Practical Research on Integrated Courses in Physics and Mathematics

物理学和数学（数学）通常是独立的，虽然它们之间有密切的关系。也就是说，物理为理解数学提供了具体的例子，数学知识在物理学习中是不可缺少的。因此，一种有效的物理和数学教学方法是将物理和数学有机地结合起来，让学生在物理楼和数学楼之间爬上“之”字形的梯子，培养学生的数学推理能力，获得推理所需的基本知识是学生学习物理和数学的重要目的。数学推理技能是通过选择合适的变量建立数学模型，找出它们之间的函数关系，解决这些关系并理解解决方案的实际意义的技能。在本课程中，学生首先需要了解变量的含义和它们之间的函数关系，并学习如何绘制和解释代表函数的图形。然后，他们学习代表振荡的三角函数，代表指数增加和衰减的指数函数，以及代表对数增加和衰减的对数函数。最后，他们学习微分、积分和微分方程，以及力学、振荡和电磁现象，教科书可以通过互联网分发，用户可以修改教科书，使其适合自己的课程。

Physics and mathematics (math) are usually taught independently though there is a close relationship between them. That is, physics provides concrete examples to understand math and the knowledge of math is indispensable in the study of physics. Thus, an effective way to teach physics and math is to teach them in an integrated way as if we let students to climb up zigzag ladders built between the physics building and the math building.The important purpose for students to study physics and math is to foster mathematical reasoning skill and to obtain basic knowledge necessary for the reasoning. The mathematical reasoning skill is a skill to build a mathematical model by choosing suitable variables, to find functional relations among them, to solve the relations and to understand the practical meaning of the solutions.I have completed a textbook suitable for the integrated course. In this course students are required to understand the meaning of variables and functional relationships among them, and to learn how to draw and interpret graphs representing the functions, at first. Then, they learn the trigonometric functions which represent oscillations, the exponential functions which represent exponential increases and decays, and the logarithmic functions which represent logarithmic increases and decays. Finally, they learn the differential, the integral and differential equations together with mechanics, oscillation and electromagnetic phenomena.The textbook can be distributed through the Internet and the users can modify them in order to make them suitable for their classes.