Based on [Applied Mathematics for Engineers II a] in the third quarter, this course focuses on Fourier analysis and its applications. In particular, we expalin a method to solve differential equations by using Fourier series. First, we explain the classification of differential equations. Then we explain general strategies to solve differential equations by using Fourier series. Finally, based on such strategy, we explain the method to solve the heat equation, the wave equation and other equations by using Fourier sereis.
Fourier analysis is an absolutely essential mathematical basis of science and engineering. The aim of this lecture is to explain the basic theory and practical way to use of Fourier analysis by an efficient way.
・Students are expected to understand general strategies to solve differential equations by using Fourier series.
・Students are expected to be able to solve the heat equation by using Fourier series.
・Students are expected to be able to solve the wave equation by using Fourier series.
・Students are expected to be able to solve the Dirichlet problem for the unit circle by using Fourier series.
Fourier series, partial differential equations, the heat equation, the wave equation
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course mixed with recitation.
Course schedule | Required learning | |
---|---|---|
Class 1 | classification of partial differential equations | Details will be announced during each lecture. |
Class 2 | strategies to solve partial differential equations by Fourier series | Details will be announced during each lecture. |
Class 3 | Fourier series and the heat equation | Details will be announced during each lecture. |
Class 4 | variants of the heat equation | Details will be announced during each lecture. |
Class 5 | Fourier series and the wave equation | Details will be announced during each lecture. |
Class 6 | variants of the wave equation | Details will be announced during each lecture. |
Class 7 | the Dirichlet problem for the unit disk | Details will be announced during each lecture. |
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.
G. Sunouchi, Fourier analysis and applications (Japanese), Saiensu-sha,1995
None in particular
Based on overall evaluation of the results for quizzes, report and final examination. Details will be announced during a lecture.
The prerequisite to take this course is that you have acquired the credits of "Applied Mathematics for Engineers Iia".
Without having acquired the credits of the above course, the credits of this course will not be counted as the necessary number of credits for graduation.
Students are expected to have completed [Calculus I / Recitation], [Calculus II] and [Calculus Recitation II].