Learning outcomes of the curricular unit (knowledge, skills and competences to be developed by the students)
To improve students competences in logics, linear algebra and analysis, to illustrate the application of Mathematics in different subjects. Objectives: acquisition of knowledge to solve simultaneous linear equations, to draw graphical regions bounded by curves, calculation of areas.
Syllabus
A - Topics on Linear Algebra and Analytic Geometry 1- Matrices: Definition of matrix; Algebra of matrices; Transposition; Invertible matrices; Rank of a matrix. 2-Determinants: Definition and properties; Calculation of 2nd and 3rd order determinants; Laplace Theorem; Inversion of matrices. Adjoint Matrix. 3- Linear equation systems: Linear Equation. Linear equation systems; Solution of a linear equation system; Discussion and solving of simultaneous linear equations. B - Integration 4-Primitivation: Definition of a primitive integral and properties; Techniques of primitives; Immediate Primitives; Primitivation by decomposition; Primitivation by parts; Primitivation of partial fractions; Primitivation by substitution; Primitivation of some types of irrational and transcendent functions 5-Integration: Integrals of Darboux and of Riemann; Functions Integrability; Calculation of integrals. Applications..
Demonstration of the syllabus coherence with the curricular unit's learning objectives
The syllabus presents theoretical Topics on Linear Algebra and Analytic Geometry and on Integration. Practical applications will lead to the fulfilment of the proposed objectives.
Teaching methodologies (including evaluation)
Class sessions: explanation in theoretical classes and demonstration in practical classes. Periodic evaluation through 2 written tests (T1 e T2), which may allow final exam exemption when (T1 + T2) / 2 >= 10 e T1 >= 8 e T2 >= 8. The enrollment in the 1st test is mandatory. Final exam consists on a written test.
Demonstration of the coherence between the teaching methodologies and the learning outcomes
The presentation of the theoretical concepts will take place in lecturing classes and its application with practical examples in practical classes. The extra-work beyond class hours, with tutorial support will lead to the accomplishment of the proposed objectives.
Bibliography (Mandatory resources)
AGUDO, F. D. (1996.)- Introdução à Álgebra Linear e Geometria Analítica. 3ª ed. Lisboa. AGUDO, F. D. -Análise Real. Vol. I. Escolar Editora. Lisboa. APOSTOL, T. (1967)- Calculus. J. Wiley. Ed. FERREIRA, M. ALBERTO & AMARAL. I( 2006.)- Primitivas e Integrais. 6ª Edição. Edições Sílabo. FERREIRA, M. ALBERTO e&AMARAL, I.( 2009) - Exercícios de Primitivas e Integrais; 5ª Edição. Edições Sílabo. FERREIRA, M. ALBERTO & AMARAL, I.( 2008.)- Álgebra Linear Matrizes e Determinantes 1º vol.; 7ª Edição. Edições Sílabo. FERREIRA, M. ALBERTO & AMARAL, I.( 2009)- Exercícios Álgebra Linear ¿ Matrizes e Determinantes 1º vol.; 4ª Edição. Edições Sílabo. FERREIRA, M. ALBERTO & AMARAL, I.( 2009.)- Álgebra Linear Espaços Vectoriais e Geometria Analítica 2º vol.; 4ª Edição. Edições Sílabo. FERREIRA, M. ALBERTO & AMARAL, I. (2013)- Exercícios Álgebra Linear Espaços Vectoriais e Geometria Analítica 2º vol.; 2ª Edição, Edições Sílabo.
