Discipline details

Course details

Recommended Prior Knowledge

Conhecimentos adquiridos na UC Matemática I das atuais licenciaturas.
Objectives

1. Understand what a matrix is, perform algebraic oper. and apply properties
2. Analyze the linear dependence/independence of the rows/columns of a matrix and calculate its rank
3. Solve and discuss systems of linear equations
4. Calculate the inverse of a matrix and apply properties
5. Understand the concept of determinant, calculate it and solve systems with Cramer's Rule
6. Understand the concept of real eigenvalue, eigenvector of a matrix and calculate them
7. Understand the dot, cross and scalar triple prod.between vectors and properties
8. Understand what a scalar and vector field is, determine domains and level sets of scalar fields defined in IR2 and IR3
9. Calculate limits and analyze the continuity of a scalar or vector field
10. Calculate partial, directional derivatives and analyze the differentiability of a scalar or vector field
11. Use the gradient for the directional derivative, the tangent plane, and the normal line, and calculate the divergence and curl
Teaching Methods

In theoretical-practical classes, the fundamental concepts of the different subjects of the syllabus are presented and the main results are demonstrated, with exercises also being solved that illustrate the topics covered; In this type of classes, students should acquire a global view of the themes and their interconnections. In practical classes, students will carry out, under the guidance of a teacher, a series of exercises, which will allow them to obtain a more in-depth understanding of the subjects covered.
Internship(s)

Não
Syllabus

1.Matrices
Def. and operations, inverse of a matrix. Linear depend./independence of rows and columns of a matrix, rank, elementary operations.
Systems of linear equations; matrix inversion
2.Determinants
Def., properties; computing methods. Inverse matrix with the adjoint matrix; Cramer's rule
3.Eigenvalues and Eigenvectors
Def.; computing eigenvalues and eigenvectors of a matrix
4.Vector Calculus
Dot product, length vector and properties. Angle between two vectors, orthogonal projection; orthogonal and orthonormal set of vectors.
Cross product and scalar triple product of vectors: properties and applications
5.Differential Calculus in IRn
Scalar and vector field; level curve/level surface. Limits, continuity of scalar and vector fields. Partial deriv., differentiability, directional
derivative and gradient vector of scalar fields; tangent plane and normal line. Differentiability, Jacobian matrix, and directional derivative of
vector fields; divergence and curl operators
Content Explanation

-
Methodology Explanation

-
Responsible Lecturer(s)

Patrícia Santos Ribeiro - 2.º Semester
Bibliography

Giraldes, E., Fernandes, V. H. e Smith, M. P. M.; Curso de Álgebra Linear e Geometria Analítica, McGraw-Hill, 1995. ISBN: 972-8298-02-1
Apontamentos e exercícios; elaborados por docentes do Departamento de Matemática (Disponíveis na página da UC no Moodle)
Luz, C., Matos, A. e Nunes, S.; Álgebra Linear (Volume I), ESTSetúbal/IPS, 2002. ISBN: ISBN 972-8431-16-9
Azenha, A. e Jerónimo, M. A.; Cálculo Diferencial e Integral em R e Rn, McGraw-Hill, Portugal, 1995, ISBN 972-8298-03-X., McGraw-Hill, Portugal, 1995. ISBN: 972-8298-03-X
Magalhães, L. T.; Álgebra Linear como introdução à Matemática Aplicada, Texto Editora, 1989. ISBN: 972-47-0007-0
Strang, G.; Linear algebra and its applications, Fort Worth: Saunders, 1988. ISBN: 0-15-551005-3 (Aconselhada a estudantes que não percebam português)
Apostol, T.; Calculus, Vol. II, Blaisdell Publishing Company, Massachusetts, 1969. ISBN: 0-471-00008-6 (Aconselhada a estudantes que não percebam português)
Laudesman, E. M. e Hestenes, M. R.; Linear Algebra for Mathematics, Science and Engineering, Prentice─Hall International, New Jersey, 1992. ISBN: 978-3-030-21323-7 (Aconselhada a estudantes que não percebam português; não está disponível na Biblioteca)