EQ205 – Mathematical Analysis III

Between 1992 and 1996 I gave the recitation sessions of Mathematical Analysis III, while professor Mário Rui Costa from the Department of Chemical Engineering was in charge of the course. From 1997 and until 1999 I was given the duty of being in charge of the course.

Objective

Learning the basic techniques to solve differential and difference equations. Developing the ability to analyze practical problems and the derivation of mathematical models to solve them. Consolidating the topics of mathematical analysis and linear algebra learned in other courses.

Program

1. First-order differential equations.
2. Applications of first-order differential equations.
3. Linear homogeneous differential equations of order 2 and above.
4. Linear non homogeneous differential equations.
5. Linear and homogeneous difference equations.
6. Series method.
7. Laplace transforms.
8. Linear and non homogeneous difference equations.
9. Systems of differential equations.
10. Partial differential equations.

Bibliography

• Villate, J. E. (2001). Equações Diferenciais e Equações de Diferenças. Author's edition, Porto.
• Costa M. R. N. (1995). Equações de Diferençaas Finitas. Author's edition, FEUP, Porto.
• Farlow, S. J. (1994). An Introduction to differential Equations and Their Applications. McGraw - Hill, Singapore.
• Kreyszig, I. E. (1992). Advanced Engineering Mathematics, 7th edition, J. Wiley.
• Churchill, R. V. (1972). Operational Mathematics, 3rd edition, McGraw-Hill.