# Syllabus 2018

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## Course Title : Applied Mathematics for Electrical Engineering

Code | 10C601 |
---|---|

Course Year | Master Course |

Term | 1st term |

Class day & Period | |

Location | |

Credits | 2 |

Restriction | No Restriction |

Lecture Form(s) | Lecture |

Language | |

Instructor | S. Doi & T. Hikihara |

### Course Description

In the class, fundamental mathematics is lectured for electrical engineering, electronics, system engineering, and material science. In particular, system theory, nonlinear dynamics, and particle dynamics in force field can be discussed with mathematical clear image.

### Grading

Students are requested to reply to report assignments. The grading is based on the evaluation of the reports.

### Course Goals

Professors expect students to model their system and analyze the models theoretically. Students will be requested to understand their system in principle mechanics and control them based on system theory.

### Course Topics

Theme | Class number of times | Description |
---|---|---|

Introduction 1 | 1 | Several examples of linear operators encountered in electrical engineering, e.g. in quantum mechanics are explained. Then, Linear vector space is reviewed and linear dynamical system is introduced. |

Fundamentals of linear vector space | 2-4 | Direct sum decomposition, projection operator, and the structure of vector spaces such as Jordan normal form are explained. |

Linear dynamical system | 3-5 | On the basis of the knowledge of the vector space, linear dynamical systems theory is explained as a simple application of vector spaces. |

Introduction 2 | 1 | The introduction to nonlinear dynamics will be explained based on oscillation theory. |

Hamiltonian mechanics | 1-3 | Hamiltonian mechanics is lectured on linear symplectic space. |

Manifold and vector field | 2-4 | Manifold is discussed in nonlinear system with relation to vector filed analysis. |

### Textbook

### Textbook(supplemental)

S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag.

### Prerequisite(s)

Linear algebra

### Independent Study Outside of Class

### Web Sites

https://www.t.kyoto-u.ac.jp/lecturenotes/gse/kueeng/10C601/syllabus

### Additional Information

Appropriate references will be shown in classes.