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工程应用数学基础

National University of Defense Technology via XuetangX

Overview

《工程应用数学基础》是国防科技大学面向工科学生数学基础课程,受益面广,每年均开设了多个教学班。从事该课程教学的主要教员有4名,后备教员3名,其中教授1名,副教授4名,讲师2名。教学队伍梯队结构较合理,近70%的教员具有博士学位,在科研方面,承担了973子专题、国家自然基金等项目,在教学方面,教学水平较高,深受学员好评,同时积极参与教学改革,总结教学经验,出版教材及教学论文多篇。在“十一五”建设期间,根据工科学生的学科特点,对课程结构进行调整,撰写了新的课程标准,以适应工科学生培养的需求。
随着当代科学技术的发展,数学的思想、方法、观点和结论正在深入地渗透到自然科学、工程技术、社会科学和人文科学等诸多领域,因此,加强工科学生的数学教育已日益为人们所共识.鉴于工科专业的需求特点,数学教育不仅要提高他们抽象思维和逻辑推理的能力,更重要的是培养其运用数学知识解决实际问题的能力.
本课程以矩阵为主线,讲解线性空间、方阵的相似标准形、矩阵分析等内容.针对应用数学基础课程学时短、内容丰富的特点,同时照顾不同专业读者的知识结构,将矩阵理论的相关内容进行精心的取舍和有机的融合,避免内容重复和简单叠加,找出它们之间的内在关系,使各部分内容既相互联系又相对独立.
课程力求从实际应用问题引入数学模型,直观、自然地建立基本概念,严谨、清晰、简明地阐述和推证基本理论和算法,使学员能清楚地了解来自不同应用背景的数学问题之间的有机联系以及研究方法的本质.

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Syllabus

  • 第一章 线性空间和线性变换
    • 第一讲 线性空间
    • 第二讲 线性表示与线性相关
    • 第三讲 子空间
    • 第四讲 线性变换
    • 第五讲 线性变换的相似化简
    • 第六讲 内积空间
    • 第七讲 正交变换与对称变换
  • 第二章 方阵的相似化简
    • 第八讲 矩阵的相似对角化
    • 第九讲 Jordan标准形
    • 第十讲 方阵多项式与最小多项式
  • 第三章 方阵函数
    • 第十一讲 矩阵范数
    • 第十二讲 矩阵序列
    • 第十三讲 方阵函数
    • 第十四讲 方阵函数的计算
  • 第四章 矩阵分解
    • 第十五讲 矩阵的三角分解
    • 第十六讲 矩阵的正交三角分解
    • 第十七讲 矩阵的满秩分解
    • 第十八讲 矩阵的奇异值分解
  • 第五章 矩阵的广义逆及其应用
    • 第十九讲 矩阵的广义逆及其应用
  • 期末考试

    Taught by

    Wenqiang Yang, wangjiongqi, tangyangbin, hezhangming, and xiehuaying

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