【正文】 代數(shù)與幾何課程編碼：08N1120220總 學(xué) 時： 60學(xué) 分： 先修課程：高中數(shù)學(xué)授課教師：孟晨輝教 材：《線性代數(shù)與空間解析幾何（第三版）》， 高等教育出版社，鄭寶東主編課程簡介：代數(shù)與幾何是高等學(xué)校功課各專業(yè)中十分重要的自然科學(xué)基礎(chǔ)。其中的線性代數(shù)部分主要運(yùn)用代數(shù)方法研究具有線性關(guān)系的數(shù)學(xué)對象，建立相應(yīng)的理論體系，它具有很強(qiáng)的邏輯性與抽象性；其中的空間解析幾何部分主要通過坐標(biāo)系，建立空間幾何圖形與方程之間的關(guān)系，利用代數(shù)理論研究空間幾何圖形的性質(zhì)?？臻g解析幾何為線性代數(shù)提供背景與示例，線性代數(shù)與空間解析幾何作為一門課程的兩個組成部分，互相滲透，互相支持。本課程系統(tǒng)的介紹線性代數(shù)與空間解析幾何的基本理論與方法，把線性代數(shù)與空間解析幾何的求解有機(jī)結(jié)合。內(nèi)容包括行列式的定義、計(jì)算及其性質(zhì)；矩陣的代數(shù)運(yùn)算、分塊矩陣、矩陣的求秩；向量代數(shù)，向量坐標(biāo)，并在其中討論幾何問題、平面與直線的方程及其相互位置關(guān)系；n維向量、向量之間的線性相關(guān)性與線性無關(guān)性；線性方程組間的結(jié)構(gòu)理論；線性變換與矩陣間的聯(lián)系；特征值、特征向量、相似變換，矩陣可對角線化的條件和方法；二次型理論、二次型簡化、二次曲面及其分類等。評分標(biāo)準(zhǔn)：作業(yè)——20% 期中考試——20% 期末考試——60%教學(xué)大綱：一、n階行列式 n階行列式的概念 行列式的性質(zhì) 行列式的展開訂立 Crammer法則二、矩陣 矩陣的概念 矩陣的運(yùn)算 可逆矩陣 矩陣的初等變換 矩陣的秩 初等矩陣 分塊矩陣的概念及其運(yùn)算 分塊矩陣的初等變換三、幾何向量四、n維向量 n維向量的概念及其線性運(yùn)算 向量組線性相關(guān)與線性無關(guān) 向量組的秩 向量空間 歐式空間五、線性方程組 線性方程組有解的充要條件 線性方程組解的結(jié)構(gòu) 利用矩陣的初等行變化解線性方程組 線性方程組的幾何應(yīng)用六、特征值、特征向量及相似矩陣 特征值與特征向量 相似矩陣 應(yīng)用舉例七、線性空間與線性變換 線性空間的概念 線性空間的基地、維數(shù)與坐標(biāo) 線性變換八、二次型與二次曲面 實(shí)二次型 化實(shí)二次型為標(biāo)準(zhǔn)性 正定實(shí)二次型 空間中的曲面與曲線 二次曲面Linear Algebra and Analytic GeometryCourse Code: 08N1120220 Hours: 60Credits: Prerequisite Course: Collegeentry level algebra and geometryInstructor: Chenhui MengTextbook:Baodong Zheng, Linear algebra and space analytic geometry, Higher Education PressCourse Description Linear Algebra and Analytic Geometry is one of the significant fundamental courses of nature science. The Linear Algebra mainly applies the algebra method to study the mathematic subjects that have the linear relation and establish corresponding theatrical system. The part of Linear Algebra introduces Basic concepts and techniques of linear algebra。 includes systems of linear equations, matrices, determinants, vectors in nspace, and eigenvectors, together with selected applications, such as Markov processes, linear programming, economic models, least squares, and population growth. The Analytic Geometry mainly applies coordinate systems to build the relationship between shapes and equations。 and use algebra theory to study the characters of space geometry. The Analytic Geometry provides the background and examples to Linear Algebra. As two parts of the course, the linear algebra and analytic geometry they permeate each other. In addition, this course introduces techniques and applications of ordinary differential equations, including Fourier series and boundary value problems, linear systems of differential equations, and an introduction to partial differential equations. It is designed for engineering majors and other who require a working knowledge of differential equations.Grading: Homework20% Midterm exam20% Final exam 60%Syllabus:Ⅰ n order determinant Basic concepts Determinant properties Determinant expansion theorem Cramer rulesⅡ matrix Basic concepts Matrix manipulation Invertible matrix Elementary transformation of matrices Rank of matrix Elementary matrix Block matrix Elementary transformation of block matricesⅢ Geometrical vectorⅣ n dimensional vector Concepts Linear dependence and linear independence Vector set rank Vector space European spaceⅤ Linear system of equations Necessary and sufficient condition for system of linear equations with solution System of linear equations’ solution structure Solving system of linear equations using matrix method Geometric application for linear system of equationsⅥ Eigenvalue, eigenvector, and similar matrix Eigenvalue and eigenvector Similar matrix ExamplesⅦ Linear space and linear transformation Basic concepts Basis, dimensionality, and coordinates Linear transformationⅧ Quadric form and Quadric surface Real quadric form Convert real quadric form into normal forms Positive definite real quadric form Surface and curve in space Quadric surface工科數(shù)學(xué)分析課程編碼：08N1120211 08N1120212總 學(xué) 時：90+90學(xué) 分：+先修課程：高中數(shù)學(xué)授課教師：白紅教 材：《工科數(shù)學(xué)分析（第三版）上冊》， 《工科數(shù)學(xué)分析（第三版）下冊》， 高等教育出版社，張宗達(dá)主編課程簡介： 本課程的教學(xué)目的是使學(xué)生較系統(tǒng)的理解該課程的基本概念、基本理論、掌握基本方法，為后繼課和進(jìn)一步獲取數(shù)學(xué)知 識奠定必要的數(shù)學(xué)基礎(chǔ)。在傳授知識的同時，著重培養(yǎng)學(xué)生抽象思維能力、邏輯推理能力、空間想象能力和自學(xué)能力，特別是綜合運(yùn)用所學(xué)知識去分析問題和解決問題能力。提高學(xué)生的素質(zhì)，培育創(chuàng)新，創(chuàng)業(yè)精神。 第一學(xué)期講授的主要內(nèi)容：函數(shù)、極限、連續(xù)，一元函數(shù)微分學(xué)，一元函數(shù)積分，導(dǎo)數(shù)與定積分的應(yīng)用；第二學(xué)期講授的主要內(nèi)容：多元函數(shù)微分學(xué)，多元函數(shù)積分學(xué)，無窮級數(shù)，常微分方程，復(fù)變函數(shù)初步、微分幾何基礎(chǔ)知識。評分標(biāo)準(zhǔn)：作業(yè)——20% 期中考試——20% 期末考試——60%Mathematics Analysis for Science and Technology Majors Course Code: 08N1120211 08N1120212 Hours: 90 + 90Credits: +Instructor: Hong BaiTextbook: Zongda Zhang, Mathematical Analysis for Engineering I II, Higher Education PressCourse Description: Mathematics Analysis for Science and Technology Majors is one of the significant fundamental courses of nature science to every students majoring in engineering. The main content of this course is calculus. The required chapters are function, limits and continuity, derivative and differential, the mean theorems, indefinite integration, definite integration, the approach of derivative and definite integration, differential equation, Derivatives, Integration, the second type curve integral, the secondking surface integral, Vector and infinite series, initial of plex function. The fundamental knowledge of differential geometry is the significant content of the course. Grading: Homework 20% Midterm exam20% Final exam60%Syllabus:I. Function Basic concepts Elementary function Examples and continuity Limit of a sequence Limit of a function Limit properties, infinitesimal and infinite Limit algorithm Criteria of limit existence Infinitesimal parison Continuity of a function ExamplesIII. Derivative and differential Basic concepts Arithmetic rules for derivative and differential Other rules for calculating derivative Higher order derivative Differential Examples me