### 2020　Applied Numerical Mathematics

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Instructor(s)
Hanamura Katsunori
Course component(s)
Lecture / Exercise
Mode of instruction
ZOOM
Day/Period(Room No.)
Mon1-2(I121)
Group
-
Course number
MEC.B332
Credits
1
2020
Offered quarter
3Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

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.

### Student learning outcomes

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.

### Keywords

Inverse problem, Eigen value decomposition, Singular value decomposition, Least square method, Differential equation

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

This course is organized by lecture and exercise.

### Course schedule/Required learning

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

### Out-of-Class Study Time (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 afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

### Textbook(s)

None(Some handouts will be distributed)

### Reference books, course materials, etc.

Masatake Mori, 'numerical analysis', Kyoritsu Shuppan Co., Ltd.
Tetsuro Yamamoto, 'Introductory 'numerical analysis', Saiensu-sha Co., Ltd. Publishers

### Assessment criteria and methods

Exercise(30%) and final exam(70%)

### Related courses

• MEC.B232 ： Fundamentals of Numerical Analysis

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Fundamentals of Numerical Analysis 