2018 Applied Numerical Mathematics

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Academic unit or major
Undergraduate major in Mechanical Engineering
Hanamura Katsunori  Okada Masafumi 
Course component(s)
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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.


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

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
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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 Aquire optimizatioin algorithm
Class 6 Least square method Understand least square method
Class 7 Numerical solution of differential equations Aqurie numerical solution of differential equation
Class 8 Explicit and implicit methods for differential equations Understand explicit and implicit methods


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

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