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 斯坦福在線大學預修數學與物理項目

項目介紹

Stanford Pre-Collegiate University-Level Online Math & Physics斯坦福在線大學預修數學與物理項目為學生提供大學水平的9門數學課程和4門物理課程。對現中學階段學習學有余力的學生即可報名，不僅上課時間靈活，且每門課程提供3個學分和成績單。不僅提前讓學生體驗了本科學習的難度，更是節約大學學費和時間的好方法之一呢。

數學類課程分類：

Multivariable Differential Calculus：學習兩個或多個變量函數的微積分，內容包括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 ：同樣學習兩個或兩個以上變量函數的積分，內容包括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 ：線性代數的入門課程，內容包括matrices, linear equations, vector spaces, bases, coordinates, linear transformations, eigenvectors, eigenvalues, and diagonalization.
Modern Algebra ：抽象代數理論，強調對稱的應用，內容包括groups, rings, fields, matrix and crystallographic groups, and constructibility.
Real Analysis ：實變函數論，內容包括sequences, series, limits, continuity, differentiation, integration, and basic point-set topology.
Differential Equations ：求解微分方程的基本技術和方法，內容包括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 ：復雜函數的微分和積分理論，內容包括：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，涉及多個變量的函數，內容包括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 ：數論的介紹及其應用，內容包括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：介紹光學和熱力學，內容包括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：介紹現代物理學的思想，內容包括Special relativity, introduction to general relativity, the experimental basis of quantum theory, atomic structure, quantization of light, Schr?dinger equation.
Intermediate Mechanics I：對粒子和系統力學更深入的學習，內容包括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：對粒子和系統力學更深入的學習，內容包括Rigid body dynamics, oscillating systems, Hamilton's principle for continuous systems, waves, general wave equation, and fluid dynamics.