《常微分方程（英语）》Teaching Quality Standards for Ordinary Differential Equations

1、Teaching Quality Standards for Ordinary Differential EquationsTotal Periods: 56 Credits:3.5Ordinary Differential Equation is the basic compulsory course. This course includes the integrating methods, the fundamental theory about initial value problem and the elementary results of linear differential

2、 equations. The purpose of this course is to provide some important methods to solve Ordinary Differential Equation and to let students grasp the basic theory of linear differential equation. Moreover, students can solve some engineering and technical problems by using the knowledge of this course,

3、and lay the foundation for further study.I. Course ObjectivesThrough this course, students can master the basic theory of ordinary differential equations and necessary professional knowledge, analyze and solve engineering and technical problems. And so, they can own the ability of scientific researc

4、h. Furthermore, learning this course is necessary preparation for further courses, such as Equations of Mathematical Physics and Nonlinear Differential Equations.II. Course content, requirements and period distributionNo.ChapterContent and requirementsPeriodRemarks1Chapter 1IntroductionTo know about

5、 the main content of this courseTo master basic concept and classification of ordinary differential equations42Chapter 2Integrating methodsTo master the solving methods to equations with separated variables, homogeneous differential equation, linear differential equation, Bernoullis equation, exact

6、equations and integrating factor method.12Exercises lesson: 2 periods3Chapter 3Initial value problemTo master the existence and uniqueness theorems, Peano existence theorem and comparison theorem 12Exercises lesson: 2 periods4Chapter 4High-order differential equationTo master basic concept of high-o

7、rder differential equationTo master Theorem on Continuous Dependence85Chapter 5Linear differential equationTo master the fundamental theory of general linear differential equation To master the solving methods to system with constant coefficients and high-order linear differential equation20Exercise

8、s lesson: 4 periodsTotal568III. Teaching staffThis course requires a course leader (above the level of associate professor) and some teachers (above the level of lecturer). The course leader should have rich teaching experience and strong ability of organization and management.Teachers should have a

9、 doctorate, enough teaching ability and professional level. Moreover, they should have enough time and effort to teaching and guiding students, and actively participate in teaching research and reform.IV. Teaching materials and references1Recommended textbook(1)An Introduction to Ordinary Differenti

10、al EquationsRavi P. Agarwal and Donal ORegan. New York: Springer.2010(2)Ordinary Differential EquationsWalter, Wolfgang . New York: Springer.20042Teaching references (1)Tongren Ding, Chengzhi Li. Ordinary Differential Equations. Higher Education Press, 2004 (2)Gaoxiong Wang, Siming Zhu. Ordinary Dif

11、ferential Equations. Higher Education Press, 2006V. Teaching organization1Teaching conception, design and methodsThe teaching of this course should pay attention to the reform of teaching methods. For stimulating the students interest, teachers should adopt different teaching methods (for example, i

12、nspiring, discussing, introducing from practical problems) according to the content, and carry on the reasonable teaching design.2Course serviceThe teachers should assign homework in each chapter, correct homework more than 1/2 and make a summary of homework at the appropriate time. They should arra

13、nge the answer time every week and adopt the method of face to face.VI. Course assessmentExamination method: final exam in form of close-book, accounting for 70%; homework, attendance, etc. for the usual results, accounting for 20%; application training in form of small paper, accounting for 10%.Scoring criteria: percentile systemVII. Notes1）This course should be arranged after Mathematical Analysis, Advanced Algebra.2）This teaching quality standard is also applicable to all majors to mathematics subject.3）Th