线性代数课程双语教学大纲.doc

线性代数课程双语教学大纲英文名称：Linear Algebra课程编号：210101课程类型：学科基础课程学 时：40学 分：2.5适用对象：工科各专业本科生先修课程：高等数学使用教材：马思遥等编：LINEAR AIGEBRA 讲义参 考 书：杨泮池, 崔荣泉编：线性代数，陕西科学技术出版社 同济大学数学系编：线性代数，高等教育出版社一、课程的性质、目的与任务1课程性质 线性代数是高等院校本科各专业的一门重要的基础理论课。由于线性问题广泛存在于科学技术的各个领域，而某些非线性问题在一定的条件下可以转化为线性问题，因此本课程介绍的方法广泛地应用于各个学科。尤其在计算机日益普及的今天，该课程的地位和作用更显得重要。2课程目的与任务通过教学，一使学生掌握该课程的基本理论与方法，培养解决实际问题的能力，并为学习相关课程及进一步扩大数学知识面奠定必要的数学基础。二是以外语作为手段，通过双语授课学习本学科领域的前沿知识，借此加深受教育者对专业课程的认知与学习，逐步使其具备国际交流与合作能力，实现综合素质的提高。二、教学内容及要求Chapter 1 Matrices Algebra【Teaching Content】Matrix ; Linear calculator of matrix; Multiplication of matrix; Transpose of matrix; Inverse of matrix; Partitioned matrix.【Teaching Request】1. Understanding the conception of matrix; Knowing identity matrix、symmetric matrix、diagonal matrix、upper triangular and lower triangulars properties.2. Mastering matrixs linear calculator, multiplication calculator, transpose of matrix and their properties; Understanding the conception of inverse matrix.3. Knowinging partitioned matrix and its calculator.【The Key Points】Calculator of matrix; The conception of inverse matrix.【The Difficulty Points】matrixs multiplication; the conception of inverse ; Partitioned matrix.【Depth and Breadth】Understanding the conception of matrix; Mastering matrixs calculator; Knowing partitioned matrix and its calculator.Chapter 2 Determinant and Cramers rule【Teaching Content】The conception of determinant and its properties; Determinant of square matrix s multiplication; Adjoint of matrix; The expansion of determinant by row or column; Cramers rule of linear equation.【Teaching Request】1. Understanding determinant; Mastering the properties of determinant; Calculator determinant by properties and the expansion of determinant; Knowing the determinant of square matrixs multiplication .2. Understanding adjoint of matrixs conception; Can solve inverse by adjoint of matrix.3. Knowing Cramers rule.【The Key Points】Determinants properties and calculator.【The Difficulty Points】Determinants properties.【Depth and breadth】Understanding determinant; Mastering determinants properties and calculator; Knowing Cramers rule.Chaper 3 Rank of Matrix and Solution of Linear Equation【Teaching Content】Elementary operations of matrix; Elementary matrix；equivalent of matrix ；Rank of matrix; The way to solve the rank of matrix and inverse by elementary operations; Theorem of linear equation has solution.【Teaching Request】1. Mastering elementary operations of matrix; Understanding elementary matrix 、equivalent of matrix and rank of matrix; Mastering the way to solve the rank of matrix and inverse by elementary operations.2. Understanding full essential condition of homogeneous linear equations has nonzero solution and non-homogeneous linear equations has solution.【the Key Points】Rank of matrix; The way to solve the rank of matrix and inverse matrix by elementary operations; Equivalent of matrix; Elementary operations and elementary matrix; Theorem of linear equation has solution)【The Difficulty Points】Eementary matrix.【Depth and breadth】Mastering inverse matrix and full essential condition of invertible; Mastering solve the rank of matrix and inverse matrix by elementary operations.Chapter 4 Vector and the Structure of Solutions【Teaching Content】Vector space; Linear combination and linear represented of vector; Linear dependence and independence of vectors; The maximal linearly independent collection of vectors; Equal of vector collection; Rank of vector collection ; The properties and structure of solution; The basis for solutions of system and solutions; Solution vector; The way to solve the solution of linear equations by elementary rows operation.【Teaching Request】1. Understanding n-dimension vector; linear combination and linear represented of vectors.2. Understanding the definition of linear dependent and independent of vector collection; Knowing the properties and the way to determine the vector collection are linear dependence or independence.3. Mastering the maximal linearly independent collection of vector and rank of vectors; Solve maximal linearly independent collection of vector and the rank of vectors.4. Knowing the conception of vector collections equal ; Understanding the relations between vector collections rank and matrixs rank.5.Knowing the conception of n-dimension vector; subspace; basis; dimension.6. Understanding the basis for solutions of system, solutions and solution vector of homogeneous linear equations.7. Understanding the structure of solution and solutions of non-homogeneous linear equations.8. Mastering the way to solve the solution of linear equations by elementary rows operation.【The Key Points】Linear dependence and independence of vectors; The maximal linearly independent collection and the rank of vectors; The way to solve the solution of linear equations by elementary rows operation .【the Difficulty Points】The conception of vector space; Linear dependence and independence of vectors; Solution space and the basis for solutions of system.【Depth and breadth】Understanding n-dimension vector; Mastering linear dependence and independence of vectors; Can solve maximal linearly independent collection of vector and the rank of vectors.Chapter 5 Eigenvalues 、Eigenvectors and Quadratic Forms【Teaching Content】Eigenvales and eigenvectors of matrix; Inner product; Form linear independence to orthogonal by Gran-Schmidt method; Orthogonal basis; Similar transformation and similar matrixs conception and properties; Full essential condition of diagonalizable and triangular matrix; Quadratic Forms and its matrix form; Rank of Quadratic Forms; Diagonal quadratic form; Positive definite quadratic forms and positive definite matrices.）【Teaching Request】1. Understanding eigenvales and eigenvectors of matrix; Can solve eigenvales and eigenvectors of matrix;)2Form linear independence to orthogonal by Gram-Schmidt method.3. Understanding similar matrix and knowing full essential condition of diagonalizable.4. Knowing Quadratic Forms and its rank; orthogonal and Positive definite theorem.5. Mastering Quadratic Forms matrix ,the way form diagonalizable by orthogonal transformation.6. Knowing quadratic Forms and its matrix s positive definite, Determine of positive definite.【The Key Points】Similar matrix; Eigenvales and eigenvectors solution; Diagonalizable of real symmetric matrix; Form diagonaliza