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Course Syllabus

1. Course Name: 
Numerical methods in engineering 
  
2. Course Hours and Credits: 
32 hours and 2 credits 
  
3.  Target Students: 
Bachelor  and master students major in mechanical engineering 
  
4.  Department: 
Faculty of Automotive engineering, Chongqing University 
  
5. Objectives: 
The objective of this course is to make students be able to know the basic concept about numerical methods, master the basic theory and procedures for the solution of the three kinds of PDEs describing the physical problems in the fields of fluid mechanics, heat transfer and acoustics with the help of their previous computer programming knowledge and other fundamental knowledge after finishing the study of this course. Another objective is to train students to be able to analyze and solve the physical problems by themselves so that lay foundation for them to solve the practical engineering problems with numerical method in their future career. 
6.  Main contents: 
§1 Introduction

  1. Numerical Methods in Engineering Computation

  2. The Taylor Series and Fourier Transformation

  3. General Features and Classification of Ordinary Differential Equations

§2 One-Dimensional Initial-Value Ordinary Differential Equations

  1. General Features of Initial-Value ODEs

  2. Euler Methods

  3. Consistency, Order, Stability, and Convergence

  4. Runge-Kutta Methods

  5. Multipoint Methods

  6. Systems of First-Order Ordinary Differential Equations

  7. Higher-order Ordinary Differential Equations

§3 General Introduction to Partial Differential Equations

  1. General Features and Classification of PDE

  2. Discretization of Differential Equations

  3. Consistency/Compatibility of Numerical Schemes

§4 Parabolic Partial Differential Equations

  1. Explicit Scheme

  2. Stability Analysis

  3.  Implicit Scheme

  4. Types of Boundary Conditions

§5 Elliptic Partial Differential Equations

  1. Five-Points Method

  2. Solution of System of Linear Algebraic Equations

§6 Hyperbolic Partial Differential Equations

  1. Use of Method of Characteristics for 2nd Order Equations

  2. Use of Method of Characteristics for 1st Order Equations

  3. Finite Difference Methods For 1st Order Equations

  
7. Practical Teaching Contents: 
1) Assignments 
2) Group Project 
  
8. Hours Distribution:

Chapter

2

3

4

5

6

7

Academic hours

2

8

4

10

4

4


9. Testing: 
Final exam (60%) + assignments + group project + Presentation (40%) 


 
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重庆大学机械工程学院 | College of Mechanical Engineering ChongQing University  地址:重庆市沙坪坝区沙正街174号
因机械工程学院(A区第7教学大楼)整体维修改造,施工期大约一年。
学院行政办公地点临时搬迁至A区机械传动重点实验室后直行50米处
(机械学院制造研究所一楼)。
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