Course title
ベクトル解析   [Vector Analysis]
Course category technology speciality courses,ets.  Requirement   Credit 2 
Department   Year 24  Semester 1st 
Course type 1st  Course code 022310
Instructor(s)
合田 洋   [GODA Hiroshi]
Facility affiliation Faculty of Engineering Office 12-211  Email address

Course description
Vector Calculus provides indispensable tools to analyze changes of states of spaces appearing in dynamics, electromagnetism and fluid dynamics. In this course, we will learn properties of vector fields, curves and surfaces, using Calculus and Linear Algebra.
Expected Learning
The goals of this course are
(1) to understand the basis of scalar and vector fields, gradient, divergence, rotation, line and surface integrations, and
(2) to understand Gauss’ divergence theorem and Stokes’ theorem, and to be capable of performing practical computations by using these theorems.

Corresponding criteria in the Diploma Policy: See the Curriculum maps.
Course schedule
1. Inner and cross products, and planes and space curves
2. Mappings and Derivatives of multivariable functions
3. Vector fields and derivatives of vector fields
4. Length of curves and Line integrals
5. Line integral and Green’s theorem
6. Geometry of surfaces
7. Midterm examination
8. Integral of multivariable functions and change of variables
9. Surface integral and flux integral
10. Rotation of vector fields and Stokes’ theorem I
11. Stokes’ theorem II
12. Gauss’ divergence theorem I
13. Gauss’ divergence theorem II
14. Green’s theorem
15. Term examination
Prerequisites
Knowledge of the courses of “Calculus Ⅰ/Ⅱ and Exercise” will be used in this course.
In addition to 30 hours that students spend in the class, students are recommended to prepare for and revise the lectures, spending the standard amount of time as specified by the University and using the lecture handouts as well as the references specified below.
Required Text(s) and Materials
I will show in the first class.
References
I will show in the first class.
Assessment/Grading
Results of the term and the midterm examinations, 50% and 50%.
Only attendance does not effect to the assessment.
Message from instructor(s)
Try to solve questions that I give in the class and exercises in the textbook very much. You can ask me anything whenever you want. Enjoy mathematics and celebrate the joy of youth.
Course keywords
Scalar field, Vector field, Divergence, Gradient, Rotation, Gauss’ divergence theorem, Stokes’ theorem.
Office hours
Before or After the class. Ask me if it is inconvenient for you. I might change the date.
Remarks 1
Remarks 2
Related URL
http://web.tuat.ac.jp/~goda/lecture/lecture3.html
Lecture Language
Japanese
Language Subject
Last update
3/7/2019 5:11:06 PM