Applied Mathematics
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.
Textbook：Physical Chemistry 3rd edition, Mortimer, 2008.
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| Instructor(s) | Department of Applied Chemistry Prof. Chao-Yuan Zhu |
|---|---|
| Course Credits | 3 Credits |
| Academic Year | 101 Academic Year |
| Level | Second year university student |
| Prior Knowledge | Chemistry I, Chemistry II, Calculus |
| Related Resources | Course Video Course Syllabus Course Calendar |
| Week | Course Content | Course Video |
|---|---|---|
| Week 01 | I. Review of differentiation and integration I-1. Introduction I-2. Review of differential calculus I-3. Review of integral calculus I-4. Graph | Watch Online |
| Week 02 | II. Calculus of several variables, partial differentiation II-1. Partial derivatives II-2. Total differential II-3. Application to physical chemistry I | Watch Online |
| Week 03 | II. Calculus of several variables, partial differentiation II-4. Cycle rule II-5. Application of derivatives II-6. van Der Waals equation of state | Watch Online |
| Week 04 | 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 | Watch Online |
| Week 05 | 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 | Watch Online |
| Week 06 | IV. Infinite series IV-1. Talyor series IV-2. Convergence and its region IV-3. Applied to Physical Chemistry II | Watch Online |
| Week 07 | 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 | Watch Online |
| Week 08 | 作業討論 Fourier series Fourier transforms | Watch Online |
| Week 10 | V. Ordinary differential equations (1/4) V-1. Introduction V-2. The first-order differential equations V-3. The second-order differential equations | Watch Online |
| Week 11 | V. Ordinary differential equations (2/4) V-4. Differential equations with total differential | Watch Online |
| Week 12 | V. Ordinary differential equations (3/4) V-5. Special functions for the second-order DE、Quantum harmonic oscillator、Quantum hydrogen atom | Watch Online |
| Week 13 | V. Ordinary differential equations (4/4) V-5. Special functions for the second-order DE、Quantum harmonic oscillator、Quantum hydrogen atom | Watch Online |
| Week 14 | VI. Partial differential equations VI-1. Introduction VI-2. The classical wave VII. Determinants and matrices (1/4) VII-1 Introduction | Watch Online |
| Week 15 | VII. Determinants and matrices (2/4) VII-2. Determinant algebra VII-3. Properties of determinant VII-4. Matrix algebra | Watch Online |
| Week 16 | VII. Determinants and matrices (3/4) VII-5. Singular matrix VII-6. Characteristic equation of a matrix VII-7. Symmetry matrix | Watch Online |
| Week 17 | VII. Determinants and matrices (4/4) VII-8. Application to physical chemistry II | Watch Online |
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 |