I.The Basic Information of the Course
Course Number: 202012420023
The EnglishName of theCourse：The Mathematical Methods of Engineering Mechanics
The ChineseName of theCourse：工程力学的数学方法
In-classHours andAllocation:total class hours:32, classroom teaching: 16 classhours, classroom discussion: 16 classhours.
Credit(s):2
Semester:2
AppliedDiscipline(Professional Degree Category)：Mathematics
CourseObjectOriented：AcademicMaster,Academic Doctor
EvaluationMode:Sample:Process Evaluation
TeachingMethod:Seminar-style Teaching, Case Teaching
CourseOpening Department:College of Mathematical Sciences
II.Prerequisite Course
College Physics, Ordinary Differential Equation, Partial Differential Equation
III. The Objectives and Requirements of the Course
The course is an important professional elective course, basic concepts and theories of some mathematical methods commonly used in engineering mechanics are introduced. Mechanical problems are discussed in the form of Mathematics. The aim of the course is to cultivate the students’s ability to solve mechanical problems with mathematical methods, understand some common mathematical theories and methods in the field of mechanics research, grasp some basic ideas, theories and mathematical methods in engineering mechanics, have the ability to apply mathematical knowledge to analyze some mechanical phenomenon. For example, the mathematical models of some mechanical problems may be built based on Newtonian mechanics or Lagrangian mechanics, then it may be solved by use of eigenvalue theory in Ordinary Differential Equation or Finite Element Method.
By learning this course, the students should reach the following basic requirements: building some simple mathematical models based on Newtonian mechanics, building mathematical model based on Lagrangian mechanics, solving some ordinary differential equations by use of finite element method, grasping one or two kinds of mathematical methods to solve the nonlinear equations in mechanical problem.
IV. The Content of the Course(Time New Rome, 12 points, bold font, 1000-2000 words)
Chapter 1 Newtonian mechanics (4classhours)
1.1Galilean transformation
1.2Motion Equation
Chapter 2Lagrangian mechanics（4classhours）
2.1Variational method
2.2Lagrangian equation
Chapter 3Finite element method（10classhours）
3.1Motion equations of beam and plate
3.2Finite element method
3.3Applications
Chapter 4Mode superposition method（4classhours）
4.1Separate variable method
4.2Mode superposition method
Chapter 5Nonlinear problems（10classhours）
5.1Introduction
5.2Perturbation method
5.3Multiscale method
Ideological and political theory construction：A brief introduction to the famous Chinese mathematicians in the development history of this course，according to the actual situation of classroom teaching, the teacher choose teaching materials.By analyzing the patriotism and scientific spirit of mathematicians, we can improve the patriotism education and cultural self-confidence of students.
1Founder of finite element method
Feng Kang, born in Shaoxing, Zhejiang Province, is a mathematician, founder of finite element method, founder and pioneer of computational mathematics research, academician of Chinese Academy of Sciences and founder of computing center of Chinese Academy of Sciences.At the end of 1950s, on the basis of collective research and practice of solving large-scale dam calculation problems, Feng Kang created a set of systematic and modern calculation methods for solving differential equation problems independently of the West, At that time, it was named the difference method based on the variational principle, which is now known as the finite element method internationally, Its systematic theory and summary paper difference scheme based on variational principle was published in Applied Mathematics and Computational Mathematics in 1965,It is a sign that China has systematically created the finite element method independently of the West.This paper presents a systematic discretization method for all kinds of boundary value problems of second order elliptic equations.
2"The father of mechanics", "the father of Applied Mathematics" in modern China
Qian Weichang, born in Wuxi, Jiangsu Province, participated in the preparation of the Institute of mechanics and the Institute of automation of the Chinese Academy of Sciences. In the 1970s, he founded the professional group of rational mechanics and mathematical methods in mechanics of the Chinese society of mechanics. In 1980, he founded the earliest Academic Journal of China, applied mathematics and mechanics, and established Shanghai Institute of Applied Mathematics and mechanics. At the same time, he opened a series of national academic conferences on modern mathematics and mechanics, and created the research direction of theoretical mechanics and the academic direction of nonlinear mechanics. It has made an important contribution to the development of mechanics and Applied Mathematics in China.
V. Reference Books, Reference Literatures, and Reference Materials
A. Text Books, Monographs and References
1.V.I.Arnold,.Mathematical methods of classical mechanics(2). World Book Publishing Company, 2019.
2. Guangyuan Zou, Ceji Fu. Mathematics Method in Physics (1). Peking University Press, 2018.
B. Learning Resources
1.http://lib.hrbeu.edu.cn.V.I.Arnold,.Mathematical methods of classical mechanics
2. MOOC platform of University of China: Vibration theory and engineering application, Tianjin University.
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