| Course title | |||||
| 幾何学 [Geometry] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 2 | |
| Department | Year | 2～4 | Semester | 1st | |
| Course type | 1st | Course code | 022603 | ||
| Instructor(s) | |||||
| 桧垣 優徳 [HIGAKI Masanori] | |||||
| Facility affiliation | Graduate School of Engineering | Office | Email address | ||
| Course description |
| As an advanced course of calculus, this course provides students with the foundation for vector analysis. This theory is an important tool to study geometry of curves and surfaces and to analyze various phenomena in dynamics, electromagnetism, fluid mechanics, etc. This course treats basic concepts in vector analysis so that students can use them as familiar tools to understand characteristics of scalar fields and vector fields. |
| Expected Learning |
|
Learners who successfully complete this course will be able to: 1. Understand basic calculus of vector-valued functions, and execute it correctly 2. Understand the fundamental concept of curves, surfaces, and vector fields, and handle it with high calculation ability 3. Understand line integrals and surface integrals, and apply fundamental theorems (especially, divergence theorem and Stokes' theorem) to their calculations. |
| Course schedule |
|
Week 1: Vector Algebra (Chapter 1.1,Chapter 1.2) Week 2: Vector Algebra (Chapter 1.3) Week 3: Differentiation and Integration of Vectors (Chapter 2) Week 4: Scalar Fields, Vector field, Gradient (Chapter 3.1) Week 5: Scalar Potential (Chapter 3.1) Week 6: Divergence (Chapter 3.2) Week 7: Rotation (Chapter 3.2) Week 8: Differential Geometry of Space Curves (Chapter 3.3) Week 9: Line Integrals (Chapter 3.4) Week 10: Differential Geometry of Surfaces (Chapter 3.4) Week 11: Surface Integrals (Chapter 3.4) Week 12: Divergence Theorem (Chapter 4.1) Week 13: Stokes' Theorem (Chapter 4.2) Week 14: Aplications of The Integration formula (Chapter 4.3) Week 15: Term Examination Homework: "Problems" and "Exercises" in the relevant part of the textbook |
| Prerequisites |
| Students entering this class are assumed to have learned Calculus I-II and Linear Algebra I-II. |
| Required Text(s) and Materials |
| YANO Kentaro, et al., Bekutoru Kaiseki (Vector Analysis), Shokabo |
| References |
| Reference publications will be introduced in the first lecture, if necessary. |
| Assessment/Grading |
| Exercise 20%, Term examination 80% |
| Message from instructor(s) |
| It is required that you clarify your questionable points by reading the textbook before attending each lecture. I want you to acquire the ability which can be applied to other subjects by enough exercises. |
| Course keywords |
| scalar fields, vector fields, divergence theorem, Stokes' theorem |
| Office hours |
| Before or After the class. |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 2/14/2019 3:23:25 PM |