Mathematical Analysis II

Mechanical Engineering
6 ECTS; 1º Ano, 2º Semestre, 30,0 T + 30,0 TP + 4,50 OT

- Maria Helena Morgado Monteiro

Knowledge of differential calculus and integral calculus in R.

Develop the skills of students to interpret data, formulate and solve problems that occur in engineering and relate to:
a) Representation of functions by series and calculate approximate values;
b) The differentiation of functions;
c) The integral of functions with two or three variables.

1.Series: series of numbers and functions.
2.Differential calculus in Rn: partial derivatives; differentiability; maxima, minima and saddle points, Lagrange´s multipliers.
3.Multiple integrals:definition, properties, evaluation and applications of the double integral and the triple integral.

Evaluation Methodology
Mid-term assessment: three tests (0-20, 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).

- Larson, R. e Hostetler, R. e Edwards, B. (2006). Cálculo. (Vol. 2). São Paulo: McGraw-Hill
- Stewart, J. (2002). Cálculo. (Vol. 2). São Paulo: Pioneira Thomson Learning
- Costa, J. e Breda, A. (1996). Cálculo com funções de várias variáveis. Lisboa: McGraw-Hill
- Monteiro, H. (2016). Apontamentos de Análise Matemática II. Abrantes: ESTA

Method of interaction
Presentation of the theoretical contents. Worksheets solved in class under the teacher's supervision.

Software used in class
Productivity tools and eLearning platform.