Course Name：Ordinary Differential Equations
Course Number：SMH1131203
Credit：3
The property and tasks of the curriculum：
Ordinary differential equations is a basic course with strong application in undergraduate profession-information and calculation science. Through the study of this course, one side, students can master the basic theory, basic concept and the basic idea and basic method of solving several classes of differential equations (Group); on the other side, we can cultivate the ability of students to link theory with practice, use ordinary differential equations to establish mathematical model to solve practical problems, strengthen the application in economy and other fields. The training of the students' mathematics thinking, application consciousness and the ability of analyzing and solving practical problems, can lay a good foundation for the subsequent learning.
Aim of the Course：
1、Master some simple types of first order differential equations and the elementary integral methods for the general solution.
2、Understand the general basic theory of initial value problems of first order differential equations.
3、Master the elementary solution of higher order linear differential equation and the basic theory of linear constant coefficient differential equation
4、Grasp the basic theory of linear differential equations elementary solving methods of linear differential equations with constant coefficients.
5、Understand the basic concept and elementary solving solutions of differential equations.
6、Use ordinary differential equations to establish simple mathematical models.
Prerequisite curriculum：
Mathematical Analysis，Higher Algebra.
Textbooks and reference materials：
Textbook used:
《Ordinary Diffrential Equatons》，Northeast Normal University Department of mathematics, Higher education press in 1982 October First Edition.
Reference
[1]《Ordinary Differential Equations and Application—methods、理theories、modelling、computer》，Zhou Yicang、Jin Zhen、Qin Junlin，Science Press, 2003 July, First Edition
[2] 《A course in ordinary differential equation》，Ding Tongren、Li Chenzhi，Higher education press, 1991, April, First Edition.
[3] 《Ordinary Differential Equations（the third edition）》Wang Gaoxiong、Zhou Zhiming、Zhu Siming、Wang Shousong， Higher education press, 2006, July, Third Edition.
Instructional mode, methods and practice:
Mode：Class Teaching；
Methods：Content Teaching, Examples Calculation.
Assessment：
Assessment form | Weight(%) |
Attendance and Homework | 20% |
The Middle Test | 0% |
The Final Test | 80% |
Teaching schedule：
Weeks | Class hours | Course contents |
The first week | 3 | §1.2 Basic concepts §2.1Equation of separated variables and variable transformation（1） |
The second week | 3 | §2.1 Separable equations and variable transformation（2） §2.2 Linear equations and methods of constant variation |
The third week | 3 | §2.3 Exact equations and integral factors（1）（2） |
The fourth week | 3 | §2.4 First order implicit differential equations and parameter expression |
The fifth week | 3 | §3.1Existence and uniqueness theorem and the stepwise approximation §3.2Continuation of Solutions |
The sixth week | 3 | §3.4 Singular solutions； |
The seventh week | 3 | Exercises |
The eighth week | 3 | §4.1General theory of linear differential equations |
The ninth week | 3 | §4.2Solution of linear equations with constant coefficients（1） |
The tenth week | 3 | §4.2Solution of linear equations with constant coefficients（2） |
The eleventh week | 3 | §4.3 Order reduction of higher-order equations and the power series method |
The twelfth week | 3 | §Application of high order differential equation in simple models Exercises |
The thirteenth week | 3 | §5.1 Existence and uniqueness theorem of differential equation groups §5.2 General theory of linear differential equation groups（1） |
The fourteenth week | 3 | §5.2 General theory of linear differential equation groups（2） §5.3 Linear differential equation groups with constant coefficients（1） |
The fifteenth week | 3 | §5.3 Linear differential equation groups with constant coefficients（2） |
The sixteenth week | 3 | §5.3 Linear differential equations with constant coefficients Exercises |
The seventeenth week | 3 | §First-order linear difference equation §Second-order and higher-order linear difference equation |
The eighteenth week | 3 | Review and Examination |
