到達目標
1. Can explain the reason why numerical calculations yield errors.
2. Can describe a solution method (algorithm) on basic math problems.
3. Can explain how to simulate different phenomena on a computer, starting from how to create a model.
ルーブリック
| Ideal Level | Standard Level | Unacceptable Level |
| Achievement 1 | Can explain the method so as to avoid major errors on numerical calculations | Can explain causes why major errors on numerical calculations occur. | Cannot explain the reasons why major errors on numerical calculations occur. |
| Achievement 2 | Can accurately explain a solution method (algorithm) for all specified problems. | Can explain an overview of the methods (algorithms) for finding solutions to some problems. | Cannot explain the method (algorithm) of finding solutions to problems. |
| Achievement 3 | Can program a method to find a solution (near real-time solution) for all specified problems | Can program a method to find solutions (near real-time solutions) for some problems. | Cannot program a method to find a solution to problems. |
学科の到達目標項目との関係
教育方法等
概要:
A simulation is the imitation of a phenomenon by reducing it into a model. The aim of this course is to conduct computer-based experiments on simple models of natural and social phenomena that are difficult to reproduce and observe, to identify the characteristics of the phenomenon and to deepen the understanding of the contents. In classes, we will introduce the basic concepts and the latest examples of modeling and simulation in the first half, and practice the methods to solve their own challenges by programming and explaining a simulator in the second half.
授業の進め方・方法:
Classes are conducted through lectures and exercises.
Lectures will be conducted through handouts.
In addition to what students learned in classes, they will perform individual activities on assignments of their choosing.
Exercises are supposed to build a system to help students in their own graduation research.
Students will be evaluated on assignment progress and the work produced during the exercises, and presentations.
注意点:
This course's content will amount to 90 hours of study in total. These hours include the learning time guaranteed in classes and the standard self-study time required for pre-study / review, and completing assignment reports.
As this course is built on the content of Data Structures and Algorithms, Computer Programming, and Probability and Statistics, it's recommended that students review these textbooks, materials, etc. as references during the classes.
Students who miss 1/3 or more of classes will not be eligible for a passing grade.
授業の属性・履修上の区分
授業計画
|
|
週 |
授業内容 |
週ごとの到達目標 |
| 後期 |
| 3rdQ |
| 1週 |
Introduction |
Understand the objectives and the grading method, etc. of the course.
|
| 2週 |
Algorithms, calculations and recurrence relations |
Understand time and space complexity of algorithms.
Can derive (time) complexity of some algorithms.
Can derive recurrence relations which give solutions of problems.
|
| 3週 |
Repetitive methods |
Can derive repetitive methods which give solutions of problems.
|
| 4週 |
Errors, loss of significance, data loss |
Can explain the cause of phenomena that occurs in numerical calculations, such as truncation errors, loss of significance, data loss
|
| 5週 |
Nonlinear equations |
Can explain the Newton method, the bisection method ,and false position method .
|
| 6週 |
Simultaneous equations 1 |
Can explain algorithms of Gaussian elimination and sweep out methods.
|
| 7週 |
Simultaneous equations 2 |
Can explain algorithms of Jacobi, Gauss-Seidel and SOR method.
|
| 8週 |
Exercise |
Exercise on the contents of classes in the first half of the semester.
|
| 4thQ |
| 9週 |
Eigenvalue |
Can explain algorithms of Jacobi and the power methods for obtaining eigenvalues of matrices.
|
| 10週 |
Interpolation of functions |
Can explain linear interpolation, Newton forward linear interpolation and lagrange linear interpolation.
|
| 11週 |
Method of least squares |
Can explain the method of least squares.
|
| 12週 |
Numerical differentials |
Can calculate first and second order numerical differentials with forward, central and backward formulas.
Can calculate first order numerical differential with laglange interpolation.
|
| 13週 |
Numerical integrals |
Can calculate numerical integrals with rectangle, trapezoidal and Simpson's rule.
|
| 14週 |
Initial value problem and Boundary value problem of ordinary differential equations |
Can explain algorithms of Euler, Heun's and Runge–Kutta method for the Initial value problem.
Can explain an algorithm of finite-dfference method for the boundary value problem.
|
| 15週 |
Review |
Review the content of classes in the second half of the semester.
|
| 16週 |
Final exam |
|
モデルコアカリキュラムの学習内容と到達目標
| 分類 | 分野 | 学習内容 | 学習内容の到達目標 | 到達レベル | 授業週 |
| 基礎的能力 | 工学基礎 | 情報リテラシー | 情報リテラシー | 同一の問題に対し、それを解決できる複数のアルゴリズムが存在しうることを知っている。 | 4 | |
| 与えられた基本的な問題を解くための適切なアルゴリズムを構築することができる。 | 3 | |
| 任意のプログラミング言語を用いて、構築したアルゴリズムを実装できる。 | 3 | |
| 専門的能力 | 分野別の専門工学 | 情報系分野 | 情報数学・情報理論 | コンピュータ上での数値の表現方法が誤差に関係することを説明できる。 | 4 | |
| コンピュータ上で数値計算を行う際に発生する誤差の影響を説明できる。 | 4 | |
| コンピュータ向けの主要な数値計算アルゴリズムの概要や特徴を説明できる。 | 4 | |
| 分野横断的能力 | 汎用的技能 | 汎用的技能 | 汎用的技能 | 書籍、インターネット、アンケート等により必要な情報を適切に収集することができる。 | 3 | |
| どのような過程で結論を導いたか思考の過程を他者に説明できる。 | 3 | |
| 態度・志向性(人間力) | 態度・志向性 | 態度・志向性 | 目標の実現に向けて計画ができる。 | 3 | |
| 目標の実現に向けて自らを律して行動できる。 | 3 | |
評価割合
| Examination | Exercise | 合計 |
| 総合評価割合 | 80 | 20 | 100 |
| Basic Proficiency | 0 | 0 | 0 |
| Specialized Proficiency | 80 | 20 | 100 |
| Cross Area Proficiency | 0 | 0 | 0 |