# 応用数理学（開講なし）

### 科目基礎情報

学校 開講年度 東京工業高等専門学校 令和03年度 (2021年度) 応用数理学（開講なし） 0018 専門 / 選択 講義 学修単位: 2 物質工学専攻 専1 前期 2 「数値解析入門」（山本哲朗、サイエンス社）、「数値計算の常識」（伊理正夫・藤野和建、共立出版）

### 目的・到達目標

Understand how to deal with mathematical problems using numerical methods from analytical viewpoint.
Understand algorithms and procedures correctly and implement them on computers.

### ルーブリック

理想的な到達レベルの目安 標準的な到達レベルの目安 未到達レベルの目安 Understand each algorithmn and the mathmatical theory which is the base of it Understand each algorithmn Don't understand algorithmns Impliment each algorithmn as a program and make sure the theory Impliment each algorithmn as a program Don't impliment algorithmns Know words and expressions to discribe these theories Know important expressions to discribe these theories Don't know words and expressions to discribe these theories

JABEE (c)

### 教育方法等

This course is designed to give an overview of the design, analysis and implementation of the several fundamental numerical method
which are used to solve practical engineering problems.

Applied Mathematics consists of 10 lectures, that emphasis the mathematics used to design numerical methods, and to analyse their properties. and 5 experiments with implementing algorithms in Computer Lab.

Prerequisite: Calculus Multivariable Calculus, Linear Algebra, Ordinary Differential Equation, Programming

### 授業の属性・履修上の区分

 アクティブラーニング ICT 利用 遠隔授業対応 実務経験のある教員による授業

### 授業計画

1stQ
1週 Guidance and Introduction
2週 Error Understand why errors are occurred in computer
3週 Linear Equations System and Matrices- Gaussian Elimination Understand the algorithm
4週 Linear Equations System and Matrices- Iterative Method 1 Understand the algorithm
5週 Linear Equations System and Matrices - Iterative Method 2 Understand the algorithm
6週 Exercise in Computer Lab. Impliment the algorithmn
7週 Non-linear Equations - Bisection Method, Secant Method Understand the algorithm
8週 Non-linear Equations- Quadrature Mensuration by parts, Newton Method Understand the algorithm
2ndQ
9週 Exercise in Computer Lab. Impliment the algorithmn
10週 Numerical Integration -Trapezium Rule & Sympson's Rule Understand the algorithm
11週 Numerical Integration - Monte Carlo Method Understand the algorithm
12週 Exercise in Computer Lab. Impliment the algorithmn
13週 Ordinary Differential Equation -Euler Method Understand the algorithm
14週 Ordinary Differential Equation- Runge-Kutta Method Understand the algorithm
15週 Exercise in Computer Lab. Impliment the algorithmn
16週 Final Examination

### 評価割合

試験 発表 相互評価 態度 ポートフォリオ その他 合計 0 0 0 0 0 100 100 0 0 0 0 0 100 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0