授業の主題
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Basic programming techniques necessary to implement programs dealing with numerical computations for solving partial differential equations such as heat and wave equations.
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授業の目標
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The goal of this class is to gain a solid programming foundation that perform numerical computations and analyze data. It should allow you to continue studying more advanced programming techniques required for research work in numerical analysis. The hope is that you will be able to implement various algorithms in numerical mathematics.
The programming techniques we will learn are general and apply to many programming languages, but in this course we will be using Fortran.
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学生の学修目標
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After successfully passing both parts 1a and 1b, you will
- become familiar with the basic ways to calculate differential equations.
- learn how to implement basic algorithms loop and branch, etc.;
- know how to write and read programs in Fortran and how to debug them.
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授業概要
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Tentative schedule
1a
1. Programming and numerical computation
2. Loop control
3. Basics in ordinary differential equations(ODEs) by Euler method
4. ODE system in first order
5. Second order ODE (1) Monkey Hunting
6. Second order ODE (2) RLC-circuit
7. Newton’s Method and cubic equation
8. Subroutines and structured programming, final report
1b
1. Heat equation (1) introduction to the heat equation
2. Heat equation (2) explicit method and instability
3. Heat equation (3) various boundary conditions
4. Wave equation (1) introduction to the wave equation
5. Wave equation (2) initial and boundary value problem
6. Wave equation (3) various boundary conditions
7. Energy conservation law for the wave equation
8. Extra topics, final report
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評価方法と割合
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評価方法
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Grade will be decided holistically as below, based on the following terms/rates.
「Ｓ（Academic achievement 90%～100%）」,「Ａ（80% or more, less than90%）」,
「Ｂ（70% or more, less than80％）」, and「Ｃ（60% or more, less than70%）」 are indicators of passing,
「不可（less than 60％）」is an indicator of failure.（Standard rating method）
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評価の割合
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Attendance to at least two-thirds of classes is required. This may be determined by a login log if lectures are given online/on-demand.
- 100% Reports
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授業時間外の学修に関する指示
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予習に関する指示
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Preparation for each lecture (if any) will be discussed during the previous lecture. It is expected that students review the content of the previous lectures and can apply it during practical exercises that are part of each lecture.
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復習に関する指示
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The students are expected to solve the exercises given in each lecture. On average, students should expect to need around 3 hours/week of self-study.
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教科書・参考書
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教科書・参考書補足
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Reference texts will be discussed during lectures.
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オフィスアワー等（学生からの質問への対応方法等）
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There is no fixed office hour. Please contact me or one of the TAs via Acanthus portal for simple questions or to arrange a meeting.
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履修条件
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The students are expected to have passed 計算科学[Computational Science] course.
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カリキュラムの中の位置づけ
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The series of 4 courses 数値解析序論[Introduction to Numerical Analysis] 1a, 1b, 2a, 2b is designed to prepare the students to successfully participate in later applied mathematics courses that require implementation of numerical algorithms on a computer, as well as their work on a research project.
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