Applied Numerical Methods

Numbering Code G-ENG05 5G001 LJ71
G-ENG07 5G001 LJ77
G-ENG06 5G001 LJ71
Year/Term 2021 ・ First semester
Number of Credits 2 Course Type Lecture
Target Year Target Student
Language Japanese Day/Period Mon.1
Instructor name INOUE YASUHIRO (Graduate School of Engineering Professor)
TSUCHIYA TOSHIYUKI (Graduate School of Engineering Professor)
Outline and Purpose of the Course  Numerical techniques, such as the finite element method and numerical control method, are indispensable in mechanical engineering. In this lecture, basics of numerical techniques which are required to study advanced methods for graduated students will be explained. The lecture will cover the linear system solution (Ax=b), eigenvalue analysis, interpolation approximation method, solutions of ordinary differential equation and partial differential equation. The programing exercise is included in this lecture.
Course Goals Understandings of mathematical theories and programing implementations of the numerical methods.
Schedule and Contents 1. Introduction Introduction of this class
- Numerical representations and errorsMacro programing using spread sheet applications
2. Linear system
- MatrixNormsSingular value decomposition
3. Linear simultaneous equation(1)
- Solution of simultaneous linear equationsdirect method
4. Linear simultaneous equation(2)
- iteration method
5. Eigenvalue analysis(1)
- Properties of eigenvalue, Eigenvalue calculation for symmetrical matrix
6. Eigenvalue analysis(2)
- Eigenvalue calculation for asymmetrical matrix
7. Interpolation(1)
- Polynomial, Hermite interpolation
8. Interpolation(2)
- Spline interpolation, interpolation errors
9. Numerical integral(1)
- Trapezoidal rule, midpoint rule, Simpson's rule, Newton-Coats rule
10.Numerical integral(2)
- Complex integration rule, Romberg integral
11.Ordinary differential equation
- Solutions (explicit and implicit), initial value problems and boundary values problem
12.Partial differential equation(1)
- Partial differential notation, convergence conditions, von Neumann stability analysis
13.Partial differential equation(2)
- Diffusion equation, wave equation
14.Partial differential equation(3)
- Poisson equation, Laplace equation
15. Feedback for homework and examination
Evaluation Methods and Policy Home works (four home works will be assigned) and examination.
Course Requirements Basic mathematics for undergraduates
Basic macro programing
Study outside of Class (preparation and review) Problems are based on macro on Microsoft Excel or LibreOffice and Visual C++.
Textbooks Textbooks/References Lecture note will be distributed through the course website.
References, etc. Matrix Computations, Golub, G. H., Loan, C. F. V., (John Hopkins University Press), ISBN:978- 1421407944
Difference Methods for Initial-Value Problems, Second Edition, R.D.Richtmyer and K.W.Morton, (John Wiley & Sons), ISBN:978-0470720400
Related URL Lecture notes, home works, and other info will be distributed through PandA: https://panda.ecs.kyoto-u.ac.jp
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