## Public University of Navarre

CastellanoEuskara | Academic year: 2024/2025 | Previous academic years:  2023/2024  |  2022/2023
 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 ]

Partes de este texto:

### Module/Subject matter

Module: Basic training

Subject matter: Mathematics

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### 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

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### 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

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### 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

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### 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.

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### 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

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### Evaluation

Learning
outcome
Assessment
activity
Weight (%) It allows
test resit
Minimum
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

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### 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.

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### 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
• Larson, Calculus of a Single Variable, 10th Edition, Brooks/Cole, Cengage Learning 2014
• S.L. Salas, E. Hille and Etgen, Calculus, Reverté

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### Languages

English, Spanish and Basque.

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