本課程的主要目的在連接同學們從高中數學到理解物理學的基礎課程之間，必須具備的數學能力。我們在不同物理課程中，經常面對運動的方程式，這是一種微分方程式，我們應該可以用最簡單的方式來理解最基本微分方程之解。至於更複雜的微分方程可以留在應用數學課中，再一步一步的學習。普通物理中我們要面對質心座標和轉動慣量的計算，這些計算需要用到一些座標轉換以及多重積分。由於課程進度上的考量，我們沒有辦法花足夠多的時間，把所有積分的細節在課堂中為同學們推導，因此我們希望能夠藉由這一門課為同學們彌補這些學習上的缺憾，同時也能作為應用數學的學習銜接。
電磁學對物理系的學生而言，是一門非常基本而重要的訓練課程。電磁學除了是發展光電科技，量子物理相關的料科學的基礎之外，學習這門課所要用到的數學也是未來在高等課程當中的基礎訓練。我們在學習的過程當中，都一再地強調要有向量的觀念，才能把電磁學的美妙之處精確應用，然而同學們對於向量的觀念以及向量微分所需要的計算技巧，在應用數學的課程的學習中都未能精確掌握，因此在這個課程中我們也把向量微分的幾個基本的運算算符的定義和最基本的操作，與相關的電磁學應用涵蓋進來，希望也能輔助各位同學在應用數學和電磁學及電磁波的進階學習。
今年度我們把這個課程放在寒假當中，希望有志要學好物理學的首要工具-數學的同學們，能夠利用假期進行自我學習，同時獲得選修科目的學分。
The main purpose of this course is to connect students with the mathematical abilities they must possess from high school mathematics to basic courses for understanding physics. In different physics courses, we often face the equation of motion, which is a kind of differential equation. We should be able to understand the solution of the most basic differential equation in the simplest way. As for more complex differential equations, you can stay in the applied mathematics class and learn them step by step. In general physics, we have to face the calculation of the center of mass coordinates and moment of inertia. These calculations require some coordinate transformations and multiple integrals. Due to course progress considerations, we are unable to spend enough time to deduce all the details of points for students in class. Therefore, we hope to use this course to make up for these learning shortcomings for students, and at the same time also Can be used as a learning interface for applied mathematics.
Electromagnetism is a very basic and important training course for students in the physics department. In addition to being the foundation for the development of optoelectronic technology and material science related to quantum physics, electromagnetism is also the basis for future basic training in higher education courses. In the process of learning, we have repeatedly emphasized that we need to have the concept of vectors in order to accurately apply the beauty of electromagnetism. However, students’ concepts of vectors and the calculation skills required for vector differentiation are not fully understood in the course of applied mathematics. We have not been able to master it accurately during study, so in this course we also cover the definitions of several basic operators and the most basic operations of vector differentiation, as well as related electromagnetic applications. We hope that it can also assist students in their studies. Applied mathematics and advanced study of electromagnetism and electromagnetic waves.
This year we put this course during the winter vacation. We hope that students who are interested in learning mathematics, the primary tool of physics, can use the vacation to conduct self-study and obtain credits for elective subjects.
Mathematical Methods for Physics and Engineering Third Edition
Riley, Hobson and Bence
mathematical methods for physics and engineering third edition
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