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所在平台: Udemy |
课程主页: https://www.udemy.com/course/conformal-mapping-2-some-special-bilinear-transformations/
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课程名称：共形映射2（一些特殊的双线性变换） 课程概要：本课程是前一部分的延续，重点讨论双线性变换、交比、固定点及双线性变换的标准形式。在《一些特殊的双线性变换》课程中，将特别强调如何在给定条件下寻找双线性变换或莫比乌斯变换。 课程内容包括：在双线性变换下，圆和直线映射为圆和直线，逆点也映射为逆点；如何计算逆点；寻找将半平面映射到w平面中的圆盘的双线性变换及其验证；寻找将半平面映射到单位圆盘以及将单位圆盘映射到w平面中单位圆盘的通用变换；在z平面中到w平面的区域的共形映射；唯一函数的存在性；寻找将z平面中的圆映射到w平面中另一个圆的莫比乌斯变换；确定最一般的变换，将z平面中的单位圆映射到w平面中的单位圆；将实轴映射到w平面中的圆的给定变换；展示变换后圆的半径、中心及圆心对应的已变换点；从给定变换中获得逆变换；寻找将z平面中的点映射到w平面中点的双线性变换，甚至适用于同心圆；在给定条件下显示结果的不变性；将给定关系用双线性变换的形式表达。 课程包括所有关键结果和解决作业，提供完整的解释和色彩丰富的图表。
The previous part discussed bilinear transformations, cross-ratio, fixed points, and the normal form of bilinear transformations. In this Course,' SOME SPECIAL BILINEAR TRANSFORMATIONS,' special emphasis will be given to finding Bilinear Transformations or Mobius transformations with Given Conditions.Contents of the Course DescribesUnder the Bilinear Transformation, Circles and Straight lines are mapped into Circles and Straight lines, and Inverse points are mapped into the Inverse points.How to calculate Inverse points.To find the Bilinear Transformation that maps Half Plane onto the Circular Disc in the w plane along with Verification.To Find The General Transformation that maps the half-plane onto the Unit Circular Disc and the Unit Circular Disc onto the Unit Circular Disc in the w-plane.Mapping of the Region in the z plane to the w Plane Conformally.Existence of a Unique FunctionTo find the Mobius Transformation that maps the Circle in the z plane onto another circle in the w plane conformally.To determine the Most General Transformation that maps the Unit Circle in the z-plane onto the Unit Circle in the w-plane.Mapping of Given Transformation from Real axis into Circle in w plane.The radius and Center of the Transformed Circle and the transformed point in the center of the Circle in the w Plane are shown.How to get the Inverse Transformation from the Given Transformation.To Find the Bilinear Transformation that maps points in z plane to the points in w plane even for Concentric Circles. Showing the Results to be Invariant under Given ConditionsExpressing the given Relation in the form of a bilinear Transformation.Including all critical results and solved assignments, with complete Explanations and colorful diagrams.
