Conformal Mapping and its Applications. Fluid flow, non-coaxial cable, steady temperatures

Master''s Thesis from the year 2017 in the subject Mathematics - Miscellaneous, grade: A, University of Notre Dame, language: English, abstract: Unlock the hidden symmetries of the mathematical universe and step into a world where complex problems yield to elegant transformations. This compelling exploration delves into the fascinating realm of conformal mapping, a powerful technique at the intersection of complex analysis and applied mathematics. Discover how these remarkable transformations, which preserve angles and local shapes, can unravel the complexities of boundary value problems and illuminate solutions in diverse fields like fluid dynamics and electrostatics. Journey through the foundational principles, starting with the essential definitions and properties that govern conformal maps, including the crucial Cauchy-Riemann equations and the concept of angle preservation. Witness the construction of these mappings through sophisticated mathematical techniques, gaining a deep appreciation for their intricate beauty and analytical power. Explore the real-world applications where conformal mapping shines, providing practical solutions to challenging problems in engineering, physics, and beyond. From visualizing fluid flow around intricate objects to calculating electrostatic potentials in complex geometries, this exploration reveals the transformative power of conformal mapping in shaping our understanding of the physical world. Whether you''re a student seeking a comprehensive introduction or a seasoned mathematician looking for fresh insights, this journey into conformal mapping will equip you with the tools and knowledge to unlock new perspectives and solve previously intractable problems. Embark on a transformative journey into complex analysis and discover how seemingly abstract mathematical concepts can provide concrete solutions to real-world engineering and physics challenges. Understand the essence of angle-preserving transformations and delve into the heart of mathematical problem-solving within electrostatics, fluid dynamics and diverse scientific and engineering applications. Grasp the profound implications of the Cauchy-Riemann equations in constructing elegant solutions to seemingly insurmountable mathematical challenges. Discover the artistry and analytical power of conformal mapping, a technique that bridges theoretical mathematics with the tangible realities of the physical universe and empowers you to solve intricate mathematical problems with newfound clarity and precision. Perfect for advanced students and researchers alike, this exploration will reshape your understanding of complex analysis and its applications.