| 课程号 |
00333148 |
学分 |
3 |
| 英文名称 |
Applied Analysis for Engineering Sciences |
| 先修课程 |
Calculus (Single variate, and multi-variate), Linear Algebra, Ordinary Differential Equations. |
| 中文简介 |
本课程的目标包括：（1）介绍广泛应用于工程科学、非线性力学和其他物理科学领域的现代（1900-1990）数学方法；（2）发动学生的科研积极性，包括启发思维，明确问题并建模，以及探索相应的数学方法；（3）弥合数学工具与其物理理解之间的鸿沟。 |
| 英文简介 |
The objectives of this course include: to show some modern (1900-1990) mathematical methods that are widely used in engineering sciences, nonlinear mechanics and other physical sciences; to help initiating research activities, namely, to boost ideas, to formulate the problem, and to explore the mathematics; to help bridging the gap between the mathematical tools and the physical understandings. |
| 开课院系 |
工学院 |
| 通选课领域 |
|
| 是否属于艺术与美育 |
否 |
| 平台课性质 |
|
| 平台课类型 |
|
| 授课语言 |
英文 |
| 教材 |
无；
Applied Analysis for Engineering Sciences,ence Shaoqiang Tang,Peking University Press,2016, |
| 参考书 |
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| 教学大纲 |
to show some modern (1900-1990) mathematical methods that are widely used in engineering sciences, nonlinear mechanics and other physical sciences; to help initiating research activities, namely, to boost ideas, to formulate the problem, and to explore the mathematics; to help bridging the gap between the mathematical tools and the physical understandings
1. The qualitative theory of Ordinary Differential Equations (ODE) systems
a) The second order ODE (plane analysis)
b) Stability analysis via the Lyapunov function
c) Chaos in the Lorenz system and the logistic map
2. Reaction-diffusion systems
a) BVP (boundary-value problem) and IBVP (initial boundary-value problem)
b) Traveling wave analysis
c) Burgers` equation and Cole-Hopf transform
d) Evolutionary Duffing equation
3. Hyperbolic equations
a) Linear advection equation
b) Discontinuities in inviscid Burgers` equation
c) Elementary waves in a polytropic gas
d) Soliton and inverse scattering transform
课堂讲授
Homework Assignments 40%
Exam (open-book) 60%
Total 100%
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| 教学评估 |
唐少强：
学年度学期：18-19-3，课程班：工程科学应用分析1，课程推荐得分：null，教师推荐得分：null，课程得分分数段：80及以下；
学年度学期：20-21-3，课程班：工程科学应用分析1，课程推荐得分：null，教师推荐得分：null，课程得分分数段：null；
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