應用數學
本課程是由 國立陽明交通大學應用化學系提供。
After studying calculus with general training, one needs to learn how to solve real problems in chemistry. Mathematical problems in chemistry can be sometime difficult, in this course we learn how to solve those problems by trial and error.
課程用書：Physical Chemistry 3rd edition, Mortimer, 2008.
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| 授課教師 | 應用化學系 朱超原老師 |
|---|---|
| 課程學分 | 3學分 |
| 授課年度 | 101學年度 |
| 授課對象 | 大學二年級學生 |
| 預備知識 | 化學I、化學II、微積分 |
| 課程提供 | 課程影音 課程綱要 課程行事曆 |
| 週次 | 課程內容 | 課程影音 | 課程下載 |
|---|---|---|---|
| 第一週 | I. Review of differentiation and integration I-1. Introduction I-2. Review of differential calculus I-3. Review of integral calculus I-4. Graph | 線上觀看 | MP4下載 |
| 第二週 | II. Calculus of several variables, partial differentiation II-1. Partial derivatives II-2. Total differential II-3. Application to physical chemistry I | 線上觀看 | MP4下載 |
| 第三週 | II. Calculus of several variables, partial differentiation II-4. Cycle rule II-5. Application of derivatives II-6. van Der Waals equation of state | 線上觀看 | MP4下載 |
| 第四週 | II. Calculus of several variables, partial differentiation II-7. Constrained maxima and minima II-8. Stirling’s formula II-9.Application to physical chemistry III III. Line integrals and multiple integrals III-1. Introduction | 線上觀看 | MP4下載 |
| 第五週 | III. Line integrals and multiple integrals III-3. Line integral III-4. Applied to Physical Chemistry I III-5. Double integral III-6. Jacobi determinant | 線上觀看 | MP4下載 |
| 第六週 | IV. Infinite series IV-1. Talyor series IV-2. Convergence and its region IV-3. Applied to Physical Chemistry II | 線上觀看 | MP4下載 |
| 第七週 | IV. Infinite series IV-4. Fourier series IV-5. Particle in one-dimensional box (PC II) IV-6. Kronecker delta function IV-7. Fourier transforms | 線上觀看 | MP4下載 |
| 第八週 | 作業討論 Fourier series Fourier transforms | 線上觀看 | MP4下載 |
| 第十週 | V. Ordinary differential equations (1/4) V-1. Introduction V-2. The first-order differential equations V-3. The second-order differential equations | 線上觀看 | MP4下載 |
| 第十一週 | V. Ordinary differential equations (2/4) V-4. Differential equations with total differential | 線上觀看 | MP4下載 |
| 第十二週 | V. Ordinary differential equations (3/4) V-5. Special functions for the second-order DE、Quantum harmonic oscillator、Quantum hydrogen atom | 線上觀看 | MP4下載 |
| 第十三週 | V. Ordinary differential equations (4/4) V-5. Special functions for the second-order DE、Quantum harmonic oscillator、Quantum hydrogen atom | 線上觀看 | MP4下載 |
| 第十四週 | VI. Partial differential equations VI-1. Introduction VI-2. The classical wave VII. Determinants and matrices (1/4) VII-1 Introduction | 線上觀看 | MP4下載 |
| 第十五週 | VII. Determinants and matrices (2/4) VII-2. Determinant algebra VII-3. Properties of determinant VII-4. Matrix algebra | 線上觀看 | MP4下載 |
| 第十六週 | VII. Determinants and matrices (3/4) VII-5. Singular matrix VII-6. Characteristic equation of a matrix VII-7. Symmetry matrix | 線上觀看 | MP4下載 |
| 第十七週 | VII. Determinants and matrices (4/4) VII-8. Application to physical chemistry II | 線上觀看 | MP4下載 |
課程目標
After studying calculus with general training, one needs to learn how to solve real problems in chemistry. Mathematical problems in chemistry can be sometime difficult, in this course we learn how to solve those problems by trial and error.
課程章節
| 章節內容 |
| Review of differentiation and integration techniques |
| Calculus of several variables, partial differentiation |
| Line integrals and multiple integrals |
| Vector analysis |
| Ordinary differential equations |
| Partial differential equations |
| Determinants and matrices |
| Probability and statistics |
課程書目
Applied Mathematics for Physical Chemistry, Barrante, 3rd , 2003.
參考書目
The Chemistry Maths Boolk, Steiner, 2004.
Physical Chemistry, A Molecular Approach, McQuarrie and Simon, 1997 .
評分標準
| 項目 | 百分比 |
| 作業 | 30% |
| 期中考 | 30% |
| 期末考 | 40% |
本課程行事曆提供課程進度與考試資訊參考。
| 章節內容 |
| Review of differentiation and integration techniques |
| Calculus of several variables, partial differentiation |
| Line integrals and multiple integrals |
| Vector analysis |
| Ordinary differential equations |
| Partial differential equations |
| Determinants and matrices |
| Probability and statistics |