Mathematical Analysis I

Mechanical Engineering, Publication in the Diário da República - Despacho nº 14312/2015 - 02/12/2015

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

Lecturer
- Maria Helena Morgado Monteiro

Prerequisites
High-school level mathematics.

Objectives
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.

Program
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: two written tests (0-20 points, with a minimum of 5 points);
Final assessment: written exam (0-20 points).
Students pass if they obtain a minimum grade of 10 points (out of a 0-20 scale).

Bibliography
- Monteiro, H. (2019). Apontamentos de Análise Matemática I. Abrantes: ESTA
- Stewart, J. (2012). Calculus. Belmont, USA: Brooks/Cole, Cengage Learning
- Edwards, B. e Hostetler, R. e Larson, R. (2006). Cálculo. (Vol. I). São Paulo: McGraw-Hill
- Carmo, M. (2005). Trigonometria-Números Complexos. Rio de Janeiro: SBM

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

Software used in class
Excel; PowerPoint