Applied Analysis

Course Information

College	Oyama College	Year	2024
Course Title	Applied Analysis
Course Code	0009	Course Category	Specialized / Elective
Class Format	Lecture	Credits	Academic Credit: 2
Department	Advanced Course of General Engineering	Student Grade	Adv. 1st
Term	Second Semester	Classes per Week	2
Textbook and/or Teaching Materials	「KOSEN text series Ouyou-Suugaku (2nd Ed)」 Kenji Ueno, MORIKITA PUBLISHING, in Japanese
Instructor	NAGAMINE Takanori,OKADA So

Course Objectives

1. Solve ordinary differential equations using Laplace transform.
2. Solve partial differential equations using Fourier series.
3. Understand Fourier integrals and Fourier transforms and calculate them.

Rubric

	Ideal Level	Standard Level	Unacceptable Level
Achievement 1	Be able to clearly explain applications of Laplace transforms in ordinary differential equations and be able to solve related exercises.	Be able to solve related exercises on applications of Laplace transforms in ordinary differential equations.	Unable to solve related exercises on applications of Laplace transforms in ordinary differential equations.
Achievement 2	Be able to clearly explain basic problems related to partial differential equations using Fourier series expansions and be able to solve related exercises.	Be able to solve related exercises on partial differential equations using Fourier series expansions.	Unable to solve related exercises on partial differential equations using Fourier series expansions.
Achievement 3	Be able to clearly explain Fourier integrals and Fourier transforms and solve related exercises.	Be able to solve related exercises on Fourier integrals and Fourier transforms.	Unable to solve related exercises on Fourier integrals and Fourier transforms.

Assigned Department Objectives

JABEE (c) （数学，自然科学，情報技術）

JABEE (C) （数学と自然科学）

JABEE (g) （自主性・継続性）

Teaching Method

Outline:

1-5ths: Learn about Laplace transform, inverse Laplace transform, solving ordinary differential equations, and convolutions.
6-10ths: Fourier series, Fourier cosine series and Fourier sine series, partial differential equations and Fourier series.
11-15ths: Complex Fourier series, Fourier transforms, and Discrete Fourier transforms.

Style:

1. The class will be an omnibus course, with three teachers sharing five lectures each.
2. Grades will be evaluated by examinations, exercises, and small tests in lectures 1-5ths (by Nakagawa), 6-10ths (by Kumashiro), and 11-15ths (by Nagamine). A total score of 60 or higher is required to pass this class.

Notice:

1. The class will consist mainly of lectures and exercises, with some exercises and small tests. Lecture notes may be used and distributed freely.
2. Students are expected to study the textbook in advance of class, take notes in class, and review the class thoroughly. It is also important to solve the exercises in the textbook and workbook by yourself.
3. All teachers of the Mathematics will accept any questions regarding all subjects of Mathematics.
4. The class content and evaluation ratio may change depending on the progress of the lectures.
5. If no exercises are given, the class will be evaluated by examinations only.

Course Plan

			Theme	Goals
2nd Semester
	3rd Quarter
		1st	Laplace transform, moving formula for image function	Be able to solve the exercises.
		2nd	Laplace transform of trigonometric functions, Inverse Laplace transform	Be able to solve the exercises.
		3rd	differential formulas for primitive functions, first-order linear ordinary differential equations, second-order linear ordinary differential equations	Be able to solve the exercises.
		4th	Step and delta functions	Be able to solve the exercises.
		5th	Convolutions	Be able to solve the exercises.
		6th	Exam
		7th	Periodic functions, trigonometric series and Fourier series	Be able to solve the exercises.
		8th	Fourier series of functions of period T, convergence theorem of Fourier series	Be able to solve the exercises.
	4th Quarter
		9th	Fourier cosine series and Fourier sine series	Be able to solve the exercises.
		10th	Partial differential equations and Fourier series, solution of heat conduction equation	Be able to solve the exercises.
		11th	Complex Fourier series and Fourier transform of functions of period T	Be able to solve the exercises.
		12th	Fourier transform, inverse Fourier transform, Fourier integral theorem	Be able to solve the exercises.
		13th	Fourier cosine transform, Fourier sine transform, application of Fourier integral theorem	Be able to solve the exercises.
		14th	Discrete Fourier transforms	Be able to solve the exercises.
		15th	Exam
		16th

Evaluation Method and Weight (%)

	Examination	Presentation	Mutual Evaluations between students	Behavior	Portfolio	Assignments	Total
Subtotal	95	0	0	0	0	5	100
Basic Proficiency	0	0	0	0	0	0	0
Specialized Proficiency	95	0	0	0	0	5	100
Cross Area Proficiency	0	0	0	0	0	0	0