数理方程复习指导 2020春数理方程08班 目录 1写给数理方程08班的同学们的一封信 2本书的使用说明 5 2.1本书的设计初衷 2.2本书的设计思想 2.3本书的使用方法 6 3课程综述 8 3.1课程主要内容 3.2课程学习日标 8 3.3课程学习方法… 9 3.4课程学习中蕴含的转化思想… 9 3.5定解问题求解方法的使用条件 10 3.6数理方程课程中的三步走战略 小4小小444小…小0 11 4第一章综合复习 12 41主要内容… 12 4.2学习目标 12 4.3学习方法… 多 4.4应用变量代换求解偏微分方程通解… 13 4.5定解问题的书写 14 4.6行波法求解一维无界区域弦振动问题… 15 4.7一维半无界区域的弦振动方程的处理之通解法和延拓法 16 4.8可以通过函数变换转化为一维无界区域波动方程问题 19 4.9通解法求解定解问题 21 5第二章综合复习… 22 5.1主要内容 22 5.2学习目标 22 5.3学习方法 23 5.4明确齐次方程的基本概念 23 1数理方程复习指导 2020 春数理方程 08 班 目录 1 写给数理方程 08 班的同学们的一封信 ······················································ 4 2 本书的使用说明 ··················································································· 5 2.1 本书的设计初衷 ·········································································· 5 2.2 本书的设计思想 ·········································································· 5 2.3 本书的使用方法 ·········································································· 6 3 课程综述 ···························································································· 8 3.1 课程主要内容 ············································································· 8 3.2 课程学习目标 ············································································· 8 3.3 课程学习方法 ············································································· 9 3.4 课程学习中蕴含的转化思想 ··························································· 9 3.5 定解问题求解方法的使用条件 ························································ 10 3.6 数理方程课程中的三步走战略 ························································ 11 4 第一章综合复习 ··················································································· 12 4.1 主要内容 ··················································································· 12 4.2 学习目标 ··················································································· 12 4.3 学习方法 ··················································································· 13 4.4 应用变量代换求解偏微分方程通解 ·················································· 13 4.5 定解问题的书写 ·········································································· 14 4.6 行波法求解一维无界区域弦振动问题 ··············································· 15 4.7 一维半无界区域的弦振动方程的处理之通解法和延拓法 ······················· 16 4.8 可以通过函数变换转化为一维无界区域波动方程问题 ·························· 19 4.9 通解法求解定解问题 ···································································· 21 5 第二章综合复习 ··················································································· 22 5.1 主要内容 ··················································································· 22 5.2 学习目标 ··················································································· 22 5.3 学习方法 ··················································································· 23 5.4 明确齐次方程的基本概念 ······························································ 23 1