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Mathematics for Informatics II

Mathematics for Informatics II

Code	6623
Year	1
Semester	S2
ECTS Credits	6
Workload	PL(30H)/TP(60H)
Scientific area	Mathematics
Entry requirements	Do not have.
Mode of delivery	Face to face
Work placements	Not applicable
Learning outcomes	The main goals of this course are to deepen knowledge in calculus, taking into account the knowledge previously acquired in secondary education in mathematics B. - Identify a function; - Calculate the limit of a function at a point; - Identify and solve indeterminate forms of limits; - Identify continuous functions and recognize their properties; - Calculate the derivative (or one of the lateral derivatives) of a function at a given point; - Identify the absolute and relative extrema of a function at a point; - Calculate the antiderivative of a function with the adequate technique; - Calculate integrals using the Fundamental Theorem of Calculus.
Syllabus	1. Functions of a Real Variable 1.1 Definitions 1.2 Limits of Functions 1.3 Continuity 1.4 Important Theorems 2 Differential Calculus 2.1 Definition of Derivative 2.2 Derivatives of Higher Order 2.3 Application of Derivatives 3 Integral Calculus 3.1 Primitives 3.2 Integrals 3.3 Improper Integrals 4 Sequences 4.1 Definition 4.2 Arithmetic Progression and Geometric Progressions 4.3 Principle of Mathematical Induction 4.4 Bounded Sequences 4.5 Convergence Criteria 5 Series 5.1 Definition of Sum 5.2 Non-negative Series 5.3 Alternating Series 5.4 Convergence tests 6 Introduction to the Theory of Probability
Main Bibliography	Bibliografia principal: – Apostol, T.M., Cálculo, Vol. 1, Reverté, 1993 – Stewart, J., Calculus (International Metric Edition), Brooks/Cole Publishing Company, 2008 – Swokowski, E. W., Cálculo com Geometria Analítica, Vol. 1 e 2, McGrawHill, 1983 Bibliografia secundária: – Dias Agudo, F.R., Análise Real, Vol. I, Escolar Editora, 1989 – Demidovitch, B., Problemas e Exercícios de Análise Matemática, McGrawHill, 1977 – Lang, S., A First Course in Calculus, Undergraduate texts in Mathematics, Springer, 5th edition – Lima, E. L., Curso de Análise, Vol. 1, Projecto Euclides, IMPA, 1989 – Lima, E. L., Análise Real, Vol. 1, Colecção Matemática Universitária, IMPA, 2004 – Mann, W. R., Taylor, A. E., Advanced Calculus, John Wiley and Sons, 1983 – J. P. Santos, Cálculo numa Variável Real, IST Press, 2013 – Sarrico, C., Análise Matemática – Leituras e exercícios, Gradiva, 3a Ed., 1999
Language	Portuguese. Tutorial support is available in English.