Linear Algebra and Analytical Geometry
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2006/2007 - 1S
Cycles of Study/Courses
Teaching language
Portuguese
Objectives
This discipline has two main objectives: the promotion of logical reasoning and methods of analysis and the introduction and theoretical development of a set of concepts that will be fundamental to support the study of other disciplines along this course of studies.
Program
Vector Algebra - The vector space of n-uples of real numbers. The dot product. Norm of a vector. Orthogonality and angle between two vectors. The linear span of a finite set of vectors. Linear independence and dependence. Bases and dimension in vector spaces. The cross product. The scalar triple product. Applications of Vector Algebra to Analytic Geometry - Lines in n-space. Properties of straight lines. Lines and vector valued functions. Linear Cartesian equations for straight lines. Planes in n-space. Properties of planes. Normal vectors to planes. Planes and vector valued functions. Linear Cartesian equations for planes. Geometric applications to three-dimensional space. Matrices - Algebraic operations. Transpose of a matrix. Square matrices: definitions and special properties. Rank of a matrix. Inverse of a square matrix. Determinants - Definition and properties. Minors and cofactors. The Laplace theorem. Computation of determinants. The determinant of the inverse of a non-singular matrix. Evaluation of the rank of a matrix with determinants. Krönecker?s theorem. Systems of Linear Equations - Gauss and Gauss-Jordan methods.
Linear Spaces - Definition and properties. Subspaces of a linear space. Dependent and independent sets in a linear space. Bases and dimension. Inner products. Euclidean spaces. Norms and orthogonality. Linear Transformations and Matrices - Definition. Null space and range. Nullity and rank. Algebraic operations. Inverses. One-to-one linear transformations. Matrix representation of linear transformations. Matrices representing the same linear transformation. Similar matrices. Eigenvalues and Eigenvectors - Definition and properties. Linear transformations with similar diagonal matrix representations.
Mandatory literature
Apostol, Tom M.;
Calculus. ISBN: 84-291-5001-3
Barbosa José Augusto Trigo;
Noções sobre matrizes e sistemas de equações lineares. ISBN: 972-752-069-3 972-752-065-0
J.A. Trigo Barbosa; ; ALGA - Apontamentos Teórico-Práticos , N (Obra a adquirir na reprografia da FEUP)
J.A. Trigo Barbosa, J.M.A. César de Sá, A.J. Mendes Ferreira;; ALGA - Exercícios Práticos , N (Obra a adquirir na reprografia da FEUP)
Teaching methods and learning activities
Theoretical classes: detailed exposition of the program of the discipline illustrated by application examples. Theoretical-practice classes: application of the theoretical concepts in the resolution of several exercises that can be found in the proposed literature.
Evaluation Type
Distributed evaluation without final exam
Assessment Components
Description |
Type |
Time (hours) |
Weight (%) |
End date |
Subject Classes |
Participação presencial |
56,00 |
|
|
|
Exame |
2,00 |
|
2007-01-05 |
|
Exame |
2,00 |
|
2007-02-09 |
|
Total: |
- |
0,00 |
|
Eligibility for exams
See art. 4º of ?Normas Gerais de Avaliação?, which is a FEUP document.
Calculation formula of final grade
Average mark of both mini-tests
Examinations or Special Assignments
Not applicable
Special assessment (TE, DA, ...)
Not applicable
Classification improvement
Not applicable