This introductory text for undergraduate and first year graduate courses explains the basic equations of mathematical physics and the properties of their solutions based on classical calculus and ordinary differential equations, including using the newest software. Stavroulakis (U. of Ioannina, Greece) and Tersian (U. of Rousse, Bulgaria) break the work down into first-order partial differential equations (PDEs), second-order PDEs, one-dimensional wave equation, one-dimensional diffusion equation, weak solutions, shock waves, conservation laws, the Laplace equation, Fourier series and Fourier methods for PDEs and diffusion and wave equations in higher dimensions. They include exercises and answers or hints for solving them.