Mathematics I

Lectures presentation of the formal bases of the course, with the presentation of examples and applications,
and practical classes. It uses a platform moodle – virtual lab math (lvm) – where are all the acetates of lectures
and support worksheets every lesson TP. Regarding the assessment students can opt for a final exam, worth
20 values, or the following method of distributed evaluation: A. Test 1 with 6 values; B. Test 2 with 3 values; C.
Final exam with 11 values. The final grade will be the grade of A + B + C. Students that opt for distributed
evaluation need a minimum of 75% attendance in practical classes taught. The completion of the first test
assumes that the student has opted for distributed evaluation.

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