1주차 |
Introduction, vector functions
(학습내용 보기)
This lecture deals with functions whose values are vectors in a 3-dimensional Euclidean space(vector functions or vector valued functions), in particular electrostatic field.
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시험 | -
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동영상 | -
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다운로드 | 567 |
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2주차 |
Gauss’ law, unit normal vector and definition of surface integrals
(학습내용 보기)
Give the definition of Gauss' law and the definition of surface integrals
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다운로드 | 247 |
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3주차 |
Evaluating surface integral.
(학습내용 보기)
This lecture is to develop methods to evaluate the surfaces integrals with various examples.
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시험 | -
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동영상 | -
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다운로드 | 149 |
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4주차 |
Flux of vectro functions, Gauss’ law to find the electric field
(학습내용 보기)
Gauss’ law gives a method to find the electric field. In this lecture we explain how to find the field using a special surface.
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시험 | -
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다운로드 | 124 |
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5주차 |
The definition of divergence, the divergence in cylindrical and spherical coordinates,
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다운로드 | 115 |
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6주차 |
The moment of inertia, how to find the electric field under symmetric conditions
(학습내용 보기)
Throughout some problems we find the electric field using Gauss' law and symmetry
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다운로드 | 99 |
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7주차 |
Application of Gauss' theorem. The differential form of Gauss' law
(학습내용 보기)
Two simple applications of the divergence theorem. Gauss’ theorem(the divergence theorem) states that the flux of a vector field out of a closed surfaces equals the integral of the divergence of that vector field over the volume enclosed by the surface
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시험 | -
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동영상 | -
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다운로드 | 100 |
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8주차 |
mid-term exam
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다운로드 | 211 |
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9주차 |
Work and Line integrals, Line integrals involving vector functions
(학습내용 보기)
In this lecture we shall introduce the concept of a path integral. This is one of the several ways in which integrals of functions of one variable can be generalized to functions of several variables.
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시험 | -
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다운로드 | 121 |
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10주차 |
Path independence. The circulation law. The curl
(학습내용 보기)
What is remarkable is that, under some conditions, the value of the path integral does not depend on the path. We give the definition of the curl.
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다운로드 | 97 |
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11주차 |
The curl in Cylindrical and spherical coordinates, the meaning of curl
(학습내용 보기)
We give the meaning of curl and express it in cylindrical and spherical coordinates, respectively.
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다운로드 | 106 |
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12주차 |
Stokes’ theorem and its application
(학습내용 보기)
Stokes’ theorem relates the path integral of a vector field around a simple closed curve in to an integral over a surface for which the curve is the boundary
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시험 | -
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다운로드 | 137 |
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13주차 |
Stokes' theorem and simply connected region. Path independence and the curl. Green's theorem
(학습내용 보기)
Under a simply connceted region, the relationship between path-independence and vanishing curl. In dimension 2, we show that Gauss' theorem and Stokes' theorem are equal.
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다운로드 | 141 |
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14주차 |
Applications of Green's theorem, Conservative vector fields
(학습내용 보기)
We give some problems to understand and give a criterion for conservative vector fields
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다운로드 | 125 |
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15주차 |
A method to find scalar potential. Relationships among conservative field, path-independent and vanishing curl
(학습내용 보기)
In this lecture we introduce a method to find the scalar potential of conservative field. In a simply connected connected region, the 3 concepts, i.e., conservative field, path-independent and vanishing curl are same.
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동영상 | -
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다운로드 | 69 |
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16주차 |
final exam
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다운로드 | 171 |