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- 工学院，物質理工学院，環境・社会理工学院共通科目
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School of Environment and Society
- Department of Architecture and Building Engineering
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- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Civil and Environmental Engineering
- Instructor(s)
- Maruyama Taizo Fujii Manabu Utsumi Nobuyuki
- Class Format
- Lecture / Exercise (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Mon1-2(W5-106) Thr1-2(W5-106)
- Group
- -
- Course number
- CVE.M201
- Credits
- 2
- Academic year
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- 2024/3/14
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This course has two parts. The first part focuses on vector calculus. This topic includes derivative of a vector function, parametric representation of a curve, tangent to a curve and arc length of a curve, gradient of a scalar field, directional derivative, divergence and curl of a vector field, line integrals, Green’s theorem in the plane, surface integrals, divergence theorem of Gauss and Stokes’s theorem. Vector calculus is important and is essential for the study of engineering. Students learn the basics of vector differential calculus and vector integral calculus and will be able to solve some practical problems in engineering (e.g., hydrodynamics). In the second part, Fourier transform and partial differential equation are dealt with. These topics are important to understand dynamic problems in the fields of civil engineering. The following topics are discussed: Fourier series, Fourier integral, formulation of partial differential equation, its general solutions, and method of separation of variables.
Student learning outcomes
By completing this course, students will be able to:
1) Understand the concepts of scalar fields and vector fields.
2) Understand and formulate line integrals and surface integrals.
3) Understand the surface integrals, divergence theorem of Gauss and Stokes’s theorem.
4) Understand the basic theory of Fourier transform.
5) Understand the relationships between frequency and time domain.
6) Formulate and solve some basic partial differential equations.
Keywords
vector functions, vector fields, gradients of scalar fields, divergence of vector fields, rotations, line integrals, area fractions, Green's theorem, Gaussian divergence theorem and Stokes' theorem, Fourier series, Fourier integral, frequency domain, partial differential equation, strings, method of separation of variables
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
Part of each class is devoted to fundamentals and the rest to advanced content or applications. To allow students to get a good understanding of the course contents and practical applications, problems related to the contents of this course are given in homework assignments.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Fundamentals of Vector calculus (1): Vectors, scalars, vector spaces, inner and outer products, vector-valued function (Fujii, Utsumi) | To understand the vectors, scalars, vector spaces, inner and outer products, etc. |
| Class 2 | Scalar and vector fields (1): Examples of scalar and vector fields, scalar fields, gradient vector (grad f) (Fujii, Utsumi) | Understand examples of scalar and vector fields, scalar fields, gradient vector (grad f) |
| Class 3 | Scalar and vector fields (2): gradient vector of a scalar field (grad) and divergence of a vector field (div) (Fujii, Utsumi) | Understand gradient vector of a scalar field (grad) and divergence of a vector field (div) . |
| Class 4 | Scalar and vector fields(3):Rotation of vector fields (rot f) (Fujii, Utsumi) | Understand the rotation of a vector field (rot f). |
| Class 5 | Line Integral and Surface integral (1): Line Integral for Scalar and Vector Fields (Fujii, Utsumi) | Understand Line Integral for Scalar and Vector Fields |
| Class 6 | Line Integral and Surface integral (2): Surface integral for Scalar and Vector Fields (Fujii, Utsumi) | Understand Surface integral for Scalar and Vector Fields |
| Class 7 | Line Integral and Surface integral (3): Gauss's Divergence Theorem (Fujii, Utsumi) | Understand Gauss's divergence theorem. |
| Class 8 | Line Integral and Surface integral (4): Divergence theorem of Gauss and Stokes’s theorem. (Fujii, Utsumi) | Understand Stokes' theorem and Green's theorem. |
| Class 9 | Fourier integral and its properties (Maruyama) | Definition of Fourier series and its mathematical properties |
| Class 10 | Fourier series (Maruyama) | definition of Fourier series, relationships between Fourier series and integral |
| Class 11 | Mathematical properties of Fourier series (Maruyama) | mathematical properties and applications of Fourier series |
| Class 12 | Formulation of partial differential equation (Maruyama) | examples of partial differential equation and its physical background |
| Class 13 | Solving wave equation and diffusion equation (Maruyama) | formulation and solution of wave equation and diffusion equation |
| Class 14 | method of separation of variables/free vibration of simple beam without damping (Maruyama) | solution of partial differential equation using method of separation of variables/formulation and solution for free vibration of simple beam without damping |
| Class 15 | Examination on Fourier transform and partial differential equation (Maruyama) | Examination on Fourier transform and partial differential equation |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Kreyszig, E., 2011, Advanced Engineering Mathematics, 10th edition, John Wiley, New York.
Material will be distributed where necessary (Fujii, Utsumi, Maruyama)
Reference books, course materials, etc.
Hildebrand, F. B., 1976, Advanced Calculus for Applications, 2nd edition, Prentice-Hall, New Jersey. (Fujii, Utsumi)
Material will be distributed where necessary (Fujii, Utsumi, Maruyama)
Assessment criteria and methods
Students' knowledge of the topics on this course, and their ability to apply them to problems will be assessed.
exercises (final exam) 35%, homework 15% (Maruyama)
exercises (final exam) 35%, homework 15%. (Fujii)
Related courses
- CVE.A210 ： Structural Dynamics in Civil Engineering
- CVE.M202 ： Basic Mathematics for System Science
- CVE.B201 ： Hydraulics I
- CVE.B202 ： Hydraulics II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
not specially.
Other
Depending on the progress of the lectures and exercises, the schedule may be changed and make-up lectures may be given.
