RT Conference Proceedings
T1 Teaching Partial Differential Equations with CAS
A1 Galán-García, José Luis
A1 Rodríguez-Cielos, Pedro
A1 Padilla-Domínguez, Yolanda Carmen
A1 Galán-García, María Ángeles
A1 Aguilera-Venegas, Gabriel
A1 Rodríguez-Cielos, Ricardo
K1 Matemáticas para ingenieros - Estudio y enseñanza
AB Partial Differential Equations (PDE) are one of the topics where Engineering studentsfind more difficulties when facing Math subjects.A basic course in Partial Differential Equations (PDE) in Engineering, usually deals atleast, with the following PDE problems:1. Pfaff Differential Equations2. Quasi-linear Partial Differential Equations3. Using Lagrange-Charpit Method for finding a complete integral for a given generalfirst order partial differential equation4. Heat equation5. Wave equation6. Laplace’s equationIn this talk we will describe how we introduce CAS in the teaching of PDE.The tasks developed combine the power of a CAS with the flexibility of programmingwith it. Specifically, we use the CAS DERIVE. The use of programming allows us to useDERIVE as a Pedagogical CAS (PECAS) in the sense that we do not only provide the finalresult of an exercise but also display all the intermediate steps which lead to find the solutionof a problem. This way, the library developed in DERIVE serves as a tutorial showing, stepby step, the way to face PDE exercises.In the process of solving PDE exercises, first-order Ordinary Differential Equations (ODE)are needed. The programs developed can be grouped within the following blocks:- First-order ODE: separable equations and equations reducible to them, homogeneousequations and equations reducible to them, exact differential equations and equationsreducible to them (integrating factor technique), linear equations, the Bernoulli equation,the Riccati equation, First-order differential equations and nth degree in y’, Genericprograms to solve first order differential equations.- First-order PDE: Pfaff Differential Equations, Quasi-linear PDE, Lagrange-CharpitMethod for First-order PDE.- Second-order PDE: Heat Equation, Wave Equation, Laplace’s Equation.We will remark the conclusions obtained after using these techniques with our Engineering students.
YR 2018
FD 2018-06-22
LK https://hdl.handle.net/10630/16002
UL https://hdl.handle.net/10630/16002
LA eng
NO Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026