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School of Environment and Society
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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Sekizawa Kazuyuki
- Class Format
- Lecture / Exercise (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Tue7-8(南4号館, 情報ネットワーク演習室, 第２演習室) Fri7-8(南4号館, 情報ネットワーク演習室, 第２演習室)
- Group
- -
- Course number
- PHY.L210
- Credits
- 2
- Academic year
- 2022
- Offered quarter
- 4Q
- Syllabus updated
- 2022/4/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This lecture provides basic knowledge and techniques to understand physical phenomena by numerically solving equations.
Modern recommended programming methods are explained.
Through practical programming experiences, basic techniques of numerically solving differential equations and data analysis are provided, which play one of the major roles in modern physics research.
Student learning outcomes
This course will provide opportunities to learn various computational techniques, which are equally important as experiments and theories.
Students will acquire knowledge and experience that can be applied to solve problems through practical training of programming.
Keywords
Programming languages, numerical integrations, numerical solutions of differential equations, data analysis, numerical simulations
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
1/3 of each class will be a lecture on basic concepts and required knowledge including explanations on important points. 2/3 of each class will be adopted to practical programming.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Preparing computation environment | Prepare computation environment on your PC or on TSUBAME. |
| Class 2 | Introduction to Unix and Fortran language | Understand basics of Unix. Write a simple Fortran program and check basic functions. |
| Class 3 | Introduction to the Finite Difference Method: 1D Diffusion Equation | Understand how to solve a differential equation with the finite difference method. |
| Class 4 | Finite Difference Methods and Numerical Accuracy I: 1D Advection Equation | Understand numerical accuracy and stability of various finite-difference schemes. |
| Class 5 | Finite Difference Methods and Numerical Accuracy II: 1D Advection Equation | Analyze accuracy and stability of various finite-difference schemes by numerically solving a 1D advection equation. |
| Class 6 | Introduction to Computational Fluid Dynamics I: 2D Vorticity Equation and Kármán vortex street | Learn basics of computational fluid dynamics (CFD). Understand the vorticity equation. |
| Class 7 | Introduction to Computational Fluid Dynamics II: 2D Vorticity Equation and Kármán vortex street | Generate Kármán vortex street by numerically solving a 2D vorticity equation. |
| Class 8 | Computational Techniques for a Time-Independent Schrödinger Equation I: Numerov's Method | Understand the Schrödinger equation for electronic wave functions in a hydrogen atom and Numerov's method. |
| Class 9 | Computational Techniques for a Time-Independent Schrödinger Equation II: Numerov's Method | Analyze electronic wave functions in a hydrogen atom by numerically solving a radial Schrödinger equation using Numerov's method. |
| Class 10 | Computational Techniques for a Time-Independent Schrödinger Equation III: Matrix Diagonalization | Understand the matrix representation of a Schrödinger equation. |
| Class 11 | Computational Techniques for a Time-Independent Schrödinger Equation IV: Matrix Diagonalization | Analyze eigenvalues and eigenvectors of a 1D Schrödinger equation by numerically diagonalizing a Hamiltonian matrix using LAPACK. |
| Class 12 | Computational Techniques for a Time-Dependent Schrödinger Equation I: Taylor Expansion Method | Understand the Taylor expansion method for a time-dependent Schrödinger equation. |
| Class 13 | Computational Techniques for a Time-Dependent Schrödinger Equation II: Taylor Expansion Method | Analyze time evolution of a wave packet scattered by a potential by numerically solving a 1D time-dependent Schrödinger equation using the Taylor expansion method. |
| Class 14 | Introduction to Quantum Hydrodynamics I: Time-Dependent Gross-Pitaevskii Equation | Understand basic properties of superfluid and the principle of quantized vortices. |
| Class 15 | Introduction to Quantum Hydrodynamics II: Time-Dependent Gross-Pitaevskii Equation | Generate Kármán vortex street by numerically solving 2D time-dependent Gross-Pitaevskii equation. |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class. They should do so by referring to textbooks and other course materials.
Textbook(s)
Lecture notes distributed by the instructor.
Reference books, course materials, etc.
Not specified.
Assessment criteria and methods
By monthly report.
Related courses
- PHY.Q207 ： Introduction to Quantum Mechanics
- LAS.M106 ： Linear Algebra II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
No prerequisites.
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
Kazuyuki Sekizawa
sekizawa at phys.titech.ac.jp
2463
Office hours
Contact by e-mail in advance.
