A conformal transformation is a function that locally preserves angles and the shapes of infinitesimally small figures, though not necessarily their size. It is widely used in complex analysis, physics, and engineering to simplify problems by mapping them onto more manageable geometries while retaining essential properties.

Conformal Transformation

conformal transformation

locally preserves angles

shapes of infinitesimally small figures

size

Complex analysis is a branch of mathematics that studies functions of complex numbers and their properties, such as differentiability and integrability, which often lead to elegant and powerful results not seen in real analysis. It plays a crucial role in various fields, including engineering, physics, and number theory, due to its ability to simplify problems and provide deep insights into the nature of mathematical structures.

complex analysis

Physics is the fundamental science that seeks to understand the nature and behavior of matter and energy in the universe, covering phenomena from the smallest subatomic particles to the largest cosmic structures. It provides the foundational principles that underpin other sciences and technologies, offering insights into the laws governing the physical world and enabling advancements in various fields.

physics

Engineering is the application of scientific and mathematical principles to design, build, and analyze structures, machines, and systems, aiming to solve real-world problems efficiently and sustainably. It encompasses a wide range of specialized fields that address various aspects of technology and innovation, driving progress in industries and improving quality of life.

Relevant Degrees

Your Lessons