### 2018　Basic Mathematics for Physical Science

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Undergraduate major in Civil and Environmental Engineering
Instructor(s)
Morikawa Hitoshi  Wijeyewickrema Anil
Course component(s)
Lecture / Exercise
Mode of instruction

Day/Period(Room No.)
Mon1-2(W932)  Thr1-2(W932)
Group
-
Course number
CVE.M201
Credits
2
2018
Offered quarter
1Q
Syllabus updated
2018/3/20
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

This course has two parts.

In the first 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.

The second part focuses on vector calculus. Topics include 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.

### Student learning outcomes

By completing this course, students will be able to:
1) Explain the basic theory of Fourier transform.
2) Explain the relationships between frequency and time domain.
3) Formulate and solve some basic partial differential equations.
4) Explain the concepts of scalar fields and vector fields.
5) Calculate line integrals and surface integrals.
6) Proof and use Green’s theorem in the plane, surface integrals, divergence theorem of Gauss and Stokes’s theorem.

### Keywords

Fourier series, Fourier integral, frequency domain, partial differential equation, strings, method of separation of variables (H. Morikawa)

vector functions, vector fields, curves, gradient of a scalar field, directional derivative, divergence of vector field, curl of vector field, line integrals, Green’s theorem in the plane, divergence theorem, Stokes’s theorem. (Anil C. W.)

### 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 Fourier series (Morikawa) definition of Fourier series
Class 2 Mathematical properties of Fourier series (Morikawa) mathematical properties and applications of Fourier series
Class 3 Fourier integral (Morikawa) definition and mathematical properties of Fourier integral
Class 4 Formulation of partial differential equation (Morikawa) examples of partial differential equation and its physical background
Class 5 Solving wave motion equation (Morikawa) formulation and solution of wave motion equation
Class 6 method of separation of variables (Morikawa) solution of partial differential equation using method of separation of variables
Class 7 exercises for Fourier transform and partial differential equation (Morikawa) exercises for Fourier transform and partial differential equation
Class 8 Vector differential calculus (1). Review of vector algebra. Vector and scalar functions and fields. Derivatives. (Anil C. W.) Review sections 9.1-9.4 of textbook.
Class 9 Vector differential calculus (2). Curves and arc length. (Anil C. W.) Review sections 9.5 of textbook.
Class 10 Vector differential calculus (3). Gradient of a scalar field. Directional derivative. (Anil C. W.) Review sections 9.7 of textbook.
Class 11 Vector differential calculus (4). Divergence and curl of a vector field. (Anil C. W.) Review sections 9.8 and 9.9 of textbook.
Class 12 Vector integral calculus (1). Line integrals. (Anil C. W.) Review sections 10.1 of textbook.
Class 13 Vector integral calculus (2). Green’s theorem in the plane. (Anil C. W.) Review sections 10.4 of textbook.
Class 14 Vector integral calculus (3). Surface integrals. (Anil C. W.) Review sections 10.5 and 10.6 of textbook.
Class 15 Vector integral calculus (4). Divergence theorem of Gauss and Stokes’s theorem. (Anil C. W.) Review sections 10.7-10.9 of textbook.

### Textbook(s)

Kreyszig, E., 2011, Advanced Engineering Mathematics, 10th edition, John Wiley, New York.

### Reference books, course materials, etc.

Hildebrand, F. B., 1976, Advanced Calculus for Applications, 2nd edition, Prentice-Hall, New Jersey. (Anil C. W.)

### Assessment criteria and methods

Students' knowledge of the topics on this course, and their ability to apply them to problems will be assessed.
exercises 35%, homework 15% (H. Morikawa)
Final exam 30%, exercise problems 20%. (Anil C. W.)

### Related courses

• CVE.A210 ： Structural Dynamics in Civil Engineering
• CVE.M202 ： Basic Mathematics for System Science

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

Basic vector algebra. (Anil C. W.)

### Other

Anil and Morikawa provide their lecture on Monday and Thursday, respectively. If necessary, we offer makeup class. 