Hiroshima University Syllabus

Back to syllabus main page
Japanese
Academic Year 2024Year School/Graduate School School of Informatics and Data Science
Lecture Code KA119001 Subject Classification Specialized Education
Subject Name システム最適化
Subject Name
(Katakana)
システムサイテキカ
Subject Name in
English
System Optimization
Instructor MUKAIDANI HIROAKI
Instructor
(Katakana)
ムカイダニ ヒロアキ
Campus Higashi-Hiroshima Semester/Term 2nd-Year,  Second Semester,  3Term
Days, Periods, and Classrooms (3T) Mon9-10,Weds9-10:ENG 107
Lesson Style Lecture Lesson Style
(More Details)
 
Lecture 
Credits 2.0 Class Hours/Week   Language of Instruction B : Japanese/English
Course Level 2 : Undergraduate Low-Intermediate
Course Area(Area) 25 : Science and Technology
Course Area(Discipline) 01 : Mathematics/Statistics
Eligible Students
Keywords Optimization 
Special Subject for Teacher Education   Special Subject  
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
 
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students)
Computer Science Program
(Comprehensive Abilities)
・D2. Ability to derive optimal system solutions based on abundant cutting-edge information technologies for cross-sectoral issues in a diversified and complicated information society.

Data Science Program
(Abilities and Skills)
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.

Intelligence Science Program
(Comprehensive Abilities)
・D3. Ability to grasp complexly intertwined social needs and issues from a bird's-eye view and solve issues with a multifaceted perspective and analytical ability based on a wide range of knowledge in intelligent science. 
Class Objectives
/Class Outline
In this lecture, optimization is discussed to analyze mathematical sciences. By using these results, various operation which should be optimized is decided. 
Class Schedule Lesson 1: What is an optimization problem?
Lesson 2: Unconstrained nonlinear optimization 1 (gradient vector and Hessian matrix)
Lesson 3: Unconstrained nonlinear optimization 2 (applied problems)
Lesson 4: Constrained nonlinear optimization (Lagrange multiplier method)
Lesson 5: Nonlinear optimization with inequality constraints (KKT conditions)
Lesson 6: Simultaneous Differential Equations
Lesson 7: Transition matrix
Lesson 8: Power series solutions
Lesson 9: Stability Theory
Lesson 10: Basics of stability
Lesson 11: Stability Theory of Physical Systems
Lesson 12: Discretization of differential equations
Lesson 13: Numerical solution of simultaneous differential equations
Lesson 14: Multidimensional Laplace Transform
Lesson 15: Partial Differential Equations Theory 
Text/Reference
Books,etc.
新刊「基礎履修  応用数学」向谷・下村・相澤
ISBN978−4−563−01172−7 
PC or AV used in
Class,etc.
 
(More Details) blackboard 
Learning techniques to be incorporated  
Suggestions on
Preparation and
Review
For each lecture, the review should be needed by reading the text book. Furthermore, the practical calculation and simulation would be helpful.

Lesson 1: Understand the meaning and purpose of optimization through specific examples of various optimization problems.
Lesson 2: Be able to calculate gradient vectors, Hessian matrices, etc., and derive optimization conditions.
Lesson 3: Recognize the importance of optimization by solving applied problems (least squares method and principal analysis).
Lesson 4: Understand the Lagrangian multiplier method and be able to derive optimization conditions.
Lesson 5: Inequality constraints can be processed using KKT.
Lesson 6: Being able to describe and solve higher-order differential equations using simultaneous differential equations.
Lesson 7: Using a transition matrix, you can display an exponential matrix.
Lesson 8: Using power series solutions, you will be able to analyze differential equations that cannot be expressed using analytical solutions.
Lesson 9: Start with the definition of stability theory and be aware of its application in the real world.
Lesson 10: Understand the importance of stability by cultivating the basics of stability in actual dynamic systems.
Lesson 11: Through practice problems, students should be able to understand various physical phenomena and discuss the theory of stability of physical systems.
Lesson 12: Confirm that differential equations can be solved numerically by discretizing them.
Lesson 13: Understand that higher-order differential equations can be found by numerically solving simultaneous differential equations using Euler's method and Runge-Kutta method.
Lesson 14: Solving simultaneous differential equations using multidimensional Laplace transform.
Lesson 15: Be able to solve simple partial differential equations using the basics of differential equations.
 
Requirements Calculus and Linear Algebra are mandatory. 
Grading Method Mini-tests (10%) and Final exam (90%) 
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
Message  
Other   
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. 
Back to syllabus main page