whs said:A year long? Probably not.. Are you going to continue math in grad school? And if so, do you see a certain area that you see yourself specializing in?
I don't know why anyone would take a full year long course... I'd suggest simply buying a book or 2 and doing it on your own. If you are talented in math, and are grad school material, then you will have no problem learning the material on your own and I'm sure you have plenty of access to different professors at your school if you have questions.
A PDE, or partial differential equation, is a mathematical equation that involves partial derivatives of a multivariable function. It is used to describe physical phenomena such as heat transfer, fluid dynamics, and quantum mechanics.
PDEs involve partial derivatives, while ODEs only involve ordinary derivatives. This means that PDEs are used to describe systems with multiple independent variables, while ODEs are used for systems with a single independent variable.
Some common examples of PDEs include the heat equation, wave equation, and Laplace's equation. These equations are used to describe the behavior of heat, waves, and electric potentials, respectively.
PDEs are used in pure mathematics to study the properties and behavior of solutions to these equations. This includes topics such as existence and uniqueness of solutions, stability, and regularity.
PDEs have a wide range of applications in various fields such as physics, engineering, finance, and biology. They are used to model and understand complex systems such as weather patterns, fluid flow, and population dynamics. PDEs also play a crucial role in the development of computer simulations and numerical methods for solving real-world problems.