Description

Theory
1

Theory/Practice
2

Instructors

Stella Abreu

Contents

1. MATRICES (CP1)
Definition and representation. Basic concepts about matrix.
Matrix operations. Properties.
Elementary row and columns operations. Matrices equivalency. Condensation of a matrix.
Rank of a matrix; Gauss Elimination's Method (GEM).
Inverse of a matrix; computation by Gauss-Jordan method.
Matrix equations
 

2. DETERMINANTS (CP2)
Evaluating 2nd and 3rd order determinants by Sarrus' Rule.
Laplace's Theorem. Evaluating determinants of any finite order.
Properties.
Inverse matrix by adjoint matrix
 

3. SYSTEMS OF LINEAR EQUATIONS (CP3)
Matrix notation.
Discussion and resolution of systems of linear equations.
The Cramer's rule. Homogeneous systems
 

4. REAL VECTOR SPACES (CP4)
Definition and properties.
Subspaces.
Linear combinations. Generated subspace. Linear dependence.
Basis and dimension.
 

5. ANALYTIC GEOMETRY (CP5)
Inner and cross products.
Equations of line and of the plane.
Metric and topologic problems

Learning Outcomes

The purpose of this subject is to give the mathematical techniques that are required in the Geotechnical and Geoenvironmental engineering degree.
It is expected that students develop ability for mathematical and abstract thinking;
It is also expected that students use the mathematical concepts learned in solving problems.
At the end of the semester, it is expected the students are able to:
- perform the elementary operations with matrices and reduce any matrix to the row echelon form (OB1);
- compute determinants (OB2);
- use matrices and determinants to solve and discuss systems of linear equations (OB3);
- identify and work in vector spaces (OB4);
- compute inner product, cross product and mixed product of vectors, define equations of lines and planes and their intersections, compute relative positions and distances between lines, planes, lines and planes in the tridimensional space (OB5).