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
Manuel Messias Rocha de Jesus
Weekly hours
6
Total hours
71
Teaching language
Português
Objectives
The student is supposed acquire basic knowledge on differential and integral calculus for functions of one real variable and on Linear Algebra and Analytical Geometry on |R2 and |R3 (vide Program). In that learning process are developed, logical reasoning and critical mind .
Prerequisites
The student must be familiar with mathematics taught at pre-university level in Portugal (science area).
Subject matter
Linear Algebra
1-Analytic Geometry: vectors, inner product, orthogonal projection, lines and planes, distance from points to lines and planes.
2-Systems of linear equations: resolution and discussion.
3-Matrices: algebra of matrices, inverse of a matrix.
4-Determinants: definition and properties of determinant, inverse matrix calculation from the adjoint matrix, Cramer''''s rule.
5- Eigenvalues and eigenvectors: linear function, eigenvalues and eigenvectors of a matrix.
Analysis
1-Limits and continuity: sequences of real numbers, limits and continuity of functions of 1 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] Blyth, T. S. & Robertson, E. F. - Basic Linear Algebra, Springer Verlag, 1998.
[3] Anton, H. & Rorres, C. - Elementary Linear Algebra, Applications version, 9th Edition, John Wiley & Sons, Inc., 2005.
[4] Sá, A. & Louro, B. – Análise Matemática, Teoria e Exercícios. (Departamento de Matemática da F.C.T-U.N.L.)
[5] Sá, A. & Louro, B. – Sucessões e Séries, Teoria e Prática. Escolar Editora, 2008.
Teaching method
Lectures and problem-solving classes.
Evaluation method
There are two possible types of evaluation: evaluation by tests or by a final exam.
Evaluation by tests - this type of evaluation is more suitable for students that want to do a progressive learning and a progressive evaluation process.
This evaluation consists of 3 tests, each test with the maximum classification of 20. Only the students with more than two thirds of presences in the problem-solving sessions (aulas práticas), until the test date, are admitted.
Final results:
1. The final grade is the average of the arithmetic sum of the 3 grades obtained in each test; if the grade of the last test is not lower than 7. For a grade lower or equal to 9.4, the student is admitted to the evaluation by final exam.
2. For grades between 9.5 and 16.4, students are approved.
3. For grades above 16.5, the final grade is 16, unless the students have decided to be submitted to a supplementary evaluation to decide the final grade.
Evaluation by final exam – this type of evaluation can be used by all students that have failed in the evaluation by tests and that have more than two thirds of presences in the problem-solving sessions (aulas práticas), until the exam date.
For exam grades lower or equal to 9.4, students have failed. For exam grades above 9.5 the students are approved and the final grade is obtained by the same process described in the previous sections, points 3 and 4.
More detailed rules are available in the Portuguese version.