Mathematics II

Code	14715
Year	1
Semester	S2
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	Do not have.
Mode of delivery	Face-to-face instruction.
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	Chapter I – Real valued funtions of a real variable 1. Real numbers 2. Types of functions 3. Notion of limit; Lateral limits; Indeterminate forms of limits 4. Continuous functions 5. Fundamental properties of continuous functions Chapter II – Differential calculus 1. Definition of derivative 2. Derivation rules 3. Higher order derivatives 4. Applications Chapter III – Integral calculus 1. Definition of primitive2. Immediate primitives 3. Other primitivation techniques 4. Riemann’s integral 5. Fundamental theorem of calculus 6. Applications
Main Bibliography	Main Bibliography: – 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 Complementary Bibliography: – 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.