1. General information
Course:
MATHEMATICAL AND COMPUTATIONAL TOOLS FOR CIVIL ENG
Code:
38301
Type:
BASIC
ECTS credits:
6
Degree:
345 - UNDERGRADUATE DEGREE PROGRAMME IN CIVIL ENGINEERING
Academic year:
2022-23
Center:
603 - E.T.S. CIVIL ENGINEERS OF CR
Group(s):
20
Year:
1
Duration:
First semester
Main language:
Spanish
Second language:
English
Use of additional languages:
English Friendly:
Y
Web site:
Bilingual:
N
Lecturer:
GABRIEL FERNANDEZ CALVO
- Group(s):
20
Building/Office
Department
Phone number
Email
Office hours
Politecnico 2-D31
MATEMÁTICAS
6218
gabriel.fernandez@uclm.es
Lecturer:
CRISTINA SOLARES MARTINEZ
- Group(s):
20
Building/Office
Department
Phone number
Email
Office hours
Edificio Politécnico/2-D32
MATEMÁTICAS
3255
cristina.solares@uclm.es
2. Pre-Requisites
Students must have basic knowledge and competences in mathematics and information and communication technologies, which are assumed to be guaranteed by the training they have obtained prior to their access to the University.
3. Justification in the curriculum, relation to other subjects and to the profession
|
In this course, mathematical and computer concepts are studied. They constitute an essential part of the training of a future engineer. Topics of Geometry, Numerical Methods, Computer Programming and Optimization are addressed, which are basic for the proper development of subsequent subjects of the Degree such as: Mathematical Instruments for Engineering II, Differential Equations, Hydraulic Engineering, Structures Calculation, Graphical-Cartographic Expression in Engineering, etc. This course will provide students with a useful toolbox of techniques, both analytical and computational, which are essential to solve a large number of engineering problems employing mathematical methods. Additionally, it will help the student understand the underlying elements of commercial software that will be used during the later professional activity, enabling the future engineer to use them critically.
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4. Degree competences achieved in this course
| Course competences | |
|---|---|
| Code | Description |
| CE01 | Students can apply their knowledge in the practical solution of civil engineering problems, with capacity for the analysis and definition of the problem, the proposal of alternatives and their critical evaluation, choosing the optimal solution with technical arguments and with capacity of defense against third parties. |
| CE02 | Students have the ability to broaden their knowledge and solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their area of study. Self-study ability, to undertake further studies with a high degree of autonomy |
| CE04 | Students have the ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential and partial derivative equations; numerical methods; numerical algorithms; statistics and optimization. |
| CE06 | Students have a basic knowledge of the use and programming of computers, operating systems, databases and software with engineering application. |
| CG01 | Students achieve general knowledge of Information and Communication Technologies (ICT). |
5. Objectives or Learning Outcomes
| Course learning outcomes | |
|---|---|
| Description | |
| Students know the fundamentals and applications of Affine and Euclidean Geometry. | |
| Students know the fundamentals and applications of Optimization in the field of civil engineering. | |
| Students are familiar with computer use: operative systems, databases, programming languages, and software applied to civil engineering. | |
| Students are able to express correctly both orally and in writing and, in particular, they can use the language of mathematics as a way of expressing accurately the quantities and operations in civil engineering. Students get used to teamwork and behave respectfully. | |
| Students use mathematical and computer tools to pose and solve civil engineering problems. | |
| Students learn the most important approximations for numerical method resolution, use some statistical, data processing, mathematical calculation and visualization software packages at user level, develop algorithms and program using a high-level programming language, visualize functions, geometric shapes and data, design experiments, analyze data, and interpret results. | |
| Additional outcomes | |
| Not established. |
6. Units / Contents
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Unit 1: INTRODUCTION TO PROGRAMMING. SYMBOLIC COMPUTATION WITH MATLAB
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Unit 1.1: Introduction. Starting in Matlab.
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Unit 1.2: Algebra and Calculus with Matlab. Variables. Arithmetic operations. Elementary functions. Definition of functions. Creating vectors and matrices with Matlab. Mathematical operations with vectors and matrices. Operations with matrices. Equations and systems of equations. Limits of functions. Derivatives. Integrals. Series.
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Unit 1.3: Graphics with Matlab. Two-dimensional plots. Three-dimensional plots.
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Unit 1.4: Programming in Matlab. Relational and logical operators. Loops. Conditional statements. Importing and exporting data. Applications.
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Unit 2: NUMERICAL METHODS WITH MATLAB
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Unit 2.1: Numerical Solution of Linear Systems. Using MATLAB for solving linear systems of equations. Direct methods: Gauss and LU decomposition. Iterative methods.
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Unit 2.2: Numerical Solution of Nonlinear Equations. Using MATLAB for solving nonlinear equations. Bisection, regula falsi, Newton-Raphson and secant methods.
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Unit 2.3: Polynomial Interpolation. Using MATLAB for data interpolation. Lagrange polynomials. Cubic splines.
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Unit 2.4: Numerical Differentiation and Integration. Using MATLAB to numerically evaluate derivatives and integrals. Finite difference formulas. Numerical quadrature. Trapezoidal and Simpson rules.
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Unit 3: ANALYTIC GEOMETRY
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Unit 3.1: Affine and Euclidean Geometry in the Plane. Affine plane. Points and vectors. Coordinate system. Transformation of the coordinate system. The straight line. Equations of the straight line. Relative positions of two straight lines. The Euclidean plane. Distances in the Euclidean plane. Angle of two straight lines. Families of lines. Concurrent lines. Area of a triangle. Bisectors of two lines. Calculation of geometric places.
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Unit 3.2: The circle. Equation of the circle. Lines tangent to a circle. Circle through three points. Power of a point with respect to a circle. Radical axis. Calculation of locus.
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Unit 3.3: Conics. Definition and equations. Metric invariants of conics. Metric classification. Lines tangent to conics. Center and asymptotes. Vertices, foci and directrices. Focal equation of a conic. Standard form equation. The ellipse. The hyperbola. The parabola. Rotations and general equation of second degree. Calculation of locus.
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Unit 3.4: Affine and Euclidean Geometry in the space. The affine space. Points and vectors. Coordinate systems. Transformation of the coordinate system. The plane. Equations of the plane. The straight line. Equations of the straight line. Relative position of straight lines and planes. The euclidean space. Distances in the euclidean space. Area of a triangle. Angle of two straight lines. Angle of straight and a plane. Angle of two planes.
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Unit 3.5: Quadric surfaces. The quadratic surfaces. Classification of the second degree surfaces. Invariant. Ellipsoid. Hyperboloid of a leaf. Hyperboloid with two leaves. Elliptical cone. Elliptic paraboloid. Hyperbolic paraboloid. Elliptical, parabolic and hyperbolic cylinder. Representation of the quadrics.
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Unit 4: OPTIMIZATION WITH GAMS
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Unit 4.1: The Gams tool. Introduction. Definition of sets. Data entry: scalars, vectors and matrices. Variables. Equations. Models and resolution.
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Unit 4.2: Linear Programming and Applications. Introduction to linear programming. Models and examples of linear programming: the transport problem, the network flow problem, etc .; Problem formulation. Linear programming problem in standard form. Basic solutions. Duality. Resolution of linear programming problems. Examples of linear programming in GAMS.
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7. Activities, Units/Modules and Methodology
| Training Activity | Methodology | Related Competences (only degrees before RD 822/2021) | ECTS | Hours | As | Com | Description | |
| Class Attendance (theory) [ON-SITE] | Lectures | CE01 CE04 CE06 | 1.32 | 33 | N | N | ||
| Class Attendance (practical) [ON-SITE] | Problem solving and exercises | CE01 CE04 CE06 | 0.56 | 14 | N | N | ||
| Problem solving and/or case studies [ON-SITE] | Problem solving and exercises | CE01 CE04 CE06 CG01 | 0.24 | 6 | Y | N | ||
| Final test [ON-SITE] | Assessment tests | CE01 CE02 CE04 CE06 | 0.2 | 5 | Y | Y | ||
| Study and Exam Preparation [OFF-SITE] | Self-study | CE01 CE02 CE04 CE06 CG01 | 3.6 | 90 | N | N | ||
| Individual tutoring sessions [ON-SITE] | CE01 CE02 CE04 CE06 CG01 | 0.04 | 1 | N | N | |||
| Group tutoring sessions [ON-SITE] | CE01 CE02 CE04 CE06 CG01 | 0.04 | 1 | N | N | |||
| Total: | 6 | 150 | ||||||
| Total credits of in-class work: 2.4 | Total class time hours: 60 | |||||||
| Total credits of out of class work: 3.6 | Total hours of out of class work: 90 | |||||||
As: Assessable training activity Com: Training activity of compulsory overcoming (It will be essential to overcome both continuous and non-continuous assessment).
8. Evaluation criteria and Grading System
| Evaluation System | Continuous assessment | Non-continuous evaluation * | Description |
| Final test | 60.00% | 100.00% | The test includes the partial examinations and the ordinary / extraordinary examinations |
| Assessment of problem solving and/or case studies | 40.00% | 0.00% | It includes exercises and problems that the students will solve individually or in groups. Includes practical exercises in the computer room. |
| Total: | 100.00% | 100.00% |
According to art. 4 of the UCLM Student Evaluation Regulations, it must be provided to students who cannot regularly attend face-to-face training activities the passing of the subject, having the right (art. 12.2) to be globally graded, in 2 annual calls per subject , an ordinary and an extraordinary one (evaluating 100% of the competences).
Evaluation criteria for the final exam:
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Continuous assessment:The minimum grade in the final exam is 4 out of 10. The assessment of each of the four blocks is made up of: 60% of the exam and 40% of problem solving, cases and/or practices. The minimum grade to pass the ordinary and extraordinary calls is 5 out of 10. Those partial exams with a minimum mark of 4 will be kept for the ordinary and extraordinary calls. Scores achieved in problem solving, cases and/or practices will be kept for the ordinary and extraordinary calls. All the assessable activities that have been carried out during the course are recovered. All the assessable activities, that have been carried out during the course, will be kept for the next year. There are three partial exams.
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Non-continuous evaluation:The student will have to do a global exam that will include all the course content. To pass the course, the student must obtain at least a 5 out of 10, which will constitute 100% of his/her grade.
Unless stated otherwise, continuous evaluation criteria will be applied to all students.
Anyone choosing non-continuous assessment must notify it to the lecturer within the class period of the subject. The option is only available if the student¿s participation in evaluation activities (from the continuous assessment) has not reached 50% of the total evaluation for the subject.
For the retake exam, the assessment type used for the final exam will remain valid.
Specifications for the resit/retake exam:
Same that in final exam.
Specifications for the second resit / retake exam:
The student will have to do a global exam that will include all the course content. To pass the course, the student must obtain at least a 5 out of 10, which will constitute 100% of his/her grade.
9. Assignments, course calendar and important dates
| Not related to the syllabus/contents | |
|---|---|
| Hours | hours |
| Unit 1 (de 4): INTRODUCTION TO PROGRAMMING. SYMBOLIC COMPUTATION WITH MATLAB | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 4.5 |
| Class Attendance (practical) [PRESENCIAL][Problem solving and exercises] | 2.5 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 1.5 |
| Final test [PRESENCIAL][Assessment tests] | 1 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 15 |
| Group tutoring sessions [PRESENCIAL][] | .5 |
| Unit 2 (de 4): NUMERICAL METHODS WITH MATLAB | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 9 |
| Class Attendance (practical) [PRESENCIAL][Problem solving and exercises] | 2.5 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 1.5 |
| Final test [PRESENCIAL][Assessment tests] | 1.5 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 22.5 |
| Individual tutoring sessions [PRESENCIAL][] | .5 |
| Unit 3 (de 4): ANALYTIC GEOMETRY | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 15 |
| Class Attendance (practical) [PRESENCIAL][Problem solving and exercises] | 6 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 2 |
| Final test [PRESENCIAL][Assessment tests] | 1.5 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 37.5 |
| Individual tutoring sessions [PRESENCIAL][] | .5 |
| Unit 4 (de 4): OPTIMIZATION WITH GAMS | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 4.5 |
| Class Attendance (practical) [PRESENCIAL][Problem solving and exercises] | 3 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 1 |
| Final test [PRESENCIAL][Assessment tests] | 1 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 15 |
| Group tutoring sessions [PRESENCIAL][] | .5 |
| Global activity | |
|---|---|
| Activities | hours |
10. Bibliography and Sources
