Mathematical Analysis I

Mechanical Engineering
6 ECTS; 1º Ano, 1º Semestre, 30,0 T + 30,0 TP + 4,50 OT

- Maria Helena Morgado Monteiro

High-school level mathematics.

a) Consolidate and expand students' knowledge of mathematics;
b) Know and apply the basic foundations to the mathematical procedures used in the curricular units of course;
c) Interpret data, formulate and solve problems related to differential and integral calculus.

1.Real functions.
2.Differential calculus - definition, differentiation formulas, derivatives and its application (related rates, extreme values, extremum problems, graph of a function).
3.Integral calculus - indefinite integral, definite integral (calculation of an area of a region between two graphs, volume of a solid of revolution and length of a plane curve), improper integral.

Evaluation Methodology
Mid-term assessment: three written tests (0-4; 0-8; 0-8), with a minimum of 2,5 points in 8 points in the last two tests;
Final assessment: written exam (0-20).
Students will pass if they obtain a minimum grade of 10 points (out of a 0-20 scale).

- Carmo, M. (2005). Trigonometria-Números Complexos. Rio de Janeiro: SBM
- Stewart, J. (2002). Cálculo. (Vol. I). São Paulo: Pioneira Thomson Learning
- Larson, R. e Hostetler, R. e Edwards, B. (2006). Cálculo. (Vol. I). São Paulo: McGraw-Hill
- Monteiro, H. (2017). Apontamentos de Análise Matemática I. Abrantes: ESTA

Method of interaction
Presentation of theoretical contents followed by exercise solving under the teacher's supervision.

Software used in class