Introduction to Partial Differential Equations

The study of partial differential equations (PDEs) is a fundamental area of mathematics that deals with functions of multiple variables and their rates of change. PDEs are used to describe a wide range of physical phenomena, including heat conduction, fluid dynamics, electromagnetism, and quantum mechanics.

The preliminary concepts necessary to understand PDEs include:

• Multivariable calculus.
• Ordinary differential equations (ODEs).
• Functional analysis.
• Measure theory.