Universidad Pública de Navarra - Nafarroako Univertsitate Publikoa
Public University of Navarre
| Course code: 240101 | Subject title: MATHEMATICS I | ||||
| Credits: 6 | Type of subject: Basic | Year: 1 | Period: 1º S | ||
| Department: Estadística, Informática y Matemáticas | |||||
| Lecturers: | |||||
| ASIAIN OLLO, MARÍA JOSÉ (Resp) [Mentoring ] | MILLOR MURUZABAL, NORA [Mentoring ] | ||||
Contents
Vector spaces
Linear applications
Matrices and systems of linear equations
Diagonalization of square matrices
Euclidean vector space
Diagonalization of symmetric matrices
Aproximate solutions
Decompositions based of eigenvalues
General proficiencies
- G8 Knowledge of basic and tecnological subjects to have the ability to learn new methods and theories, and versatility to adapt to new situations
- G9 Problem solving proficiency with personal initiative, decision making, creativity and critical reasoning. Ability to elaborate and communicate knowledge, abilities and skills in computer engineering
- T1 Analysis and synthesis ability
- T3 Oral and written communication
- T4 Problem solving
- T8 Self-learning
Specific proficiencies
- FB1 Ability to solve mathematical problems in engineering. Ability to apply theoretical knowledge on linear algebra, differential and integral calculus, numerical methods, numerical algorithms, statistics and optimization
- FB3 Ability to understand and master the basic concepts of discrete matemathics, logic, algorithmics and computational complexity, and their applications to problem solving in engineering
Learning outcomes
- RA1 - Solve systems of linear equations using different methods based on Matrix decompositions (LU, QR, generalized inverse).
- RA2 - Make matrix representations of plane and space transformations, proyections, and orthogonal proyections onto subspaces
- RA3 - Diagonalize matrices through fundamental subspaces.
- RA4 - Use matrix diagonalization to study stochastic processes (Markov chains).
- RA5 - Find the singular value descomposition of a given matrix and use it to approximate systems of linear equations by the pseudo-inverse matrix.
- RA6 - Find the least-squares polynomial approximation to a function.
- RA7 - Use some symbolic computation software such as Matlab or Mathematica.
Methodology
| Methodology - Activity | Attendance | Self-study |
| A-1 Lectures | 46 | |
| A-2 Practical clases | 14 | |
| A-3 Self-study | 75 | |
| A-4 Exam, evaluation tests | 5 | |
| A-5 Office hours | 10 | |
| Total | 75 | 75 |
Evaluation
| Learning outcome |
Assessment activity |
Weight (%) | It allows test resit |
Minimum required grade |
|---|---|---|---|---|
| RA1 - RA7 | Theoretical and practical exam concepts of vectorial space, linear application, matrices and systems of equations | 55 | Yes | |
| RA1 - RA7 | Theoretical and practical exam concepts of values and eigenvectors, diagonalization and approximation of solutions | 35 | Yes | |
| RA1 - RA7 | Tests at home and class | 10 | Yes |
Agenda
Lesson 1.- Sets, applications and relationships. Operations. Consistencies. Definitions of ring and body.
Lesson 2.- Vector spaces. Linear combinations. Linear dependence and independence. Vector subspaces. Bases and dimensions.
Lesson 3.- Linear applications. Core and image. Construction of linear applications.
Lesson 4.- Matrices. Elemental operations, range and form of Hermite. Matrix equivalence. Systems of linear equations: Rouché-Frobenius theorem. Generalized inverse.
Lesson 5.- Eigenvalues and eigenvectors. Diagonalization of square matrices.
Lesson 6.- Scalar product. Norm of a vector. Angle between two vectors. Euclidean vector space. Orthogonal and orthonormed bases. Orthogonal projection. Orthogonal matrices. Diagonalization of symmetric matrices.
Lesson 7.- Approximate solutions of a system of equations. Applications.
Bibliography
Access the bibliography that your professor has requested from the Library.
- J. Hefferon, Linear Algebra, Virginia Commonwealth University Mathematics 2009
- D. C. Lay, Linear Algebra and its applications, Pearson Education 2006
- D. J. S. Robinson, A course in Linear Algebra with applications, World Scientific
- R. A. Adams: Calculus. A complete course. Addison Wesley
- Larson, Calculus of a Single Variable, 10th Edition, Brooks/Cole, Cengage Learning 2014
- S.L. Salas, E. Hille and Etgen, Calculus, Reverté