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Mathematics I

Mathematics I

Code	16466
Year	1
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	None.
Mode of delivery	Attendance
Work placements	Not applicable
Learning outcomes	The curriculum unit Mathematics I aims: >> Specific Objectives: 1. consolidate the most important concepts related to the study of real functions of one variable, namely: limits, continuity and differentiability; 2. introduce the notion of integral and some techniques of integration of real functions of one variable; 3. extend the concepts mentioned in 1. to functions of several variables. >> General objectives: 4. develop the ability to interpret a problem, model it and solve it with the appropriate mathematical knowledge and techniques; 5. develop the capacity of abstract and logical reasoning, and linguistic rigor.
Syllabus	1. Real functions of a real variable Brief topological notions Inverse and composition of functions Inverse trigonometric functions Limits and continuity 1.1 Differential calculus Definition of derivative. Geometric interpretation. Differentiability Derivative of the composite function and derivative of the inverse function Cauchy's rule Optimization 1.2 Integral Calculus Definition and properties of the Riemann Integral Primitive and integration techniques Fundamental Theorem of Calculus Applications 2. Functions with several real variables (Part I) Brief topological notions Domains and their geometric representation Limits and continuity Partial and directional derivatives. Derivative of the composite function. Chain rule Implicit function theorem Differentiability and tangent plane
Main Bibliography	1. Stewart, James (2013), Cálculo, - Volume I e II, Cengage Learning. 2. Azenha, A. e Jerónimo, M. A. (1995), Elementos de Cálculo Diferencial e Integral em R e Rn, McGraw-Hill. 3. Pires, C. (2001), Cálculo para Economistas, McGraw-Hill. 4. Carapau, Fernando (2014), Exercícios sobre Primitivas e Integrais, Edições Silabo. 5. Hoffmann, L. e Bradley, G. (2010), Calculus for Business, Economics, and the Social and Life Sciences, McGraw-Hill.
Language	Portuguese. Tutorial support is available in English.