Applied Mathematics

Mathematical Analysis Curricular Unit of the Bachelor’s degree: Derivatives, Antiderivative, Definite Integrals, Improper integrals, First order Ordinary Differential Equations.

• Theoretical-practical classes based on the oral presentation of theoretical concepts and critical discussion of their application to the resolution of exercises.

• Use of specific software for solving complementary exercises.

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 that are 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.

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 the Laplace transform technique to solve initial value problems (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. Application of single-step numerical methods: Euler methods, Taylor and Runge-Kutta methods of the 2nd and 4th order, in solving initial value problems.

• - Teste 1 + TPC - 40.0%
• - Teste 2 + TPC - 60.0%

• - Exame - 100.0%

NAO

Support materials for the Curricular Unit available on the inforStudent platform  (https://inforestudante.ipc.pt)

Madureira, Luísa. (2010). Problemas de equações diferenciais ordinárias e transformadas de Laplace. FEUP edições.

Kreyszig, Erwin.(2011). Advanced Engineering Mathematics (Chapter 6, pp203-253).Tenth edition. Wiley.

Banner, Adrian. (2007). The Calculus Lifesaver (Chapert 26, pp551-574). Princeton University Press.

Pina, Heitor. (2010). Métodos Numéricos (Capítulo 12, pp499-517). Escolar Editora.