SFOPDES: A stepwise tutorial for teaching Partial Differential Equations using a CAS

Abstract

Partial Differential Equations (PDE) are one of the most difficult topics that Engineering and Sciences students have to study in the different Math subjects in their degree. In this talk we introduce SFOPDES (Stepwise First Order Partial Differential Equations Solver) aimed to be used as a tutorial for helping both the teacher and the students in the teaching and learning process of PDE. The type of problems that SFOPDES solves can be grouped in the following three blocks: 1. Pfaff Differential Equations, which consists on finding the general solution for: P(x; y; z) dx + Q(x; y; z) dy + R(x; y; z) dz = 0 (a) General method. (b) Particular cases: i. Separable equations. ii. Exact Pfaff equations. iii. One-separated variable equations. 2. Quasi-linear Partial Differential Equations, which consists on finding the general solution for: P(x; y; x) p + Q(x; y; z) q = R(x; y; z) (a) General method. (b) Particular solution which contents a given curve. 3. Using Lagrange-Charpit Method for finding a complete integral for a given general first order partial differential equation: F(x; y; z; p; q) = 0. (a) General method. (b) Particular cases: i. F(p; q) = 0 ii. g1(x; p) = g2(y; q) iii. z = px + qy + g(p; q)