Academic Year/course:
2019/20
423 - Bachelor's Degree in Civil Engineering
28700 - Mathematics applied to engineering I
Syllabus Information
Academic Year:
2019/20
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:
---
1.1. Aims of the course
The foreseen outcomes of this signature are based on the following approaches and objectives:
The basic mathematical tools and their methods are part of the different tools that professional engineers need, to face and solve the different sort of problems they are going to find in the real life, therefore, among the learning outcomes, students are expected to get a good knowledge and capability for implementing numerical and analytical solutions using real calculus based on high quality softwares and computer programs. Taking this into account, this is the main reason why Engineering and Architectural students need to get the learning outcomes of this subject.
Successful students must be able to gather and implement the basic tools of this subject in any aspect related to the Engineering or Architectural area, making it into the basic tool for any other subject in their chosen degree and at the same time acquiring techniques that will improve and give them a successful professional development.
1.2. Context and importance of this course in the degree
This subject is part of the basic structure of academic knowledges required for the students to overcome with success this academic degree. It is being taught in the first semester in the first course with the main purpose of providing students new mathematical tools and skills that are going to be essentials in the good learning and successful study of the different subjects they are going to face with in higher courses, such as Physics, Economy, Statistics, among others.
The main focus of this subject is to provide students high capability and skill in the comprehension, implementation and right use of the mathematical tools in any engineering problem, giving the best solution and being able to explain with it the different observed phenomena.
1.3. Recommendations to take this course
It is advisable for the students to have a good knowledge of basic integral and differential calculus along with a reasonable capability and skill using symbolic and numerical softwares.
3. Assessment (1st and 2nd call)
4. Methodology, learning tasks, syllabus and resources
4.1. Methodological overview
The learning process designed for this subject is based on the following:
Strong interaction between the teacher and the student. This interaction is brought into being through a division of work and responsibilities between the students and the teacher. Nevertheless, it must be taken into account that, to a certain degree, students can set their learning pace based on their own needs and availability, following the guidelines set by the teacher.
The current subject "Matemática Aplicada a la Ingeniería I" is conceived as a stand-alone combination of contents, yet organized into two fundamental and complementary forms, which are: the theoretical concepts of each teaching unit and the solving of problems or resolution of questions, at the same time supported by other activities.
The organization of teaching will be carried out using the following steps:
- Theory Classes: Theoretical activities carried out mainly through exposition by the teacher, where the theoretical supports of the subject are displayed, highlighting the fundamental, structuring them in topics and or sections, interrelating them.
- Practical Classes: The teacher solves practical problems or cases for demonstrative purposes. This type of teaching complements the theory shown in the lectures with practical aspects. Here, students are expected to participate actively in the class throughout the semester.
- Individual Tutorials: Those carried out giving individual, personalized attention with a teacher from the department. Said tutorials may be in person or online.
Here, the practical and theoretical classes are combined with the continuous use of high quality free and open-source sotftwares, which allows a deeper comprehension and quick visualization of new mathematical tools and concepts.
Regarding to the slides, proposed exercise photocopies, laboratory session guides and other materials used in class, all of them are going to be available on the Moodle platforma of this subject.
Material |
Format |
Topic theory notes |
Paper/repositry |
Topic problems |
Topic theory notes |
Digital/Moodle, E-mail |
Topic presentations |
Topic problems |
Related links |
Educational software |
Open source Maxima and Octave |
4.2. Learning tasks
The programme offered to the student to help them achieve their target results is made up of the following activities:
Involves the active participation of the student, in a way that the results achieved in the learning process are developed, not taking away from those already set out; the activities are the following:
Face-to-face generic activities:
- Theory Classes: (2 ECTS: 20 h) The theoretical concepts of the subject are explained and illustrative examples are developed as support to the theory when necessary.
- Practical Classes: (1.77 ECTS: 17.7 h) Problems and practical cases are carried out, complementary to the theoretical concepts studied.
Generic non-class activities: (1.5 ECTS: 15 h)
- Study and understanding of the theory taught in the lectures.
- Understanding and assimilation of the problems and practical cases solved in the practical classes.
- Preparation of seminars, solutions to proposed problems, etc.
- Preparation of the written tests for continuous assessment and final exams.
The subject has 6 ECTS credits, which represents 150 hours of student work in the subject during the semester, in other words, 10 hours per week for 15 weeks of class.
A summary of a weekly timetable guide can be seen in the following table. These figures are obtained from the subject file in the Accreditation Report of the degree, taking into account the level of experimentation considered for the said subject is moderate.
Activity |
Weekly school hour |
Lectures |
6 |
Other activities |
3 |
Nevertheless, the previous table can be shown into greater detail, taking into account the following overall distribution:
- 52 hours of lectures, with 50% theoretical demonstration and 50% solving type problems.
- 8 hours of written assessment tests, one hour per test.
- 90 hours of personal study, divided up over the 15 weeks of the 1st semester.
There is a tutorial calendar timetable set by the teacher that can be requested by those students who are interested in tutorials.
4.3. Syllabus
Introduction to the open-source software Maxima and revision of real functions of real variables
Limits and Continuity of functions
- Limits, indeterminate forms, equivalence functions
- Continuity and discontinuity of functions
- Classical theorems
- Bisection method
The derivative
- The derivative, the tangent (straight) line, properties and rules
- The chain rule
- Implicit differentiation, inverse function and parametric functions
- Newton's Method
- Classical theorems: Rolle, Mean value and L'Hôpital
- Taylor polynomials and approximations
- Interpolation and numerical differentiation
- Monotonic function, increasing and decreasing functions, concavity and convexity of functions
Integration
- Riemmann Integral and its basic properties
- Antiderivatives and indefinite integration
- Fundamental theorems of Calculus
- Improper integrals
- Geometric applications
- Numerical integration
System of linear equations
- Groups, rings and fields
- System of linear equations: elementary operations
- Gaussian elimination and rank of a matrix
- Theorems of characterization (Rouché-Frobenius)
- Determinants
- Numerical Gaussian elimination, condition number
- Decompositions: LU, QR and Cholesky
- Iterative methods
Vector spaces with inner products
- Linearly independent sets, dimension and basis
- Subspaces of vector spaces
- Inner product
- Length, angles and orhtogonality
- Orthogonal subspaces and sets
- Orthogonal projection and optimal approximation
Diagonalization
- Eigenvalues and eigenvectors
- Spectral decomposition and polynomials of matrices
- Normal matrices
- Numerical methods for approximating eigenvalues
- Compatible matrices
- Singular value decomposition (SVD)
4.4. Course planning and calendar
The dates of the final exams will be those that are officially published at Distribución de exámenes.
The written assessment tests will be related to the following topics:
- Test 1: Limits and continuity.
- Test 2: The derivative.
- Test 3: Infinitesimal calculus.
- Test 4: System of linear equations.
- Test 5: Vector spaces.
- Test 6: Linear Algebra.
Week |
Topic |
Contents |
Test |
Weight |
Themes |
1 |
1 |
Maxima - functions |
First test |
5% |
Limits - Continuity |
2 |
2 |
Limits - Continuity |
3 |
3 |
The derivative |
Second test |
5% |
The derivative |
4 |
Taylor |
5 |
Interpolation |
6 |
4 |
Integration |
First written exam |
40% |
Infinitesimal calculus |
7 |
Applications |
8 |
Numerical integration |
9 |
5 |
System of linear equations |
Third test |
5% |
Linear systems |
10 |
Determinants |
11 |
Numerical Linear Algebra |
12 |
6 |
Vector spaces |
Fourth test |
5% |
Vector spaces |
13 |
Optimal approximation |
14 |
7 |
Diagonalization |
Second written exam |
40% |
Linear Algebra |
15 |
Singular value decomposition |