Applied Mathematics
TeachersKAMIDE, Norihiro
Grade, SemesterYear 2 II/IV [Department of Information Science Correspondence Course, Faculty of Science and Engineering]
CategoryBasic Major Subjects
Classesメディア授業
Elective, CreditsElective 2credit
 Syllabus Number2B203

Course Description

 The contents of the lectures are summarized as follows: (1) foundations of differential equations, (2) Laplace transform (Laplace transform and inverse Laplace transform), (3) applications of Laplace transform for solving differential equations and (4) Fourier analysis (Fourier series, Fourier transform, inverse Fourier transform and their applications to solving differential equations).

Course Objectives

 The aim of this course is to understand the following items: (1) basic concepts of differential equations, (2) how to use Laplace transform for solving differential equations and (3) how to use Fourier transform and Fourier series for solving differential equations.

Grading Policy

 Students are evaluated by a term examination, some midterm examinations, and some quizzes.

Textbook and Reference

KindTitleAuthorPublisher
TextbookNo textbook. The original slides and video contents are used.
ReferencesNo reference. The original slides and video contents are used.

Requirements(Assignments)

 The slides of the lecture should be read. The video contents of the lecture should be viewed.

Note

 LMS is used in this course.

Schedule

1Foundations of differential equations (1): Basic definitions and backgrounds.
2Foundations of differential equations (2): Separation of variables. First-order differential equations.
3Foundations of differential equations (3): Linear differential equations.
4Foundations of differential equations (4): Symbolic method for solving linear differential equations.
5Foundations of differential equations (5): Picard iteration. Power series solution.
6Laplace transform (1): Outline and background. Midterm examination 1.
7Laplace transform (2): Improper integral. Infinite integral. Special functions.
8Laplace transform (3): Properties of Laplace transform.
9Laplace transform (4): Properties of inverse Laplace transform.
10Laplace transform (5): Applications to solve differential equations.
11Fourier analysis (1): Backgrounds of Fourier transform and Fourier series. Midterm examination 2.
12Fourier analysis (2): Periodic function. Fourier series expansion.
13Fourier analysis (3): Fourier transform. Inverse Fourier transform.
14Fourier analysis (4): Applications of Fourier transform to solve differential equations.
15Fourier analysis (5): Applications of Fourier series to solve differential equations. Term examination.