| Program / Major | mDP | Goals |
|---|---|---|
| Mechatronics Course | DP-4・1 | 機械・電気系エンジニアとしての基礎的素養 機械工学・電気工学の基礎知識となる数学、機械力学、プログラミング、ものづくりに必要な実践的スキルを修得し、ものづくりのための基礎的素養を理解し、利用できる。 |
Differential equations are widely used to describe and formulate problems in science and engineering because they offer advantages
such as allowing the governing rules of change to be expressed directly and enabling the treatment of continuous variation
in time or space.
Although there are many types of differential equations and many methods for solving them, here only those that are fundamental and important in applications in engineering and physics are considered, including their solution methods, with the aim of enabling students to solve them using the tools of the Laplace transform and the Fourier transform.
Although there are many types of differential equations and many methods for solving them, here only those that are fundamental and important in applications in engineering and physics are considered, including their solution methods, with the aim of enabling students to solve them using the tools of the Laplace transform and the Fourier transform.
In this course, students will learn the applications and solution methods of ordinary differential equations that are fundamental
and important in science and engineering.
In the first half of the course, after surveying the modeling of physical phenomena and systems, as well as the existence and classification of solutions, students will study the Laplace transform, including related background knowledge. Next, the course discusses methods for solving initial value problems for linear ordinary differential equations using the Laplace transform and derives the responses of linear systems.
In the second half, an introduction to Fourier series expansion is provided, followed by methods for solving partial differential equations using it, as well as its applications to the analysis of physical phenomena.
In the first half of the course, after surveying the modeling of physical phenomena and systems, as well as the existence and classification of solutions, students will study the Laplace transform, including related background knowledge. Next, the course discusses methods for solving initial value problems for linear ordinary differential equations using the Laplace transform and derives the responses of linear systems.
In the second half, an introduction to Fourier series expansion is provided, followed by methods for solving partial differential equations using it, as well as its applications to the analysis of physical phenomena.
- Students will be able to explain the relationship between differential equations and phenomena in science and engineering.
- Students will be able to solve initial value problems for constant-coefficient linear ordinary differential equations using the Laplace transform.
- Students will be able to understand the fundamentals of Fourier series expansion and apply them to solving partial differential equations.
- Students will be able to explain the physical meaning of solutions of differential equations and the responses of linear systems.
| assignments | mid-term exam | final-term exam | Total. | |
|---|---|---|---|---|
| 1. | 5% | 5% | 10% | 20% |
| 2. | 10% | 10% | 10% | 30% |
| 3. | 10% | 10% | 10% | 30% |
| 4. | 5% | 5% | 10% | 20% |
| Total. | 30% | 30% | 40% | - |
Grades will be evaluated based on the weighting of reports (30%), midterm exams (30%), and final exams (40%).
A score of 60 indicates the ability to correctly solve the exercises covered in lectures and reports.
NOTE: Student will not be eligible for credit unless all reports are submitted and both the midterm and final exams are taken.
A score of 60 indicates the ability to correctly solve the exercises covered in lectures and reports.
NOTE: Student will not be eligible for credit unless all reports are submitted and both the midterm and final exams are taken.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | - Necessity of differential equations - Examples of use in science and engineering fields, advantages and disadvantages - Modeling of physical phenomena |
- Basics of differential and integral calculus - Organization of variables, unknown functions, and parameters necessary when expressing familiar scientific and engineering phenomena using differential equations |
190minutes |
| 2. | - Engineering classification of differential equations, existence and uniqueness of solutions - Homogeneous linear differential equations, solution methods using separation of variables |
- Basic methods for solving separable and homogeneous linear differential equations | 190minutes |
| 3. | - Introduction to the Laplace transform (definition and properties) - Laplace transform of elementary functions 1 |
- Linearity, differential formulas, integral formulas, exponents formulas - Final value theorem |
190minutes |
| 4. | - Solving non-homogeneous fixed-form linear differential equations using Laplace transforms | - Convolution integral | 190minutes |
| 5. | Differential equations of 1st order (4) type reduced to 1st order | - Initial conditions for differential equations | 190minutes |
| - Partial fraction expansion, Heaviside expansion formula | |||
| 6. | - Initial value problems for differential equations and their solutions 1 | - Homogeneous solution | 190minutes |
| 7. | - Initial value problems for differential equations and their solutions 2 | - Non-homogeneous solution | 190minutes |
| 8. | - Heaviside’s formula and its generalization, and how to use it to solve initial value problems | - Generalized Heaviside’s formula | 190minutes |
| 9. | - Mid-term examination | - Pit fall of points | 190minutes |
| 10. | - Fourier series expansion 1 - Orthogonality of trigonometric function systems, Fourier coefficients |
- Orthogonality of trigonometric functions - Derivation of Fourier coefficients |
190minutes |
| 11. | - Fourier series expansion 2 - Even function expansion, odd function expansion, half-interval expansion |
- Differences between even function expansion, odd function expansion, and half-interval expansion | 190minutes |
| 12. | - Application to partial differential equations 1 - Separation of variables, heat conduction equation |
- Separation of variables and its application to heat conduction equation | 190minutes |
| 13. | - Applications to partial differential equations 2 • Wave equations and Fourier series expansion |
- Application of Fourier series expansion to wave equations | 190minutes |
| 14. | Term-end examination and comments on it | - Pit fall of points | 190minutes |
| Total. | - | - | 2660minutes |
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback in the class | Done during class, or via ScombZ, email |
- How to find the limit of an indeterminate form (L’Hôpital’s rule) and its prerequisites
- Correspondence between complex numbers and the complex plane, integral formulas for trigonometric functions
- Correspondence between complex numbers and the complex plane, integral formulas for trigonometric functions
- Please also use the learning support room before and after class.
- If you have any questions before or after the lecture, please feel free to ask me directly. You can also submit questions when submitting your report on ScombZ. Please make use of this feature.
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic interpersonal skills
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| Applicable | Leveraging our experience in characteristic analysis and control system design in the manufacturing division of a construction machinery company, the introduction of an intuitive understanding of differential equations and practical application examples are introduced. |
Last modified : Wed Apr 01 04:04:16 JST 2026