個(gè)或多個(gè)變量函數(shù)的微積分，內(nèi)容包括vectors and vector-valued functions in 2-space and 3-space, tangent and normal vectors, curvature, functions of two or more variables, partial derivatives and differentiability, directional derivatives and gradients, maxima and minima, optimization using Lagrange multipliers.
Multivariable Integral Calculus ：同樣學(xué)習(xí)兩個(gè)或兩個(gè)以上變量函數(shù)的積分，內(nèi)容包括double and triple integrals, change of variables and the Jacobian, vector fields, line integrals, independence of path and the fundamental theorem of line integrals, Green's theorem, divergence theorem, and Stokes' theorem.
Linear Algebra ：線性代數(shù)的入門課程，內(nèi)容包括matrices, linear equations, vector spaces, bases, coordinates, linear transformations, eigenvectors, eigenvalues, and diagonalization.
Modern Algebra ：抽象代數(shù)理論，強(qiáng)調(diào)對(duì)稱的應(yīng)用，內(nèi)容包括groups, rings, fields, matrix and crystallographic groups, and constructibility.
Real Analysis ：實(shí)變函數(shù)論，內(nèi)容包括sequences, series, limits, continuity, differentiation, integration, and basic point-set topology.
Differential Equations ：求解微分方程的基本技術(shù)和方法，內(nèi)容包括linear, separable, and exact equations, existence and uniqueness theorems, difference equations, basic theory of higher order equations, variation of parameters, undetermined coefficients, series solutions, Laplace transform, systems of equations.
Complex Analysis ：復(fù)雜函數(shù)的微分和積分理論，內(nèi)容包括：algebra of complex numbers, complex functions, multi-valued functions, exponentials, logarithms, analyticity, integrals, power series, Laurent series, residues, isolated singularities, poles and zeros.
Partial Differential Equations ：微分方程的理論，涉及多個(gè)變量的函數(shù)，內(nèi)容包括first order equations, classification of second order equations, initial-boundary value problems for heat equation, wave and related equations, separation of variables, eigenvalue problems, Fourier series, existence and uniqueness questions.
Elementary Theory of Numbers ：數(shù)論的介紹及其應(yīng)用，內(nèi)容包括Euclid's algorithm, divisibility, prime numbers, congruence of numbers, theorems of Fermat, Euler, Wilson, Lagrange's theorem; residues of power, quadratic residues, introduction to binary quadratic forms.

物理類課程分類：

Light and Heat：介紹光學(xué)和熱力學(xué)，內(nèi)容包括temperature, properties of matter, introduction to the kinetic theory of matter, light and electromagnetic waves, reflection and refraction of light, lens systems, interference and diffraction.
Modern Physics：介紹現(xiàn)代物理學(xué)的思想，內(nèi)容包括Special relativity, introduction to general relativity, the experimental basis of quantum theory, atomic structure, quantization of light, Schr?dinger equation.
Intermediate Mechanics I：對(duì)粒子和系統(tǒng)力學(xué)更深入的學(xué)習(xí)，內(nèi)容包括Tensors, vector calculus, Newtonian laws of mechanics and gravitation, oscillations, Green's functions, calculus of variations, Lagrangian mechanics, orbits, and physics in rotating frames of reference.
Intermediate Mechanics II：對(duì)粒子和系統(tǒng)力學(xué)更深入的學(xué)習(xí)，內(nèi)容包括Rigid body dynamics, oscillating systems, Hamilton's principle for continuous systems, waves, general wave equation, and fluid dynamics.