工程數學(二)

臺北科技大學 114-2 學期課程，課號 355022。

課程大綱

本課程以講述物理化學上，尤其是量子化學上，必須用到的數學為主。內容主要涵蓋三大部分。第一部分為基本線性代數，包含向量，矩陣，以及行列式等，第二部分為特殊函數，第三部分則為傅立葉轉換。 The course is designed to provide the mathematic background for physical chemistry especially for quantum chemistry. The teaching materials will include Laplace transform, Basic Linear Algebra, Differential Equation, Fourier Analysis, and special functions. Outline: 1. Series Solutions of Differential Equation 2. Linear Algebra : Vector, Matrix, Determinants, Eigenvalues, Eigenvectors, Diagonalization 3. Laplace transformation 4. Fourier Series, Fourier Transformation 5. Special function : Hermite polynomials, Laguerre polynomials, Legendre polynominals

課程進度

Week 1. Review of Power Series Week 2. Power Series Solutions Week 3. Solution about Singular Points Week 4. Special Functions (I) Week 5. Special Functions (II) Week 6. Vector Space and Matrix Algebra Week 7. Eigenvalue Problem Week 8. Laplace transformation (I) Week 9. Midterm Exam. Week 10. Laplace transformation (II) Week 11. Fourier Series Week 12. Complex Fourier Series Week 13. Fourier Integral Week 14. Fourier transformation Week 15. Fast Fourier transformation Week 16. Integration in the Complex Plane (I) Week 17. Integration in the Complex Plane (II) Week 18. Final Exam.

評量方式

(1) 期中考 : 30% (2) 期末考: 30% (3) 平時成績: 40%

教材

【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 Textbook: 1. Dennis G. Zill: Advanced Engineering Mathematics, 7th. Ed. References: 1. Hans J. Weber and George B. Arfken, Essential Mathematical Methods for Physicists, 2004. 2. Robert G. Mortimer : Mathematics for Physical Chemistry, 4th ed., 2013.