The methods of numerical analysis and numerical experiments are major pillars in Earth and planetary sciences, ranging from large-scale numerical calculation methods for various processes on earth and in space to numerical computations for analysis. In this course, the instructor will give lectures about basic usage of programing language (Fortran90/95), and exercises about the fundamentals of numerical calculations – matrix computations, solutions of non-linear equations and ordinary differential equations, numerical integration, solutions of partial differential equations, and the like. Students will also learn to use UNIX at the basic level and create graphs. In addition, students themselves work on numerical calculations for advanced problems applied to actual problems with earth and planetary sciences, from problem setting, development of a calculation method, execution, to the physical interpretation. They will make a presentation on their own study toward the end of the exercises. One class session consists of lectures and exercises for two periods each.
The goal of this course is to acquire the ability to make basic numerical calculations to carry out numerical analysis and numerical experiments necessary for the earth and planetary science research. Specifically, students will be given lectures and exercises about basic UNIX, programing languages and numerical calculation methods. In addition, students are expected to acquire the ability to apply numerical calculations to various processes on earth and in space and to make a physical interpretation on the calculation results.
numerical calculation methods and exercises
|✔ Specialist skills||Intercultural skills||Communication skills||✔ Critical thinking skills||✔ Practical and/or problem-solving skills|
Numerical calculation methods in the first half of the course and exercises in the second half
|Course schedule||Required learning|
|Class 1||the basics of UNIX and programing||the basics of UNIX and programing|
|Class 2||the basics 1 of Fortran (conditional branching)||the basics 1 of Fortran (conditional branching)|
|Class 3||the basics 2 of Fortran (loop)||the basics 2 of Fortran (loop)|
|Class 4||the basics 3 of Fortran (array)||the basics 3 of Fortran (array)|
|Class 5||how to plot figures||how to plot figures|
|Class 6||nonlinear equation||nonlinear equation|
|Class 7||numerical differentiation and integration, and their precision||numerical differentiation and integration, and their precision|
|Class 8||system of linear equations and matrix||system of linear equations and matrix|
|Class 9||ordinary differential equation, Euler method and Runge-Kutta method||ordinary differential equation, Euler method and Runge-Kutta method (No.1)|
|Class 10||ordinary differential equation, Euler method and Runge-Kutta method 2||ordinary differential equation, Euler method and Runge-Kutta method (No.2)|
|Class 11||data analysis 1 (the basics of Python)||set the research problem|
|Class 12||perform calculations 1||perform calculations 1|
|Class 13||perform calculations 2||perform calculations 2|
|Class 14||analysis of the results||analysis of the results|
To enhance effective learning, students are encouraged to spend a certain length of time outside of class on preparation and review (including for assignments), as specified by the Tokyo Institute of Technology Rules on Undergraduate Learning (東京工業大学学修規程) and the Tokyo Institute of Technology Rules on Graduate Learning (東京工業大学大学院学修規程), for each class.
They should do so by referring to textbooks and other course material.
announced during the lectures
report and presentation of exercises