About This Book
Partial Differential Equations (PDEs) are mathematical equations that involve multiple independent
variables, an unknown function, and partial derivatives of that function. They are used to describe a wide
range of physical phenomena such as heat conduction, wave propagation, fluid flow, and
electromagnetic fields. Unlike ordinary differential equations (ODEs), which involve derivatives with
respect to a single variable, PDEs contain derivatives with respect to two or more variables. The order of a
PDE is determined by the highest derivative involved. PDEs are generally classified into three types:
elliptic, parabolic, and hyperbolic, based on the behavior of their solutions. For instance, the Laplace
equation is elliptic and is used in steady-state heat distribution, the heat equation is parabolic and
models diffusion processes, while the wave equation is hyperbolic and represents vibration or wave
phenomena. Solving PDEs can be complex and often requires techniques such as separation of variables,
Fourier series, or numerical methods like finite difference and finite element methods. Understanding
initial and boundary conditions is crucial in determining unique solutions. PDEs play a foundational role
in engineering, physics, and applied mathematics, making their study essential for modeling real-world
systems. Basic Concepts of Partial Differential Equations provides a foundational introduction to the
theory, methods, and applications of PDEs in mathematical modeling.
Contents: 1. Introduction, 2. Basic Ideas of Partial Differential Equations, 3. Method of Separation of
Variables, 4. Parametric Formulation of a Plane in 3D Space, 5. Classification of Differential Equations,
6. Solutions of Some Differential Equations, 7. First Order Linear Differential Equations, 8. Systems of
Equations, 9. The Wave Equation.
