2025
Mathematical Analysis I
Name: Mathematical Analysis I
Code: MAT12877L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Regime de Frequência: Presencial
Presentation
In this course, the knowledge of mathematical analysis essential for the formation of students is addressed.
Sustainable Development Goals
Learning Goals
The intended learning outcomes of the curricular unit are the following:
Learn the basics of Mathematical Analysis;
Know how to apply the main concepts acquired and make rigorous demonstrations, justifying the several steps;
Know how to formulate a problem mathematically and identify and implement strategies appropriate to its analytical
resolution;
Master the main concepts and tools of differential and integral calculus in R and know how to apply them in the
different contexts of the curricular units of the specialty that this curricular unit serves;
Demonstrate analysis, calculation and deductive reasoning skills;
To develop the abstract reasoning.
The skills and competencies developed in the curricular unit are the following:
Ability to understand and solve mathematical problems;
Construction of mathematical models;
Abstraction skills;
Creative intuition and critic capability
Spoken and written capability to solve and explain the results.
Learn the basics of Mathematical Analysis;
Know how to apply the main concepts acquired and make rigorous demonstrations, justifying the several steps;
Know how to formulate a problem mathematically and identify and implement strategies appropriate to its analytical
resolution;
Master the main concepts and tools of differential and integral calculus in R and know how to apply them in the
different contexts of the curricular units of the specialty that this curricular unit serves;
Demonstrate analysis, calculation and deductive reasoning skills;
To develop the abstract reasoning.
The skills and competencies developed in the curricular unit are the following:
Ability to understand and solve mathematical problems;
Construction of mathematical models;
Abstraction skills;
Creative intuition and critic capability
Spoken and written capability to solve and explain the results.
Contents
1. Sequences and series
2. Limits and continuity of real functions of one real variable
3. Differential Calculus in R
4. Integral Calculus in R
2. Limits and continuity of real functions of one real variable
3. Differential Calculus in R
4. Integral Calculus in R
Teaching Methods
Theoretical classes with exposition of the concepts, results and some of the respective demonstrations, as well as examples of application; and practical classes, where theoretical and theoretical-practical exercises are solved in which the concepts taught in theoretical classes are applied. Special emphasis is given to problems that link the tools developed with the concepts studied, and lists of exercises are available for an effective follow-up and consolidation of the presented knowledge. Several schedules of attendance are available to the students, for the clarification of doubts and personal accompaniment.
Assessment
Continuous assessment consists of two tests (with a minimum required grade of 7 out of 20) and four mini-tests, carried out during the teaching period. The final grade is given by MF = (0.85) Mfreq + (0.15) Mt, where Mfreq is the arithmetic mean of the grades obtained in the two tests, and Mt is the arithmetic mean of the three mini-tests with the highest grades. Assessment by examination consists of a comprehensive written examination, which may be taken during the regular examination period and/or the resit examination period. In all examination periods, obtaining a grade higher than 17 in the written examination requires the student to take an oral examination. If the oral examination is not taken, the final grade will be capped at 17. Due to the nature of the examinations, any student may be required to take an oral examination.
Accreditations and Certifications
