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Mathematical Calculation

Mathematical Calculation

Code	14025
Year	1
Semester	S2
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	Not applicable.
Mode of delivery	Face-to-face
Work placements	Not applicable
Learning outcomes	This course aims to promote the learning of mathematical concepts in the field of matrix and integral calculus, and the development of skills to enable students to understand and use mathematics as a tool to aid in solving practical problems. At the end of curricular unit, the student should be able to: understand the concepts of the continuity and differentiability of a Function of One Variable and apply the standard results about continuous and differentiable Functions of One Variable; solve problems involving the Integral Calculus of Functions of One Variable; apply the basic techniques of matrix algebra, including finding the inverse of an invertible matrix and calculating the Determinant of a matrix; solve Systems of Linear Equations by using Gaussian Elimination and Cramer Rule.
Syllabus	1. Functions of One Variable: Domain and Graph; Exponential and Logarithmic Function; Limits and Continuity; Differentiation: Rules; Cauchy Rule and Indeterminations; Weierstrass Theorem; Differential; Extreme Values; 2. Integration of Functions of One Variable: Indefinite Integral/Antiderivative; Integration Techniques; Applications of the Definite Integral; 3. The Set of Complex Numbers: Definition and Examples, Geometric Representation, Operations with Complex Numbers; 4. Systems of Linear Equations and Matrices: Introduction to Systems of Linear Equations; Gaussian Elimination; Matrix Operations; Inverse Matrix; Diagonal, Triangular and Symmetric Matrices; 5. Determinants: Determinant Function; Properties of the Determinants; Cramer Rule.
Main Bibliography	Azenha, A., Jerónimo, M. A. (1995), Elementos de Cálculo Diferencial e Integral em R e R^n, McGraw-Hill. Cabello, J. G. (2006), Álgebra Lineal. sus aplicaciones en Economía, Ingenierías y otras ciencias, Delta. Cabral, I., Perdigão, C., Saiago, C. (2009), Álgebra Linear, Escolar. Lay, D. C. (1999), Álgebra linear e suas aplicações, LTC. Hoffmann, L., Bradley, G. (2010), Calculus for Business, Economics, and the Social and Life Sciences, McGraw-Hill. Pires, C. (2001), Cálculo para Economistas, McGraw-Hill. Santos, R. (2010), Introdução à Álgebra Linear}, http://www.mat.ufmg.br/~regi/livros.html Stewart, J. (2013), Cálculo - Volume 1, Cengage Learning.
Language	Portuguese. Tutorial support is available in English.