To lead ordinary differential equations and partial differential equations, applied analysis covers mathematical modelling
in biology, economics, physics, and chemistry as an introduction against undergraduate students.
Students should study a mathematical modelling which lead to ordinary differential equations and partial differential equations
through practicing experimentations and observations. In addition, students should learn a theoretical method and numerical
analytical approach for solving these differential equations.
- Students can express physical phenomena related to mechanical engineering by differential equations.
- Students understand and be able to explain the discretization of mechanical problems.
- Students can program to simulate mathematically modeled physical phenomena.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | About the equations of the field of mechanics ・ Equilibrium of Force ・ Displacement-strain relational expression ・ Constitutive equation ・ Boundary condition expression |
Preparation: Reviewing the equations of the field of mechanics | 90minutes |
| Reviewing the representation of three-dimensional field equations | 100minutes | ||
| 2. | Discrete solution ・ Discretization of space ・ About the finite element method |
Preparation: Reviewing the expression of the strain field and the displacement-strain relational expression. | 90minutes |
| Solving examples explained during class | 100minutes | ||
| 3. | Element definition ・ Displacement field in the element ・ Strain in the element |
Preparation: Review the expression of the strain field and the displacement-strain relational expression. | 90minutes |
| Creating an Excel sheet to solve the exercises during the class and solve the tasks. | 100minutes | ||
| 4. | Element stiffness equation ・ Derivation of the element stiffness matrix |
Preparation: Reviewing the expression of stress field and constitutive equation | 90minutes |
| Creating an Excel sheet to solve the exercises during the class and solve the tasks. | 100minutes | ||
| 5. | Globally assembled stiffness equation ・ Derivation of the globally assembled stiffness matrix |
Preparation: Reviewing the concept of discretization | 90minutes |
| Creating an Excel sheet to solve the exercises during the class and solve the tasks. | 100minutes | ||
| 6. | Execution of the finite element method ・ Boundary condition ・ Solving a simple problem with the finite element method |
Preparation: Reviewing the boundary conditions. | 90minutes |
| Creating an Excel sheet to solve the exercises during the class and solve the tasks. | 100minutes | ||
| 7. | Basics of measurement by embedded computer ・ Real-time measurement ・ Arduino development environment setup |
Preparation ・ Find out about Arduino |
90minutes |
| Review ・ Solve examples or exercises related to the content explained during the lesson to deepen your understanding. |
100minutes | ||
| 8. | Basics of analog value measurement, sampling cycle ・ Quantization of analog values ・ Analog sensor and interface circuit ・ Sampling cycle |
Preparation ・ Find out about the sampling theorem |
90minutes |
| Review ・ Solve examples or exercises related to the content explained during the lesson to deepen your understanding. |
100minutes | ||
| 9. | Measurement of analog electrical circuits ・ RC circuit ・ RLC circuit |
Preparation ・ Investigate the basic characteristics of RC circuits and RLC circuits |
90minutes |
| Review ・ Solve examples or exercises related to the content explained during the lesson to deepen your understanding. |
100minutes | ||
| 10. | Group work 1 ・ Measurement plan using sensors |
Preparation ・ Investigate the types and principles of analog sensors |
90minutes |
| Review ・ Make a plan for what kind of measurement will be performed using which sensor in the group. |
100minutes | ||
| 11. | Group work 2 ・ Measurement using sensors |
Preparation ・ Investigate what kind of output the selected sensor outputs with respect to the measured physical quantity. |
90minutes |
| Review ・ Organize the recorded data and check if there is any excess or deficiency in the implementation for analysis. |
100minutes | ||
| 12. | Group work 3 ・ Measurement analysis using sensors |
Preparation ・ Consider analysis methods for measured data |
90minutes |
| Review ・ Analyze the measurement results. Create materials for the recital. |
100minutes | ||
| 13. | Group work presentation 1 | Preparation ・ Examine the contents of the presentation materials and practice the presentation. |
90minutes |
| Review ・ Understand the results of other groups and evaluate their contents mutually. |
100minutes | ||
| 14. | Group work presentation 2 | Preparation ・ Examine the contents of the presentation materials and practice the presentation. |
90minutes |
| Review ・ Understand the results of other groups and evaluate their contents mutually. |
100minutes | ||
| Total. | - | - | 2660minutes |
| Homework and quiz | Total. | |
|---|---|---|
| 1. | 33% | 33% |
| 2. | 33% | 33% |
| 3. | 34% | 34% |
| Total. | 100% | - |
The grading for this class was broken down as follows:
Homework and quiz (100%)
Homework and quiz (100%)
D.N. Burghes and M.S. Borrie, Modelling with differential equations
S.J. Farlow, Partial differential equations for scientists and engineers
S.J. Farlow, Partial differential equations for scientists and engineers
- Friday lunch break (You should make an appointment via e-mail in advance.)
- Course that cultivates a basic problem-solving skills
- Course that cultivates a basic self-management skills
- Course that cultivates an ability for utilizing knowledge
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Thu Sep 23 04:05:15 JST 2021