ABSTRACT
Often real world problems are described by partial differential equations (PDEs) with or without boundary and initial value conditions. PDEs involve unknown functions of two or more variables and their partial derivatives. There is a wide class of PDEs which play a significant role in electromagnetic theory, fluid dynamics, traffic flow, medical imaging, financial engineering and many other disciplines. The chapter focuses on basic ingredients of PDEs and applications of important classes such as the wave equation, heat equation, and Laplace equation. Seismic waves are used to infer properties of subsurface geological structures. The physical model is a heterogeneous elastic medium where sound is propagated by small elastic vibrations. Sound waves arise from pressure and density variations in fluids. The starting point of modeling sound waves involves the basic equations for a compressible fluid where ones’ omit viscous forces, body forces and temperature effects.
