2024
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 IR 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 IR 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. Real functions of one variable.
3. Differential calculus.
4. Sequences and series of functions.
5. Integral calculus and applications.
2. Real functions of one variable.
3. Differential calculus.
4. Sequences and series of functions.
5. Integral calculus and applications.
Teaching Methods
Theoretical classes with exposition of the concepts, results and some of the respective demonstrations, as well as
examples of application; and theoretical-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.
The assessment of knowledge comprises two alternative aspects: evaluation by frequency and evaluation by
examination.
The frequency evaluation is composed of two tests carried out during the period, each of which weighs in the
final mark of 50%. In this evaluation aspect students can be required a minimum percentage of attendance to
theoretical classes.
The examination evaluation consists of a global exame, which will be carried out in the normal season and / or at the
appeal.
examples of application; and theoretical-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.
The assessment of knowledge comprises two alternative aspects: evaluation by frequency and evaluation by
examination.
The frequency evaluation is composed of two tests carried out during the period, each of which weighs in the
final mark of 50%. In this evaluation aspect students can be required a minimum percentage of attendance to
theoretical classes.
The examination evaluation consists of a global exame, which will be carried out in the normal season and / or at the
appeal.
Assessment
The assessment of knowledge comprises two alternative aspects: assessment by frequency and assessment by examination. The assessment by frequency is composed of two or more tests performed during the period, with 100/k (%) weight of each in the final grade. The evaluation by exam consists of a global exam, which will be carried out in the normal period and/or in the appeal period.