Course 
No. 
Title 
Classification 
Credits 
Prerequisites 
Semester 

COE351 
Engineering Mathematics 1 
required 
330 
None 
1st 

Lecturer 
Department 
Name 
Phone 
EMAIL 

Automotive Engineering 
Srungjae Min 
☎22200457 
seungjae@hanyang.ac.kr 

Course Description 
This course introduces students to the ideas and techniques for solving ordinary differential equations. It will emphasize both mathematical methods and conceptual understanding of engineering disciplines. The principal topics covered will include 1storder ODEs, 2ndorder linear ODEs, series solutions of ODEs and Laplace transforms. Applications of these techniques for the solution of boundary value and initial value problems will be given. 

Goal 
The main objectives of this course are twofold: the study of ordinary differential equations and their most important methods for solving them and the study of modeling. 

Textbook 
Erwin Kreyszig, Advanced Engineering Mathematics (10th ed), 2011, Wiley 

Reference 
Clevw B. Moler, Numerial Computing with MATLAB, 2004, SIAM 

Evaluation 
Midterm 
Final 
Attendence 
Homework 
Participation 
etc 
Total 

40 
40 
0 
20 
0 
0 
100 

Week 
Lecture 
Textbook 

1 
Introduction
1storder ODEs: basic concepts, modeling, separable ODEs 
1.1~1.3 

2 
1storder ODEs: exact ODEs, integrating factors, linear ODEs, Bernoulli equation 
1.4~1.5 

3 
2ndorder linear ODEs: homogeneous linear ODEs of 2nd order 
2.1 

4 
2ndorder linear ODEs: homogeneous linea ODEs with constant coefficients 
2.2 

5 
2ndorder linear ODEs: EulerCauchy equation, existence and uniqueness of solutions, Wronskian 
2.5~2.6 

6 
2ndorder linear ODEs: nonhomogeneous ODEs, solution by variation of parameters 
2.7~2.10 

7 
Midterm Exam 


8 
series solutions of ODEs: power series method 
5.1 

9 
series solutions of ODEs: extended power series method, Frobenius method 
5.3 

10 
series solutions of ODEs: Bessel’s equation, Bessel functions 
5.4~5.5 

11 
Laplace transforms: linearity, first shifting theorem 
6.1 

12 
Laplace transforms: transforms of derivatives and integrals, unit step function, second shifting theorem 
6.2~6.3 

13 
Laplace transforms: short impulses, Dirac’s delta function, convolution 
6.4~6.5 

14 
Laplace transforms: differentiation and integration of transforms, systems of ODEs 
6.6~6.7 

15 
Final Exam 

