Calculus I

Trigonometry and elementary geometry.
Study of real functions and their inverse.
Trigonometric functions.
Differential calculus.

In the theoretical classes the expository method is applied, for introductory explanation of the subject with exemplification through solving exercises to acquire basic knowledge.

In the remaining classes, the shared resolution, individual and / or group, of exercises that leads to the understanding and application of the syllabus and specific activities of synthesis and analysis is used.

On the MOODLE platform, documents, discussion forums, learning suggestions are available.

Use of free mathematical software (Geogebra, Symbolab e Photomath).

The main objective of the Curricular Unit is to promote the learning of the concepts of mathematics so that the student acquires a reasoning ability and skills that allow him to understand and use mathematics as an aid tool in the different subjects of the course.

At the end of the academic semester, students must, in each of the following aspects, be able to:

Knowledge – Describe the main results in the area of ​​basic training in mathematical analysis, namely in the domain of differential and integral calculus, numerical series and differential equations. Identify the techniques to be used in problem solving;

Understanding – Build an appropriate attitude and thinking to solve Engineering problems;

Application – Develop a solid training base for later disciplines, which allows the correct use of techniques and the rigorous formulation of problems.

1. Real functions of one real variable.
Limit and continuity, basic theorems, trigonometric and inverse trigonometric functions, basic properties of the logarithm and the exponential.

2. Differential calculus on R.
Derivation: definitions and calculus rules. Linear interpolation (Taylor’s polynomial). 

3. Root determination of non-linear equations.
Bisection and Newton-Raphson methods. 

4. Antiderivative.
Antiderivative definition and basic rules.

5. Integral calculus on R.
Definite integral (Riemann’s integral) and the fundamental theorem of calculus. Applications of integration to the calculation of area, volume and length of planar curves. Numerical integration: trapezoidal rule and Simpson’s rule.

6. Indefinite integrals and improper integrals.
Definition and convergence analysis of improper integrals.

7. Integration techniques. 
Integration by parts, integration of rational functions, integration of trigonometric functions and integration by substitution. 

8. Series.
Numerical series: convergence definition and criteria. Power series.

Periodic Evaluation:

Assessment consists of two written tests, with minimum marks required in both:

- Test 1 will cover Chapters 1 to 5 and will be graded out of 11 points (with a minimum of 3 required);

- Test 2 will focus on Chapters 6 to 8 (as well as the contents of previous chapters essential to understanding those ones), and will be graded out of 9 points (with a minimum of 2.5 required).

The final classification will be the sum of the classification obtained in both tests.

The distributed evaluation will replace the exam of the normal season.

At appeal season, the student in periodic evaluation may choose to perform only one of the tests, preserving the marks obtained on the tests realized during the semester.

Assessment by Exam:

The exam (normal season or appeal season) consists of two parts, corresponding to the subjects of each test, with the mandatory minimums being applied in each of the parts. 

Remarks:

1 - The student obtains approval in the curricular unit whenever the final classification is greater than or equal to 9.5 points and minimums in both parts (3 points in Part I and 2.5 points in Part II).

2 - In the assessment tests and exams, students can not use a cell phone, calculator or any other communication device. The only authorized documents are the Tables of Mathematics (DFM) and Form provided on the Curricular Unit.

3 - In Test 1 / Exam (normal or appeal season) the student may choose to replace the question referring to Chapter 1 (worth 2 points) for modality A or B, provided that is completed before the respective test:

- A: 20h in person at CeAMatE, to carry out the Individual Work Plan and test;

- B: 10h in person at CeAmatE, for presentation/validation of autonomous fulfillment of the Individual Plan Work and test.

4 - The assessment methods may change, if the extraordinary conditions so justify.If the assessment is not in person, students who obtain more than 9.5 points are subject to an oral test to validate the classification.

NAO