Complex Analysis explores the properties and applications of complex numbers and functions, emphasizing their geometric interpretations and analytical techniques.
Complex analysis is a secret weapon in describing how fluids move, especially in two dimensions. By using analytic functions, we can model the behavior of water or air around objects.
Certain complex functions (called potential functions) describe the velocity and direction of the flow. Conformal mapping can be used to design airfoils or predict how water flows around rocks.
These techniques are crucial in engineering, from designing airplane wings to predicting weather patterns.
Designing the shape of a wing to minimize air resistance using conformal maps.
Predicting water flow around a bridge pillar with potential flow theory.