| Code |
15758
|
| Year |
2
|
| Semester |
S1
|
| ECTS Credits |
6
|
| Workload |
TP(60H)
|
| Scientific area |
Mathematics
|
|
Entry requirements |
Knowledge of real functions with several variables, derivation and integration.
|
|
Learning outcomes |
This curricular unit is an introduction to the study of differential equations, Laplace transforms and Fourier series.
At the end of the course unit the student should be able to:
- distinguish and solve the different types of differential equations
- solve initial value problems
- calculate direct and inverse Laplace transforms of usual functions. Solve differential and integral equations using Laplace transforms
- determine Fourier series of periodic functions and functions defined in bounded intervals
- use the method of separation of variables in obtaining solutions to partial derivative problems
|
|
Syllabus |
1 - Introduction to Complex Analysis.
2 - Ordinary differential equations of first order.
3 - Ordinary linear differential equations of higher order than the first.
4 - Systems of linear ordinary differential equations of first order.
5 - Laplace transforms and application to the resolution of ordinary differential equations and systems of ordinary differential equations.
6 - Fourier series and application to solving partial derivatives equations.
7 - Fourier Transforms.
|
|
Main Bibliography |
R. Churchill, Operational Mathematics, McGraw-Hill
R. Churchill and J. Brown, Complex Variables and Applications, McGraw-Hill
W. Boyce and R. Di Prima, Elementary Differential Equations and Boundary Value Problems, Fourth Edition, John Wiley & Sons, 1986
|
|
Language |
Portuguese. Tutorial support is available in English.
|