學習基礎數學知識，作為後續專業級選修課程之預備。Learn basic mathematical knowledge as a preparatory plan for subsequent professional selection courses.
※介紹基礎理論物理課程中所需使用的基本數學技巧與觀念，藉以為後續課程的學習墊立良好的基礎。
※培養學生核心能力：1.理解與運用物理、數學知識2.數值計算與數據分析3.陳述、分析與解決問題。
※內容主題為：
第一學期
1.向量與矩陣代數
2.向量場的微積分運算複習（optional）
3.曲線座標系中的向量分析
4.δ函數（optional）
5.張量代數簡介與二階張量的對角化、線性空間
6.常微分方程式簡介與方程式的級數解（optional）
第二學期
1.複變函數
2.傅立葉級數與邊界值問題
3.積分轉換（傅立葉與Laplace）
4.積分轉換的應用（optional）
※Introduce the basic mathematical skills and concepts required in the physics course to establish a good foundation for the learning of the subsequent course.
※Cultivate students' core abilities: 1. Understand and use physics and mathematical knowledge 2. Numerical calculation and data analysis 3. Describe, analyze and solve problems.
※The content theme is:
The first period
1.Vector and matrix generation number
2. Micro-segment calculation complex of vector field (optional)
3. Vector analysis in curve coordinate system
4. δ function (optional)
5. Introduction to the number of numbers and the diagonalization and linear space of the second-level numbers
6. Introduction to ordinary differential equations and the level of the equation (optional)
Second period
1. Complex function
2. Questions about Fu Li's Leaf Level and Neighbor Delivery Value
3. Points conversion (Fu Liye and Laplace)
4. Application of points conversion (optional)
Textbook:
Mathematical Methods and Physical Insights: An Integrated Approach by A. J. Schramm
References:
1. Mathematical Physics: Applied Mathematics for Scientists and Engineers, by B. R. Kusse and E. A. Westwig
2. Introduction to Mathematical Physics. Methods and Concepts 2nd Ed, by C. W. Wong
3. A Course in Mathematical Methods for Physicists-CRC Press (2013), by Herman, Russell L.
4. A First Course in Mathematical Physics, by Colm T. Whelan. Wiley-VCH
5. Mechanics, by Landau and Lifshitz
6. Vector Calculus, Classical Dynamics, by David Tong. http://www.damtp.cam.ac.uk/user/tong/teaching.html (ALL the lecture notes are highly recommended.)
7. Classical Mechanics, by J. R. Taylor
Textbook:
Mathematical Methods and Physical Insights: An Integrated Approach by A. J. Schramm
References:
1. Mathematical Physics: Applied Mathematics for Scientists and Engineers, by B. R. Kusse and E. A. Westwig
2. Introduction to Mathematical Physics. Methods and Concepts 2nd Ed, by C. W. Wong
3. A Course in Mathematical Methods for Physicists-CRC Press (2013), by Herman, Russell L.
4. A First Course in Mathematical Physics, by Colm T. Whelan. Wiley-VCH
5. Mechanics, by Landau and Lifshitz
6. Vector Calculus, Classical Dynamics, by David Tong. http://www.damtp.cam.ac.uk/user/tong/teaching.html (ALL the lesson notes are highly recommended.)
7. Classical Mechanics, by J. R. Taylor
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 期中考期中考 Midterm exam |
50 | |
| 期末考期末考 Final exam |
50 |
