复变函数与数理方程教学大纲.doc

复变函数与数理方程Functions of Complex Variables and Equations of Mathematical PhysicsFall Semester 201XSyllabusCourse Description: 本课程是理工科有关专业的一门基础课，主要由复变函数“数学物理方程”和“特殊函数”三部分内容组成。“复变函数”部分介绍解析函数的基本性质，积分，级数，留数等内容。“数学物理方程”部分介绍数学物理方程的一些基本概念及三种典型方程、各种定解问题的常用解法，包括分离变量法、行波法、积分变换法和格林函数法等。“特殊函数”部分讨论贝塞尔函数及勒让德多项式。 通过这门课程的学习，学生应掌握复变函数论的基本知识和方法，三类典型方程定解问题的解法，了解贝塞尔函数及勒让德多项式的简单性质及其在数学物理方程中的应用，为学习电磁场、量子力学等有关后继课程和进一步扩大数学知识面奠定必要的数学基础，也为进一步了解和应用现代偏微分方程的有关内容解决科学技术和工程实际问题提供重要帮助。This is a foundation course for engineering students. It mainly consists of three parts: functions of complex variables, equations of mathematical physics and special functions.By this course, the students are expected to grasp the basic knowledge and techniques in solving questions of complex variables and the three types of partial differential equations. The contents of this course will be of great benefit for later curriculums and applied in many aspects.Prerequisite: calculus, or equivalent courses.Textbook: A first course in partial differential equations with complex variables and transform methods, by H.F.Weinberger. Dover Pub.Inc.Examinations: One 120-minute midterm examination, and a comprehensive final examination given during the final examination period. Calculators: A calculator may be useful for some homework problems involving graphing. However, the use of calculators is not permitted on exams.Grading Policy: Grades will be assigned on the basis of 100 points distributed as follows30 points midterm examination 30 points quizzes/homework40 points final examination Tentative Course Outline: Chp 1 The one dimensional wave equation 一维波动方程Chp 2 linear 2nd-order partial differential equations in 2 variables 二元二阶线性偏微分方程Chp 3 Some properties of elliptic and parabolic equations 椭圆和抛物型方程的性质Chp 4 Separation of variable and Fourier series 分离变量法和Fourier级数Chp 5 Nonhomogeneous problems 非齐次问题Chp 6 Problems in higher dimensions and multiple Fourier series 高维问题和多元Fourier级数Chp 7 Sturm-Liouville theory and general Fourier expansions 斯特姆-刘维尔理论和广义Fourier展开理论Chp 8 Analytic functions of a complex variable 一元解析函数Chp 9 Evaluation of integrals by complex variable methods 复变函数积分的方法Chp 10 The Fourier transform 傅里叶变换Chp 11 The Laplace transform 拉普拉斯变换Chp 12 Approximation methods 近似方法（有限元方法） Details of the content(This schedule is subject to ch