Course Objectives
(1) Can make a deductive inference based on basic matters, including reading and writing logical sentences containing mathematical formulae.
(2) Can perform basic calculations in Fourier analysis and apply them to engineering and physics on a basic level.
Rubric
| Ideal Level | Standard Level | Unacceptable Level |
Achievement 1 | Can accurately make a deductive inference based on basic matters. | Can make a deductive inference based on basic matters. | Cannot make a deductive inference based on basic matters. |
Achievement 2 | Can fully perform basic calculations in Fourier analysis and fully apply them to engineering and physics on a basic level. | Can perform basic calculations in Fourier analysis and apply them to engineering and physics on a basic level. | Cannot perform basic calculations in Fourier analysis and apply them to engineering and physics on a basic level. |
Assigned Department Objectives
Teaching Method
Outline:
In this course, we will learn the basics of Fourier analysis (including topics on the Laplace transform) based on the calculus and linear algebra learned so far. This is also applied to engineering and physics, so this class will also cover them, including basic applications.
Style:
Classes will be taught in a lecture style, and there will also be exercises and quizzes.
Notice:
Instead of memorizing theorems and formulae individually, carefully follow the development of discussions and the proof of theorems given in each lecture, so that you can understand it yourself. In problem exercises, do not try to remember the steps to solve a problem, but rather try to solve it yourself based on definitions and basic theorem and ideas. Also, if necessary, review the content learned during the previous years.
The schedule of the midterm exam may be changed.
Students who miss 1/3 or more of classes will not be eligible for evaluation.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
1st Semester |
1st Quarter |
1st |
Review and supplementary lesson on calculus |
Can handle the basic matters of calculus that's necessary for future learning.
|
2nd |
Organize data |
Can organize data.
|
3rd |
Laplace transform |
Can calculate and discuss based on the basic matters of the Laplace transform.
|
4th |
Laplace transform |
Can perform calculations and discussions related to the inverse Laplace transform.
|
5th |
Application to vibration phenomena |
Can apply the Laplace transform to mechanical vibration phenomena.
|
6th |
Application to vibration phenomena Fourier series |
Can apply the Laplace transform to AC circuits. Can calculate and discuss based on the basic matters of the Fourier series.
|
7th |
Fourier series |
Can calculate and discuss based on the basic matters of the Fourier sine / cosine series.
|
8th |
Midterm exam Fourier series |
Can calculate and discuss based on the basic matters of the complex Fourier series.
|
2nd Quarter |
9th |
Fourier series Fourier transform |
Can handle the formulae related to Fourier series. Can extend Fourier series expansion for non-periodic functions.
|
10th |
Fourier transform |
Can calculate and discuss based on the basic matters of the Fourier transform.
|
11th |
Fourier transform Wave equation |
Can handle the formulae related to Fourier transform.
|
12th |
Wave equation |
Can handle wave phenomena based on the laws of motion and the methods of Fourier analysis.
|
13th |
Heat equation |
Can handle standing waves based on Fourier series. Can derive the heat equation.
|
14th |
Heat equation |
Can handle heat conduction phenomena based on the methods of Fourier analysis.
|
15th |
Supplementary lesson on the Laplace transform |
Can calculate and discuss matters related to delta function and convolution.
|
16th |
Final exam
|
|
Evaluation Method and Weight (%)
| Examinations | Exercises / Quizzes | Attendance / Behavior | Total |
Subtotal | 40 | 30 | 30 | 100 |
Basic Proficiency | 40 | 30 | 30 | 100 |
Specialized Proficiency | 0 | 0 | 0 | 0 |
Cross Area Proficiency | 0 | 0 | 0 | 0 |