Course Objectives
Learning purpose :
Understand the basics of differential geometry tht is a field in modern mathematics.
Course Objectives :
1. To apply mathematical methods to solve problems in your area of expertise.
2. To understand the basic concept of differential geometry, and can calculate the basic form and curvature of concrete curves and curved surfaces.
Rubric
| Excellent | Good | Acceptable | Not acceptable |
Achievement 1 | The student can find various curvatures. | The student can find about 70% of various curvatures. | The student can find about 60% of various curvatures. | The student can not find about 60% of various curvatures. |
Achievement 2 | The student can find basic forms. | The student can find about 70% of basic forms. | The student can find about 60% of basic forms. | The student can not find about 60% of basic forms. |
Achievement 3 | The student can find Riemannian metrics. | The student can find about 70% of Riemannian metrics. | The student can find about 60% of Riemannian metrics. | The student can not find about 60% of Riemannian metrics. |
Assigned Department Objectives
Teaching Method
Outline:
General or Specialized : Specialized
Field of learning : Mathematics / Physics
Required, Elective, etc. : Elective must complete subjects
Foundational academic disciplines:
Mathematical science / Mathematics / Analysis basics
Relationship with Educational Objectives :
This class is equivalent to "(3) Acquire deep foundation knowledge of the major subject area".
Relationship with JABEE programs :
The main goal of learning / education in this class are "(A), and A-1".
Course outline :
It deals with the basics of Differential Geometry, using Curves and Curved Surfaces as subjects.
Style:
Course method :
Lectures are basically given, but exercises are also given to deepen understanding.
Grade evaluation method :
Exams [60%] + Others (exercises, reports, lessons, etc.)[40%].
Regular examinations will be conducted a total of 2 times, and the evaluation ratios will be the same. Depending on the grade, the student may be required to retake the exam or submit additional report.
Notice:
Precautions on the enrollment :
This course is an elective course. In addition, this subject is a "subject that requires study outside of class hours". Classes are offered for 15 credit hours per credit, but 30 credit hours are required in addition to this. Follow the instructions of your instructor for these studies.
Course advice :
Make sure to check what you have learned in Mathematics up to the 4th year, such as Trigonometric functions, Vectors, Matrices, One-variable and Multi-variable Differential Equations, Ordinary Differential Equations, and Vector Analysis.
Foundational subjects :
Fundamental Mathematics (1st year), Fundamental Linear Algebra (2nd), Differential and Integral I and II (2nd and 3rd), Fundamental Differential Equations (3rd), Applied Mathematics (4th)
Related subjects :
Physics after 4th year, specialized subjects
Attendance advice :
If you are late a lot, you may be treated as absent after giving a warning.
Course Plan
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Theme |
Goals |
2nd Semester |
3rd Quarter |
1st |
Guidance, Plane curve and its curvature / rotation speed Learning content outside class hours: Distribution assignment |
Students can find the curvature and rotation speed of a plane curve.
|
2nd |
Spatial curve and Frenet-Serret formula Learning content outside class hours: Distribution assignment |
Students can find the curvature and torsion of the space curve.
|
3rd |
Curved surface and tangent plane Learning content outside class hours: Distribution assignment |
Students can find the tangent plane.
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4th |
First basic form, second basic form Learning content outside class hours: Distribution assignment |
Students can find first and second fundamental forms.
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5th |
Legal curvature, principal curvature Learning content outside class hours: Distribution assignment |
Students can find the law curvature and the principal curvature.
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6th |
Gaussian curvature, mean curvature Learning content outside class hours: Distribution assignment |
Students can find Gaussian curvature and mean curvature.
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7th |
Specific examples of basic form and curvature Learning content outside class hours: Distribution assignment |
Confirmation of basic matters so far through concrete examples
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8th |
2nd semester mid-term exam |
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4th Quarter |
9th |
How to use an orthonormal system Learning content outside class hours: Distribution assignment |
Students can use the orthonormal system to represent the various basic quantities they have learned so far.
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10th |
Two-variable differential form Learning content outside class hours: Distribution assignment |
Students can calculate the differential form of two variables.
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11th |
Riemannian metric and structural equations on curved surfaces Learning content outside class hours: Distribution assignment |
Students can find Riemannian metric on curved surfaces.
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12th |
Vector field and covariant derivative Learning content outside class hours: Distribution assignment |
Students can find parallel vector fields along a curve.
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13th |
Geodesic Learning content outside class hours: Distribution assignment |
Students can find the geodesic equation.
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14th |
Gauss-Bonnet theorem Learning content outside class hours: Distribution assignment |
Students can use Gauss-Bonnet's theorem.
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15th |
2nd semester final exam |
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16th |
Return and commentary of exam answers |
Confirmation of basic matters
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Evaluation Method and Weight (%)
| Examination | Presentation | Mutual Evaluations between students | Behavior | Portfolio | Other | Total |
Subtotal | 60 | 0 | 0 | 0 | 0 | 40 | 100 |
Basic Proficiency | 30 | 0 | 0 | 0 | 0 | 20 | 50 |
Specialized Proficiency | 30 | 0 | 0 | 0 | 0 | 20 | 50 |
Cross Area Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 |