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Be English-friendly or any other language-friendly means that UC is taught in a language but can either of the
following conditions:
1. There are support materials in English / other language;
2. There are exercises, tests and exams in English / other language;
3. There is a possibility to present written or oral work in English / other language.
1
6.0
0.0 h/sem
54.0 h/sem
0.0 h/sem
0.0 h/sem
0.0 h/sem
0.0 h/sem
1.0 h/sem
55.0 h/sem
95.0 h/sem
0.0 h/sem
150.0 h/sem
Since year
2017/2018
Pre-requisites
The students should be familiar with the main concepts and techniques concerning the topics "Sequences of real numbers" and "Functions of a real variable", as studied in (the Portuguese) high school. In particular: limits, monotonicity, continuity and differentiability. The students are also expected to have experience in manipulating polynomials and dealing with trigonometric functions, the exponential function and the logarithmic function.
Objectives
Learn the fundamental concepts of one variable differential and integral calculus which are essential to the formulation and resolution of engineering problems. Apply basic techniques and methodologies of mathematical analysis to the natural and computer sciences.
Program
PC1. Differential calculus. 1. Continuity. 2. Derivatives and differentiability. 3. Chain rule and inverse function theorem. 4. Taylor's formula. 5. Applications. PC2. Antiderivatives. 1. Basic antiderivatives. 2. Rational functions. 3. Integration by parts. PC3. Integral calculus. 1. The notion of integral. 2. The fundamental theorem of calculus. 3. Change of variables formula. 4. Improper integrals. PC4. Series. 1. The notion of series. 2. Geometric series. 3. Some convergence criteria. 4. Power series. PC5. Ordinary differential equations (ODEs) 1. Separation of variables. 2. First order linear ODEs. 3. Power series solutions.
Evaluation Method
A student must obtain an overall grade of at least 10 (out of 20) in one of the assessment modes: -Continuous assessment: Weekly online Mini-tests (10%), 2 written tests (45% each one with minimal grade of 8 values); -Exam assessment: in any of the exam seasons (100%). A student that obtained the minimal grade in the first test may nonetheless choose, in the regular exam season, to be evaluated by exam. Pay attention (below) to additional remarks about the Continuous assessment.
Teaching Method
The lectures are of theoretical and practical nature according to the following learning methodologies (LM): LM1. Exposition and discussion. LM2. Problem solving. LM3. Self-study, according to the autonomous work by the student, in accordance with the weakly class planning. Besides participating in the classes, the student is expected to spend from 4 to 6 hours per week in autonomous activities, such as reading the indicated text book and solving exercises/problems and Online Mini-tests.
Observations
Additional rules about the Continuous assessment: 1 - There are weekly Mini-tests which are performed along the semester using the e-learning platform. Each test has a maximum duration of 30 minutes, is available for a full week and is focused on the course materials lectured in the previous week(s). A missing online Mini-test implies a null grade in the corresponding assessment moment. The final grade in the online Mini-tests component is computed after discarding the two worst grades. The grade corresponding to this component will then be the average of the remaining Mini-tests. 2 - Eventual problems in the access to the e-learning platform won't change the deadlines of any of the Online Mini-tests. So, the students are therefore encouraged to perform the Online Mini-tests as soon as they are available. 3 - A student is excluded from the Continuous assessment mode (automatically enters the exam assessment mode) if any of the following conditions apply: (i) Missing four or more Online Mini-tests; (ii) Missing or getting a test grade below 7.5 values; (iii) Getting caught in an academic fraud attempt.
Basic Bibliographic
1 - Cadernos de apoio à cadeira, da autoria de João L. Costa, Rosário Laureano e Sérgio Mendes, a disponibilizar na página de e-learning da cadeira. 2 - Strang, G; "Calculus", Wellesley-Cambridge Press.
Complementar Bibliographic
1 - Campos Ferreira, J.; "Introdução à Análise Matemática", Fundação Calouste Gulbenkian. 2 - Girão, Pedro Martins; "Introdução à Análise Complexa, Séries de Fourier e Equações Diferenciais", IST press.
