Mathematics I

Secondary education mathematics – Scientific branch

Expository classes to present the formal bases of the curricular unit, with presentation of examples and applications, as well as the theoretical-practical classes, with resolution of exercises and monitoring of students. A moodle platform is used where the class transparencies are made available lectures, the workbook and the support sheets for each TP class; on this platform will be launched challenges throughout the semester in order to motivate students. Some software will also be used (Wolfram Alpha, Mathematica, Matlab and Moodle) for a complementary treatment of subjects studied.

Knowledge of the basics of mathematical analysis and comprehension and appliance of integral calculus on IR. Understanding the fundamental concepts of matrices. Solve and interpret real problems. The student is expected to be able to: Explain the concepts, discuss and present each problem solution in an appropriate way; Solve practical problems with an increasing autonomy; Find and select relevant information from different sources such as textbooks and the web.

1. Real Functions on IR – Hyperbolic functions; Inverse trigonometric functions.

2. Antiderivatives – Techniques of calculus by decomposition, parts and substitution, and of trigonometric and rational functions.

3. Integral Calculus on IR – Definite integral (Riemann’s integral); Fundamental theorem of calculus; Applications of integrals to the calculus of areas, volumes and length; Indefinite and improper integrals.

4. Linear Algebra – Matrices, Linear Equations Systems and Determinants.

NAO

1. Larson, R., Hostetler, R.P. e Edwards, B.H., Cálculo Vol. 1, McGraw-Hill, 2006, (Capítulos 1,2,3).
2. Rodrigues, R., Notas Teóricas de Análise Matemática, Departamento de Física e Matemática, Secção de
textos do ISEC (Capítulos 1,2,3).
3. Ferreira M.A.M. e Amaral, I., Álgebra Linear: Matrizes e Determinantes, Vol.1, Edições Sílabo, 2006,
(Capítulo 4).
4. Fidalgo, C., Álgebra Linear, Departamento de Física e Matemática, Secção de textos do ISEC (Capítulo 4).
5. Slides with theoretical part and book of exercises, Patrícia Santos, ISEC/DFM – moodle.
6. Practical sheets for practical classes and challenges, Pascoal Silva, ISEC/DFM, moodle.