2024 Faculty Courses School of Computing Undergraduate major in Computer Science
Numerical Analysis
- Academic unit or major
- Undergraduate major in Computer Science
- Instructor(s)
- Masahiro Takinoue
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Tue / 3-4 Fri
- Class
- -
- Course Code
- CSC.T362
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Numerical calculation is the basis for numerically analyzing and simulating the real world using computers. In this class, students learn how to make mathematical models of the real world using differential equations, and the essential knowledge of numerical calculation and some famous methods and algorithms in order to apply them to real-world analysis.
Course description and aims
・Learn how to model the real world and how to numerically analyze the model using computers
・Learn analytical and numerical solutions of differential equations
・Learn the important topics when you perform numerical analysis (e.g., errors, loss of digits)
・Learn numerical solution of simultaneous linear equations
・Learn numerical solutions of nonlinear equations
・Learn numerical differentiation and numerical integral, and apply them to the numerical solution of ordinary/partial differential equations
・Learn interpolation and data fitting based on the least-square method
Keywords
Ordinary differential equations, Partial differential equations, Numerical integral, Nonlinear equations, Simultaneous linear equations, Interpolation, Least-square method, Monte-Carlo method, Errors, Dynamical systems, System modeling
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The class style is basically the lecture style. Students are required to promote a better understanding of the lectures by performing report assignments.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Introduction to numerical calculation methods (1) | Modeling of the real world and numerical analysis, Units and dimensions, Expression of the real number (floating number), Types of errors |
| Class 2 | Introduction to numerical calculation methods (2) | Analysis of errors, Loss of significant digits, Amount of calculation, Step size， Numerical analysis libraries, and applications |
| Class 3 | Numerical differentiation and numerical integral | Difference, Trapezoidal rule, Simpson's rule |
| Class 4 | Numerical solution of nonlinear equations | Bisection method, Newton method |
| Class 5 | Analytical solution of ordinary differential equations, Numerical solution of ordinary differential equations (1) | Analytical solution of ordinary differential equations (non-computational solution), Initial value problem of ordinary differential equations, Explicit methods, Euler method, Runge-Kutta method |
| Class 6 | Numerical solution of ordinary differential equations (2) | Stiff equations, Implicit methods, Boundary value problem of ordinary differential equations |
| Class 7 | Numerical solution of ordinary differential equations (3) | Second-order ordinary differential equations, Modeling of dynamical systems, Examples of dynamical systems (damped oscillation, van der Pol equation) |
| Class 8 | Numerical solution of simultaneous linear equations (1) | Direct methods: Gaussian elimination, LU decomposition |
| Class 9 | Numerical solution of simultaneous linear equations (2) | Iteration methods: Jacobian iteration method, Gauss-Seidel method, Successive over-relaxation (SOR) method |
| Class 10 | Estimation methods of curves (1) | Interpolation and approximation of functions, Lagrange interpolation, Spline interpolation |
| Class 11 | Estimation methods of curves (2) | Least-square method, data fitting |
| Class 12 | Analytical and numerical solution of partial differential equations (1) | Basics of partial differential equations, Analytical solution of partial differential equations (non-computational solution) |
| Class 13 | Analytical and numerical solution of partial differential equations (2) | Finite-difference method, Gauss-Seidel method, Successive over-relaxation (SOR) method |
| Class 14 | Introduction to Monte Carlo method and statistical analysis of experimental data | Numerical calculation using stochastic processes, Statistical analysis of experimental data |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterward (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None
Reference books, course materials, etc.
Lecture slides (Japanese) will be uploaded on T2SCHOLA.
Reference books: 数値計算（高橋大輔，岩波書店），数値計算の常識（伊理正夫・藤野和建，共立出版）， Numerical Recipes in C (W. H. Press et al., Cambridge University Press).
Evaluation methods and criteria
It will be explained in the first class.
Related courses
- CSC.T351 ： System Analysis
- CSC.T373 ： Dynamical Systems
- CSC.T374 ： Control Systems
- CSC.T342 ： Problem Solving and Decision Making
- CSC.T353 ： Biological Data Analysis
- ART.T456 ： Non-linear Dynamical Systems
- ART.T452 ： Modeling of Continuous Systems
- ART.T455 ： Modeling of Discrete Systems
- CSC.T365 ： Time Series Modeling
- ART.T468 ： Mathematical Modeling
Prerequisites
None
Other
None