2022　Applied Mathematics for Engineers Ila

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Academic unit or major
Undergraduate major in Mathematics
Instructor(s)
Takiguchi Takashi
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(H112)
Group
-
Course number
MTH.U213
Credits
1
2022
Offered quarter
3Q
Syllabus updated
2022/4/20
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

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.

Student learning outcomes

・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.

Keywords

the heat equation, the wave equation, the Laplace equation, series of functions, Fourier series

Competencies that will be developed

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

Class flow

Standard lecture course mixed with recitation.

Course schedule/Required learning

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.

Out-of-Class Study Time (Preparation and Review)

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.

Textbook(s)

G. Sunouchi, Fourier analysis and applications (Japanese), Saiensu-sha,1995

Reference books, course materials, etc.

None in particular

Assessment criteria and methods

Based on overall evaluation of the results for quizzes, report and final examination. Details will be announced during a lecture.

Related courses

• MTH.U211 ： Applied Mathematics for Engineers Ia
• MTH.U212 ： Applied Mathematics for Engineers Ib
• MTH.U214 ： Applied Mathematics for Engineers Iib

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

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].