Base Knowledge
Mathematical Analysis of the Bachelor’s degree:
Derivatives, Antiderivative, Definite Integrals, Improper integrals, First order Ordinary Differential Equations.
Teaching Methodologies
Guided individual study, based on solving specifically designed exercises of increasing difficulty. Use of specific software for solving complementary exercises.
Two examinations are used to measure the students’s progress in achieving each of the learning objectives of the course.
Learning Results
The aim of this course is to promote the learning of concepts and the practice of mathematical methods and techniques often used to solve a wide range of engineering problems.
At the end of the learning process the students are expected to:
Be able to formulate and explain complex concepts and ideas using a well-structured reasoning typical of mathematical thinking
Understand and make effective use of advanced mathematical methods and techniques fundamental to their understanding of scientific texts, thereby allowing them to more easily develop and update their scientific knowledge throughout their professional lives.
Use computer tools for analyzing and solving problems.
Program
1. Laplace transforms. Definition and properties of the Laplace transform and its inverse transform. Direct and inverse transforms of elementary functions, such as the step, the ramp, the rectangular impulse and Dirac delta functions. Techniques for calculating inverse transforms. Application of Laplace transforms to solving differential equations and systems of linear differential equations with constant coefficients.
2. Power series. Radius of convergence and interval of convergence. Operations with power series, differentiation and integration. Brief reference to real functions of real variables. Taylor series of functions of several variables.
3. Numerical integration. Differential equations. Simple step methods: Euler, Taylor and Runge-Kutta 2nd and
4th order methods for solving 1st order differential equations.
Grading Methods
- - Teste 1 + TPC - 40.0%
- - Teste 2 + TPC - 60.0%
- - Exame - 100.0%
Internship(s)
NAO
Bibliography
Kreyszig, E., 2010. Advanced Engineering Mathematics. Wiley
Spiegel, M.R., 1971. Transformadas de Laplace. McGraw-Hill
Chapra,S., Canale, R., 2009. Numerical Methods for Engineers. McGraw-Hill
Pina H., 1995. Métodos Numéricos. McGraw-Hill
Krasnov M.L. et al, 1994. Problemas de Equações Diferenciais Ordinárias. McGraw-Hill
Breda A., Costa J., 1996. Cálculo com funções de várias variáveis. McGraw-Hill