Introduction to Numerical Analysis 1
数値解析序論１

Lecture notes (レクチャーノート)

Syllabus

Part a

• Lecture a1: Fortran review; programming and numerical computation
• Lecture a2: Loop control (do loops)
  • Solution Lecture a2
• Lecture a3: The Euler method for ODEs
  • Solution Lecture a3
• Lecture a4: ODE system and other methods, Report 1
  • Solution Lecture a4
• Lecture a5: Second order ODE: pendulum
  • Solution Lecture a5
• Lecture a6: System of ODEs: Lotka–Volterra system
  • Solution Lecture a6
• Lecture a7: Newton’s method and the cubic equation
  • Solution Lecture a7
• Lecture a8: Newton’s method and backward Euler method, Report 2 (Final report)

Part b

• Lecture b1: Introduction to the heat equation
• Lecture b2: Heat equation: Explicit finite difference method
• Lecture b3: Heat equation: Instability and various boundary conditions, Report 1
  • Solution Lecture b3
• Lecture b4: Introduction to the wave equation
• Lecture b5: Wave equation: initial and boundary value problem
• Lecture b6: Wave equation: Various boundary conditions
• Lecture b7: Energy conservation for the wave equation. Report 2
• Lecture b8: Extra topics: allocatable arrays

Class information

• Evaluation 評価方法: based on reports (probably 2 large reports each quarter and some small ones). You need at least 60% points to get C. Please submit the reports through LMS on the Acanthus portal.

  Academic integrity: Submit only your own code or code that I provide. Do not share the solutions with other students! If I notice copying, I automatically give 0 points and might take other steps.

• Self study: about 3 hours/week is expected

• Contact:

  • email npozar@se.kanazawa-u.ac.jp
  • office #228 (自然科学５号館)

Goals

Programming is very important in modern science to perform computations, modeling, data analysis etc. Our goal is to develop basic programming skills for implementing important numerical methods for solving differential equations.

The best way to learn programming is to write programs yourself. To build larger programs, you need skills to implement simple algorithms. Please try to solve as many of the provided exercises as possible.

We will use the Fortran programming language. It is one of the oldest programming languages and it is still used to some extend in scientific computing. The skills that you learn should be applicable to other popular programming languages like C/C++ and Python.

Fortran reference (参考書)

Here are a few OK references for Fortran and programming in Fortran.

• Fortran cheatsheet: my short Fortran reference

• Fortran 入門: extensive online reference (in Japanese)

• Fortranによるプログラミング超入門: In Japanese

• Introduction to Programming with Fortran: textbook from Springer available for free download from Kanazawa University network

• Fotran 90/95 reference

• Fortran quirks: Surprising Fortran behavior I found.

Text editor

To write programs, you need a text editor.

• Emacs: Most of you are probably using this. Be careful not to submit files whose name ends with ~.

• Visual Studio Code: a simple free modern editor with sane key shortcuts. It is very popular these days for C/C++/Python/Javascript etc. programming. I recommend trying it out if you are not quite happy with Emacs.