Solution of differential equations is very important in the study of mechanical engineering.
This course deals with various kinds of technique to solve the 1st order and 2nd order differential equations.
Also the modeling technique in heat and fluid problems using differential equations are explained.
This course deals with various kinds of technique to solve the 1st order and 2nd order differential equations.
Also the modeling technique in heat and fluid problems using differential equations are explained.
The aim of this course is to acquire fundamental solutions of differential equations and to acquire the ability to apply these
techniques to various problems in mechanical engineering.
- Students can solve linear first-order differential equations using direct integration method, integration by substitution, or partial integration method.
- Students can solve first-order homogeneous or inhomogeneous differential equations.
- Students can solve linear first-order differential equations using the technique of separation of variables.
- Students can solve Bernoulli type differential equations.
- Students can solve 2nd-order homogeneous or inhomogeneous differential equations.
- Students can solve particular solutions of inhomogeneous differential equations using the differential operator technique.
- Students will acquire the ability to apply these techniques to various problems in thermal, fluid and mechanical engineering.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Review of Calculus, Fundamentals of differential equations differential and integral，Trigonometric function， Euler's theorem Types of differential equations |
Preparation and review using reference materials | 190minutes |
| 2. | Linear first-order differential equation Direct integration method, Integration by substitution, Partial integration method Differential equation model (Population problem) |
Preparation and review using reference materials | 190minutes |
| 3. | Homogeneous first-order differential equation (1) Homogeneous equation with a constant coefficient Homogeneous equation with a functional coefficient |
Preparation and review using reference materials | 190minutes |
| 4. | Homogeneous first-order differential equation (2) Examples and solutions Differential equation model (Radiocarbon dating) |
Preparation and review using reference materials | 190minutes |
| 5. | Homogeneous first-order differential equation (3) Review of Homogeneous first-order differential equation Differential equation model (Free-fall problem, Kettle heater) |
Preparation and review using reference materials | 190minutes |
| 6. | Inhomogeneous first-order differential equation (1) Inhomogeneous equation with a constant coefficient Inhomogeneous equation with a functional coefficient |
Preparation and review using reference materials | 190minutes |
| 7. | Inhomogeneous first-order differential equation (2) Examples and solutions Differential equation model (Vibration of the spring-mass model) |
Preparation and review using reference materials | 190minutes |
| 8. | Mid-term examination and review Review of Inhomogeneous first-order differential equation |
Preparation and review using reference materials | 190minutes |
| 9. | Separation of variables (1) Fundamentals of separation of variables |
Preparation and review using reference materials | 190minutes |
| 10. | Separation of variables (2) How to apply the technique of separation of variables Differential equation model (Free-fall problem with air resistance) |
Preparation and review using reference materials | 190minutes |
| 11. | Separation of variables (2), Bernoulli's differential equation How to apply the technique of separation of variables Bernoulli's differential equation Differential equation model (Design of rocket) |
Preparation and review using reference materials | 190minutes |
| 12. | Higher first-order differential equation Homogeneous 2nd-order differential equation Real root, cmplex root, and double root Differential equation model (Design of rocket) |
Preparation and review using reference materials | 190minutes |
| 13. | Inhomogeneous 2nd-order differential equation Fundamentals of special solution Special solution in complex exponential function or trigonometric function Differential equation model (Fick's law, differential equation) |
Preparation and review using reference materials | 190minutes |
| 14. | Differential operator Fundamentals of differential operator How to solve differential equations using differential operator Applications on various equations Term-end examination and summary of lecture |
Preparation and review using reference materials | 190minutes |
| 15. | |||
| Total. | - | - | 2660minutes |
| Intermediate test | term-end exam | Total. | |
|---|---|---|---|
| 1. | 5% | 5% | |
| 2. | 5% | 5% | 10% |
| 3. | 5% | 5% | 10% |
| 4. | 5% | 5% | |
| 5. | 25% | 25% | |
| 6. | 25% | 25% | |
| 7. | 10% | 10% | 20% |
| Total. | 30% | 70% | - |
Final grade will be calculated according to mid-term examination (30%) and term-end examination (70%).
Mid-term examination includes issues 1, 2 and partly issue 4 in 'Goals and objectives'.
Term-end examination includes issues 3 and 4 in 'Goals and objectives'.
Mid-term examination includes issues 1, 2 and partly issue 4 in 'Goals and objectives'.
Term-end examination includes issues 3 and 4 in 'Goals and objectives'.
Reference materials will be provided before each lecture (in the file folder of network system).
'Elementary Mathematics (Analysis)' and 'Differential and Integral Calculus, and Exercise' should be completed before this
lecture.
- Tuesday 10: 00-12: 00. It is desirable to notify the visit in advance.
Accept questions during the class and any time by e-mail.
- Non-social and professional independence development course
Last modified : Wed Oct 17 06:24:11 JST 2018