## Applied Numerical MethodsBack JP / EN

Numbering Code Year/Term G-ENG05 5G001 LJ71G-ENG07 5G001 LJ77G-ENG06 5G001 LJ71 2021 ・ First semester 2 Lecture Japanese Mon.1 INOUE YASUHIRO (Graduate School of Engineering Professor)TSUCHIYA TOSHIYUKI (Graduate School of Engineering Professor) 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. Understandings of mathematical theories and programing implementations of the numerical methods. 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 Home works (four home works will be assigned) and examination. Basic mathematics for undergraduates Basic macro programing Problems are based on macro on Microsoft Excel or LibreOffice and Visual C++. Lecture note will be distributed through the course website. Matrix Computations, Golub, G. H., Loan, C. F. V., (John Hopkins University Press), ISBN:978- 1421407944Difference Methods for Initial-Value Problems, Second Edition, R.D.Richtmyer and K.W.Morton, (John Wiley & Sons), ISBN:978-0470720400 Lecture notes, home works, and other info will be distributed through PandA: https://panda.ecs.kyoto-u.ac.jp