### 2016　Exercises in Applied Mathematics

Font size  SML

Instructor(s)
Takahara Hiroki  Oshima Shuzo  Yamazaki Takahisa  Sasabe Takashi  Hasegawa Jun  Inoue Takayoshi
Course component(s)
Lecture / Exercise
Day/Period(Room No.)
Fri7-8(I121)
Group
-
Course number
MEC.B242
Credits
1
2016
Offered quarter
2Q
Syllabus updated
2016/7/13
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

【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.

### Student learning outcomes

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.

### Keywords

Vector analysis, Partial differential equations, Laplace transform

### Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
- - -

### Class flow

Students are given exercise problems and solutions of the problems are reviewed.

### Course schedule/Required learning

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.

### Textbook(s)

Toda,　Morikazu, Vector　Analysis, Tokyo: Iwanamai-shoten; ISBN4-00-007773-2

### Reference books, course materials, etc.

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.

### Assessment criteria and methods

Students’ knowledge on the vector analysis, the partial differential equations and Laplace transform will be assessed by attendance and exercise problems.

### Related courses

• MEC.B214 ： Vector Analysis
• MEC.B213 ： Partial Differential Equations

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed Calculus I&II, Linear algebra I&II and Ordinary Differential Equations, or have equivalent knowledge.