CONFORMAL MAPPING 2 (Some Special Bilinear Transformations)

🚀 Course Title: CONFORMAL MAPPING 2 - Some Special Bilinear Transformations 🧮

Course Headline: Master Bilinear Transformations, Mobius Transformations, Inverse Points, and Fixed Points! 📊✨

Dive deeper into the fascinating world of Conformal Mapping with our expert-led course, "SOME SPECIAL BILINEAR TRANSFORMATIONS." This advanced course is designed to build upon the foundational concepts covered in the previous part and focus on finding Bilinear and Mobius Transformations under specific conditions.

Course Description:

In the realm of complex analysis, Conformal Mapping stands out as a cornerstone technique that maps complex functions into simpler forms. Our comprehensive course will guide you through the intricacies of this process. 🌟

• Bilinear Transformations: We'll explore how these transformations maintain the conformality between the domains in the ( z ) and ( w ) planes, ensuring that circles and straight lines are mapped to their corresponding forms.

• Inverse Points and Fixed Points: Learn the significance of inverse points and fixed points within Bilinear Transformations, and understand how they impact the mapping process.

• Normal Form of Bilinear Transformations: Revisit and reinforce your knowledge of cross ratio and fixed points in the context of Bilinear Transformations.

What You Will Learn:

• Inverse Points Calculation: We'll cover step-by-step methods for calculating inverse points under Bilinear Transformations, ensuring you can apply these concepts with confidence.

• Mapping Half Plane to Circular Disc: Discover how to map the half plane onto a circular disc in the ( w ) plane and learn how to verify your results.

• Finding General Transformations: Gain proficiency in identifying general transformations that map half planes and unit circular discs conformally, with clear examples and verification methods.

• Conformal Mapping of Regions: Learn the techniques for mapping regions from the ( z ) plane to the ( w ) plane conformally.

• Unique Function Existence: Understand the conditions under which a unique function exists, and learn how to prove it.

• Mobius Transformation for Circle Mapping: Explore the Mobius Transformation that maps circles in the ( z ) plane onto other circles in the ( w ) plane, including the mapping of the unit circle to another unit circle.

• Most General Transformation Determination: Determine the most general transformation that maps a given circle to another circle, ensuring you understand the implications for complex analysis.

• Mapping from Real Axis to Circle: Learn how to map points from the real axis in the ( z ) plane onto circles in the ( w ) plane, including the calculation of the resulting circle's radius and center.

• Inverse Transformation Acquisition: Acquire the skill to find the inverse transformation from a given transformation, providing you with a powerful tool for problem-solving.

• Conformal Mapping for Concentric Circles: Master the art of mapping concentric circles using Bilinear Transformations, and understand how these transformations keep invariants under certain conditions.

Course Highlights:

• Complete Explanation with Diagrams: Every concept is accompanied by clear, colorful diagrams to aid your understanding.

• Solved Assignments: Work through solved assignments with thorough explanations to reinforce your learning and see the application of these concepts in action.

📚 Join our course today and transform your understanding of Conformal Mapping and Bilinear Transformations! With expert guidance, interactive content, and a wealth of resources, you'll be well-equipped to tackle complex problems with confidence. Enroll now and unlock the power of analytic functions and conformal mapping! 🚀