《數(shù)學(xué)物理方程A》Teaching Quality Standards for Mathematical Physics Equation A

1、Teaching Quality Standards for Mathematical Physics Equation ATotal Periods: 48 Credits:3Mathematical Physics Equation A is the subject foundation compulsory course whose prerequisite course is College Physics, Mathematical Analysis and Ordinary Differential Equation. This course is not only the fur

2、ther deepening of mathematics theory, but also provides some important methods to solve practical problems. This course is applicable to mathematics and applied mathematics, information and computing science and other majors. This course introduces the derivation of basic equations, solutions of IVP

3、s and BVPs for wave equation, heat equation and harmonic equation and their physical meaning, well-posedness of IVPs and BVPs, etc. Through this course, students can master the construction of mathematical models for practical problems, typical methods for solving IVPs and BVPs of partial differenti

4、al equations, qualitative analysis of the related problems. Moreover, students can solve some engineering and technical problems by using the knowledge of this course, and lay the foundation for further study.I. Course ObjectivesThrough this course, students can master the basic theory of partial di

5、fferential equations and necessary professional knowledge, the thinking method of solving and analyzing IVPs and BVPs, the ability of mathematical modeling, analyzing and solving engineering and technical problems. And so, they can own the ability of scientific research, teaching, management, techno

6、logical development in mathematics, finance and engineering, etc.II. Course content, requirements and period distributionMain course contentNo.ChapterContent and requirementsPeriodRemarks1Chapter 1IntroductionTo know about the main content of this courseTo master basic concept, derivation of basic e

7、quations, IVPs and BVPs, classification of second order linear partial differential equations62Chapter 2Wave equationTo master unbounded string vibration, semi-bounded string vibration, forced vibration of unbounded string, bounded string vibration, spherical averaging method, dimension reducing met

8、hod, well-posedness of IVPs and BVPs for wave equation20Including exercises lesson: 2 periods3Chapter 3Heat equationTo master separation variable method of heat equation, theoretical basis of separation variable method, well-posedness of IVPs and BVPs for heat equation64Chapter 4Harmonic equationTo

9、master fundamental solutions, Green formulas and their applications, Green functions, strong extremum principle and its applications16Including exercises lesson: 2 periodsTotal48Including exercises lesson: 4 periodsIII. Teaching staffThis course requires a course leader (above the level of associate

10、 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 doctorate, enough teaching ability and professional level. Moreover, they should have enough time and effort to

11、 teaching and guiding students, and actively participate in teaching research and reform.IV. Teaching materials and references1Recommended textbookW. Liu, etc. Mathematical Physics Equation (Second Edition). Xuzhou: China University of Mining and Technology Press, 20022Teaching references1）Z. Chen.

12、Mathematical Physics Equation. Beijing: Higher Education Press, 19902）Department of mathematics, Fudan University. Mathematical Physics Equation. Beijing: People Education Press, 19793）W. Ou. Mathematical Physics Equation. Jilin: Jilin University Press, 19914）S. Qiu. Mathematical Physics Equation. B

13、eijing: Capital Normal University Press, 1997V. 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, inspi

14、re, discuss, introduce 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 1/3 and make a summary of homework at the appropriate time. They should arrange the ans

15、wer time every week and adopt the method of face to face.VI. Course assessmentExamination method: final exam in form of close-book, accounting for 60%; homework, attendance, etc. for the usual results, accounting for 20%; application training in form of small paper, accounting for 20%.Scoring criteria: percentile systemVII. Notes1）This course should be arranged after Mathematical Analysis, Ordinary Differential Equations, College Physics and other courses.2）This teaching quality standard is also applicable to engineering mechanics and other