Lecturer: Ching-Yeh Hsin (辛敬業)
Email: hsin@mail.ntou.edu.tw
Phone: 2462-2192 #ext. 6037
Webpage: https://se.ntou.edu.tw/p/412-1058-7647.php?Lang=zh-tw
Course ID: B5103H15
Credits: 3
Objective: The course aims to assist students in reviewing and understanding topics related to partial differential equations based on their existing knowledge of calculus. Additionally, it will help students grasp the applications of partial differential equations in engineering problems. Three types of partial differential equations related to mechanics and mechatronics will be introduced, along with methods for solving and analyzing them using separation of variables. Through this course, we hope to rekindle students' interest in mathematics and teach them how to apply mathematics to solve engineering-related problems.
Course Prerequisites: Engineering Mathematics.
Outline:
1. Course Introduction
2. Review of Ordinary Differential Equations
3. Series
4. Orthogonality of Functions
5. Fourier Series
6. Wave Equation
7. Heat Equation
8. Laplace Equation and Boundary Value Problems
9. Bessel Functions and Legendre Functions
10. Partial Differential Equations in Cylindrical and Spherical Coordinate Systems
Teaching Method:
*Classroom: Instruction on theory and methods.
*Computer: Teaching students to solve mathematical problems using simple programs and software.
Reference:
“Advanced Engineering Mathematics” by Erwin Kreyszig
Course Schedule (subject to change):
Week 1: Course Introduction
Week 2: Review of Ordinary Differential Equations
Week 3: Series
Week 4: Orthogonality of Functions
Week 5: Fourier Series
Week 6: Quiz I
Weeks 6-8: Wave Equation
Weeks 8-10: Heat Equation
Week 11: Quiz II
Weeks 12-13: Laplace Equation and Boundary Value Problems
Week 14: Bessel Functions and Legendre Functions
Weeks 15-17: Partial Differential Equations in Cylindrical and Spherical Coordinate Systems
Week 17: Quiz III
Week 18: Numerical Methods for Solving PDEs
Evaluation:
1.Three Exams: Based on 1-2 pages of "reference materials."
2.Team Tests/Assignments
3.Numerical Methods Assignments
4.Reference Assignments
5.Class Participation