Elements of Analysis and Algebra I
Code
10707
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Maria do Céu Cerqueira Soares
Weekly hours
6
Total hours
78
Teaching language
Português
Objectives
To provide the basis for some working knowledge of mathematical techniques (in the Linear Algebra and Analysis domains).
Prerequisites
The student must be familiar with mathematics taught at pre-university level in Portugal (science area).
Subject matter
Part I - Linear Algebra
1- Matrices: algebra of matrices, inverse of a matrix.
2- Systems of linear equations: resolution and discussion.
3- Determinants: definition and properties of determinant, inverse matrix calculation from the adjoint matrix, Cramer''''s rule.
4- Eigenvalues and eigenvectors: linear function, eigenvalues and eigenvectors of a matrix.
Part II - Analysis
1-Limits and continuity: limits and continuity of functions of one variable.
2-Differential calculus: derivative of a function, Taylor''s theorem and applications of Taylor''s formula.
3-Integral Calculus: antiderivatives, Riemann integral.
Bibliography
[1] Cabral, I. & Perdigão, C. & Saiago, C. - Álgebra Linear, Escolar Editora, 2008.
[2] Anton, H. & Rorres, C. - Elementary Linear Algebra, Applications version, 9th Edition, John Wiley & Sons, Inc., 2005.
[3] Lang, S. - A first course in Calculus. Springer-Verlag, 1986.
[4] Sá, A. & Louro, B. – Análise Matemática, Teoria e Exercícios (Departamento de Matemática da F.C.T-U.N.L).
Teaching method
In this course there are lectures (3 hours weekly) and solving-problems classes (3 hours weekly).
Students have, in advance, at their disposal a guide with all the theoretical and practical notes for classes.
There is also some office hours where each student can individually talk to and/or seek the help of the teacher.
Evaluation method
Conditions for evaluation admittance:
• for freshmen student - maximum of 3 unjustified absences to classes;
• for other students - maximum of 8 unjustified absences to classes.
Evaluation can be done through tests during classes period, or by final exam.
More details available in the portuguese version.