### 2017　Applied Theory on Differential Equations

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Undergraduate major in Mathematical and Computing Science
Instructor(s)
Miura Hideyuki  Nishibata Shinya
Course component(s)
Lecture
Day/Period(Room No.)
Mon5-6(W834)  Thr5-6(W834)
Group
-
Course number
MCS.T311
Credits
2
2017
Offered quarter
2Q
Syllabus updated
2017/3/17
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

The course teaches the fundamentals of mathematical analysis of partial differential equations modeling various phenomena.
Students learn the derivation of the partial differential equations and the method of the Fourier series.
Students will be able to apply them to various problems.

### Student learning outcomes

By completing this course, students will be able to;
1) derive the partial differential equations as the models of various phenomena.
2) understand the theory of Fourier series and solve the partial differential equations.
3) understand properties of the solutions by using the character of each equations.

### Keywords

partial differential equations, heat equation, wave equation, Laplace equation, Fourier series

### Competencies that will be developed

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

### Class flow

The lecture is devoted to the fundamentals to the derivation and the resolution of partial differential equations. In order to cultivate
a better understanding, some exercises are given.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Some examples of partial differential equaitons Understand the contents in the lecture.
Class 2 Derivation of the heat equation Understand the contents in the lecture.
Class 3 Maximum principles and their applications Understand the contents in the lecture.
Class 4 Fourier’s method and separation of variables Understand the contents in the lecture.
Class 5 Theory of Fourier series Understand the contents in the lecture.
Class 6 Hilbert spaces and complete orthonormal system Understand the contents in the lecture.
Class 7 Completeness of Fourier series Understand the contents in the lecture.
Class 8 Solving heat equations via Fourier series Understand the contents in the lecture.
Class 9 Derivation of the wave equation Understand the contents in the lecture.
Class 10 Energy conservation law and its applications Understand the contents in the lecture.
Class 11 d'Alembert 's solution for the wave equation Understand the contents in the lecture.
Class 12 Solving the wave equation via Fourier series Understand the contents in the lecture.
Class 13 Derivation of the Laplace equation Understand the contents in the lecture.
Class 14 Solving the Laplace equation Understand the contents in the lecture.
Class 15 Mean value theorem and its applications Understand the contents in the lecture.

### Textbook(s)

Textbook specified by the instructor

Unspecified

### Assessment criteria and methods

Learning achievement is evaluated by a final exam and so on.

### Related courses

• LAS.M101 ： Calculus I / Recitation

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

No prerequisites. Students should understand the fundamentals of calculus. 