Description

Theory
2

Theory/Practice
2

Instructors

Isabel Pinto

Contents

1. Matrices (CP1):
1.1 Definition and representation
1.2 Matrix operations. Properties
1.3 Elementary row and columns operations
1.4 Condensation of a matrix
1.5 Rank of a matrix; Gauss Elimination's Method (GEM)
1.6 Inverse matrix

2. Determinants (CP2):
2.1 Definition
2.2 Properties
2.3 Computation of the determinant
2.4 Laplace's theorem

3. Systems of linear equations (CP3):
3.1 Definition and matricial form
3.2 Cramer's Rule
3.3 Classification of systems in function of parameters

4. Real vector spaces (CP4):
4.1 Definition and properties
4.2 Subspaces
4.3 Base and dimension

5. Linear transformations (CP5):
5.1 Definition and properties
5.2 Matricial representation
5.3 Kernel and image
5.4 Eigenvalues and eigenvectors

6. Analytic Geometry (CP6):
6.1 Inner and cross products
6.2 Equations of line and of the plane
6.3 Metric and topologic problems

Learning Outcomes

OB1: Demonstrate proficiency in mathematical language, calculation methods, and problem-solving techniques.

OB2: Apply logical reasoning and critical thinking in the analysis of mathematical problems.

OB3: Develop abstraction and problem-structuring skills for mathematical problem solving.

OB4: Apply mathematical concepts and techniques to real-life and engineering problems.