學習基礎數學知識，作為後續專業級選修課程之預備。Learn basic mathematics knowledge as preparation for subsequent professional-level elective 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）
※Introducing the basic mathematical skills and concepts required in basic theoretical physics courses, so as to lay a good foundation for subsequent courses.
※ Cultivate students' core abilities: 1. Understand and apply physics and mathematics knowledge 2. Numerical calculation and data analysis 3. Presentation, analysis and problem solving.
※The content theme is:
first semester
1. Vector and matrix algebra
2. Review of calculus operations of vector fields (optional)
3. Vector analysis in curved coordinate system
4.δ function (optional)
5. Introduction to tensor algebra and diagonalization of second-order tensors and linear spaces
6. Introduction to ordinary differential equations and series solutions of equations (optional)
second semester
1. Complex variable function
2. Fourier series and boundary value problems
3. Integral conversion (Fourier 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 lecture 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 |
