Academic Year/course:
2023/24
423 - Bachelor's Degree in Civil Engineering
28700 - Mathematics applied to engineering I
Syllabus Information
Academic year:
2023/24
Subject:
28700 - Mathematics applied to engineering I
Faculty / School:
175 - Escuela Universitaria Politécnica de La Almunia
Degree:
423 - Bachelor's Degree in Civil Engineering
ECTS:
6.0
Year:
1
Semester:
First semester
Subject type:
Basic Education
Module:
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1. General information
The basic mathematical methods which form part of the number of tools with which all engineers must count on to solve any problem that might appear on their work. The learning results include precisely the mastery of not only theoretical but also practical techniques, which allow the direct application of the methods considered in the subject to real problems, with realistic calculation methods that are incorporated in effective and proven softwarepackages.
It is therefore fundamental in the correct training of an engineer to obtain the learning results covered by this subject.
These approaches and objectives are aligned with the following Sustainable Development Goals (SDGs) of the United Nations Agenda 2030 (https://www.un.org/sustainabledevelopment/es/) so that such that the acquisition of the learning results of the subject provides training and competence to contribute to some extent to their achievement:
-Objective 4 Quality education.
2. Learning results
In order to pass this subject, the students shall demonstrate they have acquired the following results:
- Solve mathematical problems that may arise in Engineering.
- Have aptitude to apply the acquired knowledge of Linear Algebra and Analytic Geometry.
- Know how to use numerical methods in the solution of some mathematical problems.
- Know the reflexive use of symbolic and numerical calculation tools.
- Possess scientific-mathematical thinking skills that enable him/her to ask and answer certain mathematical questions.
- Be skilled in handling mathematical language, particularly symbolic and formal language.
3. Syllabus
The contents of the subject are:
Introduction to Maxima and review of real functions of real variables
Limits and Continuity
- Limits, indeterminacies, equivalences
- Continuity and discontinuity of functions
- Classical Theorems
- Bisection method
Referral
- Derivative and tangent line, properties
- Chain rule
- Implicit function derivative, inverse function and function in parametrics
- Newton's method
- Classical theorems: Rolle, average value, L' Hôpital
- Taylor's limited developments
- Interpolation and numerical derivation
- Monotonicity, maxima and minima, concavity and convexity
Integration
- Riemann integral and its basic properties
- Calculation of primitives
- Fundamental theorems of calculus
- Improper integrals Geometric applications
- Numerical quadrature methods
Systems of linear equations
- Groups, rings, bodies
- Systems of linear equations: elementary operations
- Gaussian elimination and rank of a matrix
- Characterization theorem for linear systems (Rouché-Frobenius)
- Determinants
- Numerical Gaussian elimination, condition number
- LU, QR and Cholesky decompositions
- Iterative methods
Vector spaces with scalar product
- Linear independence, dimension and basis
- Subspaces
- Scalar product
- Distances, angles and orthogonality
- Orthogonal systems and subspaces
- Projectors and optimal approximation theorem
Diagonalization
- Eigenvalues and eigenvectors
- Spectral decomposition and matrix functions
- Normal matrices
- Numerical calculation of eigenvalues
- Compatible matrices
- Decomposition into singular values
4. Academic activities
The activities to be developed in the subject are the following:
- Theoretical classes, in which the fundamental concepts that constitute the basic body of knowledge that must be learned in order to achieve the learning results listed below are presented. The theoretical concepts are complemented by detailed examples that illustrate how they work in a concretecontext.
- Practical classes, in which problems are proposed to be solved using the methods and concepts previously considered . Discussion, participation, cooperation and reflection are encouraged in these classes.
- Evaluation sessions, in which students are submitted to written tests on certain well-specified parts of the subject matter covered, or they publicly present the work done in groups proposed in the previous activity.
- Personal work, in which students dedicate time outside of class to study the concepts taught in class, solve problems analogous and/or complementary to those considered in class, solve problems analogous and/or complementary to those considered in class.
- Global evaluation test, which consists of a written test of the whole subject. There are two global tests, one for each official convocation, and both take place after the end of the classes and when the rest of the activities have been concluded and evaluated.
5. Assessment system
At the beginning of the subject the student will choose one of the following two assessment methodologies:
- A continuous assessment system, which will be carried out throughout the entire teaching period.
- A global assessment test, reflecting the achievement of the learning results, at the end of the teaching period period.
Continuous assessment system:
- Written tests: Individual exercises remain a reliable way to know if the student has the capacity to apply the methods under consideration. Two exams are distributed throughout the semester, each covering different parts of the syllabus, although they cannot always be mutually exclusive due to the nature of Mathematics.
The written tests comprise 80% of the total grade, divided into two tests with values of 40% and 40%. A minimum grade of 3 on each written test is required to continue with the continuous assessment.
- Participation controls: Some classes of problems are complemented with the elaboration of exercises analogous to those considered to be submitted for evaluation, similar to the previous tests but focused on more concrete and lower value problems. In this way, the collaboration of the students is evaluated, both among themselves and with the class discourse, and their involvement in the previous activities that lead to the resolution of these controls. The participation controls comprise 20% of the total grade, distributed in four controls with equal values. Students will be able to pass the course by progressive evaluation if the arithmetic average of of the written tests and the participation controls is a 5.
Global assessment test: In each of the two official examinations, a global test can be taken, which consists of a global written test comprising 100%. Thus, if a student has not been able to pass the written tests and the controls, they can opt through this test to achieve the highest grade. All students have right to this global test.