【Course description】
The course enhances mathematical knowledge of the vector analysis, the partial differential equations and Laplace transform through lectures and exercises.
【Aims】
The vector analysis, the partial differential equations and Laplace transform are required to analysis the subjects in wide mechanical engineering fields and this course covers their fundamentals.
By the end of this course, students will be able to:
1) Explain basic problems of the vector analysis.
2) Solve basic problems of the vector analysis.
3) Explain basic problems of the partial differential equations.
4) Solve basic problems of the partial differential equations.
5) Explain basic problems of Laplace transform.
6) Solve basic problems of Laplace transform.
Vector analysis, Partial differential equations, Laplace transform
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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- | - | ✔ | - | ✔ |
Students are given exercise problems and solutions of the problems are reviewed.
Course schedule | Required learning | |
---|---|---|
Class 1 | Basic properties of vector | Perform vector operation using formulae of vector algebra. |
Class 2 | First order partial differential equations | Solve the first order partial differential equations. |
Class 3 | Differential calculus of vector and curved lines | Understand the differential calculus of vector and gauging of curved line by vector, and compute the motion of particle and curvature. |
Class 4 | Second order partial differential equations with homogeneous boundary condition | Solve the second order partial differential equations with homogeneous boundary condition. |
Class 5 | Second order partial differential equations with nonhomogeneous boundary condition and integral equations | Solve the second order partial differential equations with nonhomogeneous boundary condition and integral equations. |
Class 6 | Curved surface and vector field I (gradient of scalar field, divergence of vector field) | Understand how to calculate surface area, gradient of scalar field and divergence of vector field |
Class 7 | Vector field II (rotation of vector field) and integral theorem of vector field | Understand the rotation of vector field, Gauss’ theorem and Green’s theorem, and apply them to problem of mechanics. |
Class 8 | Laplace transform and differential equations | Solve differential equations by using Laplace transform. |
Toda, Morikazu, Vector Analysis, Tokyo: Iwanamai-shoten; ISBN4-00-007773-2
H.P.Hsu, Vector Analysis, Tokyo: Morikita-shuppan; ISBN978-4-627-93020-9
Shimizu, Yuji, Fundamentals and applications of Vector analysis, Tokyo Science-sha;ISBN4-7819-1133-1,(Japanese)
Handouts will be distributed when necessary.
Students’ knowledge on the vector analysis, the partial differential equations and Laplace transform will be assessed by attendance and exercise problems.
Students must have successfully completed Calculus I&II, Linear algebra I&II and Ordinary Differential Equations, or have equivalent knowledge.