This paper analyzes the textbooks of mechanics, especially the textbooks and their teaching systems of theoretical mechanics and materials mechanics, including the national states of the mechanics courses, the textbooks, the achievements and problems of the teaching systems for elementary mechanics, the introduction of overseas elementary mechanics textbooks, focusing on the theoretical mechanics teaching and the teaching system in foreign countries.
Student-centered teaching and learning is now widely accepted in the modern higher education worldwide with active learning as its core. It is a big challenge for both the teachers and the students to turn successfully from the traditional teacher-centered teaching to the relatively new student-centered learning. This paper presents a discussion on the feasible and efficient ways from the traditional“teacher-centered teaching”to the “student-centered learning” organized by the Quality Assurance Office and the Center for Excellent Teaching of the Tongji University. Being used to the cramming teaching, some students lack the initiative of active learning, teachers should do their best to arouse students in class. Effective ways to encourage active learning include designing an appropriate quality evaluation system, focusing on student learning efficiency and ability improvement, with an effective teaching pedagogy such as the “peer instruction”, and the introductions of problems or projects without preset answers in class.
The paper introduces the basic situation, characteristics and problems of the 7th teaching competition of youth faculty of Fundamental Mechanics Courses, which was held by the teaching guidance committee of foundation mechanics courses in colleges and universities of the Ministry of Education. Some suggestions were given to improve in teaching abilities of teachers. Through this paper, the teachers in colleges and universities in China can know this teaching competition and the problems reflected in the competition. This paper is also a reference for improving the teaching level and quality of fundamental mechanics courses in China.
The stress transformation formula, which is also called the Cauchy's formula for stresses on slanted surfaces, is widely used in solid mechanics. No explicit statement has been found on its limitations in application. The stresses at the sharp point of a V-shaped free-surface notch on a bar under axial loading at both ends are examined as an example. With the two intersecting surfaces being free, it is deduced from the transformation equations that the sharp point is stress free. This deduction is however contradictory to the fact that the stress concentrates near the sharp point. Clearly the stress transformation formula leads to incorrect results and thus is not valid at that sharp point. It is known that if the stress transformation formula is valid, the stress components constitute a stress tensor, but the stress at the sharp concave corner is shown to be discontinuous and double-valued. It is further pointed out that stress transformation formula is not applicable to any point where a stress component has discontinuity or lacks of uniqueness at a surface passing through that point. The tip of any crack is the case.
This is the preface to Calculus II, a textbook to be published by Peking University Press. We explore the purpose and the pedagogy for teaching calculus in theoretical and applied mechanics curriculun.