Introduction to patrial diffrential equations with applications - Dale W Thoe (Dover, 1986)
The book begins with a short review of calculus and ordinary differential equations, then moves on to explore integral curves and surfaces of vector fields, quasi-linear and linear equations of first order, series solutions and the Cauchy-Kovalevsky theorem. It then delves into linear partial differential equations, examines the Laolce, wave and heat equations, and concludes with a brief treatment of hyperbolic systems of equations