Eigen value decomposition and numerical solution of differential equations are widely used in not only mechanical engineering but also most of science and engineering research fields. Because of a benefit of innovation of technology, many generalized software and simulators are available, but it is required to understand operating principle of mathematics and physics.
This course focuses on mathematical principle for programming which contains applied linear algebra, optimization method and numerical solution of differential equations.
By the end of this course, students will be able to;
(a) Understand Eigen value and Eigen vector of a matrix,
(b) Calculate inverse/pseudo-inverse of a large scale matrix.
(c) Understand the solution of the least square and optimization.
(d) Learn numerical solution of differential equation and it stability.
(e) Learn programming skill applying the above methods.
This class aims at learning of 6 and 7 in learning objective.
Inverse problem, Eigen value decomposition, Singular value decomposition, Least square method, Differential equation
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
This course is organized by lecture and exercise.
Course schedule | Required learning | |
---|---|---|
Class 1 | Vector, Space, Matrix and Projection | Acquire a concept of n-dimensional space. Projection is represented by a matrix |
Class 2 | Positive and negative of matrix, null space | Understand positive/negative of matrix and null space |
Class 3 | Norm of vector and matrix (eigenvalue and power of matrix) | Understand norm, eigenvalue decomposition |
Class 4 | Solution of inverse problem (inverse matrix, singular value decomposition) | Understand inverse/pseudo-inverse matrix and singular value decomposition |
Class 5 | Optimization method and Least square method | Understand optimizatioin algorithm and least square method |
Class 6 | Numerical solution of differential equations | Aqurie numerical solution of differential equation |
Class 7 | Explicit and implicit methods for differential equations | Understand explicit and implicit methods |
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
None(Some handouts will be distributed)
Masatake Mori, 'numerical analysis', Kyoritsu Shuppan Co., Ltd.
Tetsuro Yamamoto, 'Introductory 'numerical analysis', Saiensu-sha Co., Ltd. Publishers
Exercise(30%) and final exam(70%)
Fundamentals of Numerical Analysis