The subject of this course is Fourier analysis. In particular, we learn a method to solve differential equations by using Fourier series. First, we learn the heat equation, the wave equation and the Laplace equation together with their basic properties as typical examples of differential equations. Then, we learn sequences of functions and series of functions as the preparation for the learning of Fourier series. Finally, we learn Fourier series and its basic properties. This course will be succeeded by [Applied Mathematics for Engineers II b] in the fourth quarter.
Fourier analysis is an absolutely essential mathematical basis of science and engineering. In this course, we learn the basic theory of Fourier analysis and a way to use it in an efficient manner.
・Students are expected to understand basic properties of the heat equation, the wave equation and the Laplace equation.
・Students are expected to be able to calculate Fourier series of basic functions.
・Students are expected to be familiar with convergence conditions of Fourier series.
the heat equation, the wave equation, the Laplace equation, series of functions, Fourier series
✔ 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 | the heat equation and its fundamental properties | Details will be announced during each lecture. |
Class 2 | the wave equation and its fundamental properties | Details will be announced during each lecture. |
Class 3 | the Laplace equation and its fundamental properties | Details will be announced during each lecture. |
Class 4 | sequences of functions and series of functions | Details will be announced during each lecture. |
Class 5 | Fourier series | Details will be announced during each lecture. |
Class 6 | properties of Fourier series | Details will be announced during each lecture. |
Class 7 | convergence of Fourier series | 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.
This is the prerequisite course to take "Applied Mathematics for Engineers Iib".
Students are expected to have completed [Calculus I / Recitation], [Calculus II] and [Calculus Recitation II].