Course competences
Code	Description
AFC1	Ability to address and solve advanced mathematical engineering problems, from problem solving to formulation development and implementation in a computer program. In particular, the ability to formulate, program and apply advanced analytical and numerical models for calculation, design, planning and management, as well as the ability to interpret the results obtained, in the context of civil engineering.
CB06	Possess and understand knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context.
CB07	Apply the achieved knowledge and ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to the area of study
CB09	Know how to communicate the conclusions and their supported knowledge and ultimate reasons to specialized and non-specialized audiences in a clear and unambiguous way
CB10	Have the learning skills which allow to continue studying in a self-directed or autonomous way
G01	Scientific-technical and methodological capacity for the continuous recycling of knowledge and the exercise of the professional functions of consultancy, analysis, design, calculation, project, planning, leadership, management, construction, maintenance, conservation and exploitation in the fields of civil engineering.
G17	Adequate knowledge of the scientific and technological aspects of mathematical, analytical and numerical methods of engineering, fluid mechanics, mechanics of continuous means, structural calculations, ground engineering, maritime engineering, water resources and linear works.
G18	Ability to participate in research projects and scientific and technological collaborations within its thematic area, in interdisciplinary contexts and, where appropriate, with a high knowledge transfer component.
G19	Knowledge of the latest developments and applications of technology to civil engineering in all its fields, as well as its new challenges.
G21	Ability to apply optimization tools to aid decision making, as well as to discern exploitation proposals compatible with the constraints and peculiarities of the built infrastructure.
G25	Ability to identify, measure, enunciate, analyse, diagnose and scientifically and technically describe a civil engineering problem
G27	Ability to communicate in a second language.
G28	Ability to work in an international context.
G29	Management capacity and teamwork.

Course learning outcomes
Description
Students mathematically formulate and quantitatively solve a problem involving (ordinary and/or partial) differential equations using analytical techniques and/or numerical methods.
Students develop and program codes to implement the numerical methods studied to solve ordinary and/or partial differential equations that occur in the field of civil engineering.
Students address computationally intensive problems efficiently.
Students can use estimation techniques for quantities and associated errors.
Reinforcement of the students' deductive reasoning capacity.
Students solve basic problems of optimization and optimal control that arise in the planning and management of civil engineering.
Increase in the students' capacity for abstraction.
Students use software platforms to numerically address problems arising in the field of civil engineering.
Additional outcomes
Not established.

• Unit 1: Introduction to Mathematical Modelling in Civil Engineering
• Unit 2: Introduction to Platforms for Advanced Numerical Computation: MATLAB
• Unit 3: Review of Basic Numerical Methods
• Unit 4: Numerical Solution of Ordinary Differential Equations
• Unit 5: Numerical Solution of Partial Differential Equations
• Unit 6: Optimization Methods in Civil Engineering

Training Activity	Methodology	Related Competences (only degrees before RD 822/2021)	ECTS	Hours	As	Com	Description
Class Attendance (theory) [ON-SITE]	Lectures	AFC1 CB06 CB07 CB09 CB10 G01 G17 G18 G19 G21 G25 G27 G28 G29	1.36	34	N	N	The topics covered in the course will be presented in the classroom through transparencies/blackboard. Notes and bibliographic excerpts will be made available in the Campus Virtual.
Problem solving and/or case studies [ON-SITE]	Project/Problem Based Learning (PBL)	AFC1 CB06 CB07 CB09 CB10 G01 G17 G18 G19 G21 G25 G27 G28 G29	0.6	15	Y	N	Following every lecture, problem sets will be proposed to the students to be solved and presented during class. These sessions are at the heart of the course as they provide the required skills to assimilate the contents of the course and facilitate the preparation of the exam. In order for this training activity to be assessable, it will be necessary for the student to present individually, during the sessions (which will be reported in advance throughout the course), to the rest of the class the partial/complete solutions to the problems addressed by him/her. Depending on the level of difficulty of the problems (which will be specified in advance in the problem collections), as well as on the performance shown by the student, a score will be assigned for each problem presented.
Computer room practice [ON-SITE]	Project/Problem Based Learning (PBL)	AFC1 CB06 CB07 CB09 CB10 G01 G17 G18 G19 G21 G25 G27 G28 G29	0.76	19	Y	Y	Another key aspect of the course is learning to develop programs to solve computational problems using the studied numerical methods. Students are encouraged to bring their own laptops to the computer sessions, which will take place after completing each lesson (the specific dates will be announced in advance during the course). Students will learn how to use at least one programming environment: preferentially MATLAB. Open source environments, such as Python, Julia, Maxima or Octave will also be accepted if the students are proficient in their use, although less support will be provided. During these computer sessions, a computational problem, chosen within the realm of Civil Engineering, will be proposed. This problem will be solved either individually or in small teams (the modality and time available will be previously specified). Most of the computational problems will need to be completed during class. Students must send their developed programs through Virtual Campus. These sessions will not be repeated nor are they recoverable.
Practicum and practical activities report writing or preparation [OFF-SITE]	Self-study	AFC1 CB06 CB07 CB09 CB10 G01 G17 G18 G19 G21 G25 G27 G28 G29	0.8	20	N	N
Final test [ON-SITE]	Assessment tests	CB06 CB07 CB09 G01 G17 G18 G19 G21 G25 G27 G28 G29	0	0	Y	Y	Students will have two opportunities to take the exam: the Ordinary and the Extraordinary calls. In either of the two calls, the test will have the same structure: it will consist of a questionnaire in which the student can choose a subset of questions from the total proposed followed by three-four development problems to be completed within about 4 hours. Any of these exams will incorporate the contents from the entire course. Since the exams will require different competences aimed at solving problems, it is highly advisable that students attend the problem sessions regularly or, independently, try to solve as many as they can. This activity takes place outside the class period.
Study and Exam Preparation [OFF-SITE]	Self-study	AFC1 CB06 CB07 CB09 CB10 G01 G17 G18 G19 G21 G25 G27 G28 G29	3.68	92	N	N
On-line debates and forums [OFF-SITE]	Online Forums	CB06 CB07 CB09 G01 G17 G18 G19 G27 G28 G29	0.2	5	N	N
Writing of reports or projects [OFF-SITE]	Project/Problem Based Learning (PBL)	AFC1 CB06 CB07 CB09 CB10 G01 G17 G18 G19 G21 G25 G27 G28 G29	1.6	40	N	N
Total:			9	225
Total credits of in-class work: 2.72			Total class time hours: 68
Total credits of out of class work: 6.28			Total hours of out of class work: 157

As: Assessable training activity
Com: Training activity of compulsory overcoming (It will be essential to overcome both continuous and non-continuous assessment).

Evaluation System	Continuous assessment	Non-continuous evaluation *	Description
Assessment of problem solving and/or case studies	15.00%	0.00%	Students will have to actively solve and present individually, during the problem sessions, their solutions to some of the proposed problems chosen within the proposed collections. The number of problems to be solved by each student throughout the course will depend on their level of difficulty (it will be indicated in advance when providing the collections). The methodology used and the degree of performance in the resolution and presentation shown by the student will be assessed. The weighting of the grade achieved in solving problems in the overall grade for the subject is 20%. This assessable activity is recovered in the final exam (either the Ordinary / Extraordinary calls).
Final test	50.00%	100.00%	Ordinary/Extraordinary exams. The exam, in any of the Ordinary/Extraordinary calls, will have the same structure: it will consist of a short questionary followed by three-four full-development problems to be completed within 4 hours. Any of these exams will be global and, therefore, will include all the contents of the course. It is important to emphasise that a minimum grade will be required for the final exam (either the Ordinary/Extraordinary call) so as to take into account the assessment from the other activities as well. This minimum grade is 5/10. If this minimum grade is not reached in any of the two exams (Ordinary/Extraordinary), the student will not pass the course.
Assessment of activities done in the computer labs	35.00%	0.00%	The programming codes submitted by the students (via web upload through the Campus Virtual) for each assigned problem will be evaluated. Both interaction with the professor and active participation during these sessions will also be valued. This compulsory training activity is not recoverable. The weighting of the mark achieved in the computer sessions with computers in the overall grade for the subject is 30%.
Total:	100.00%	100.00%

Not related to the syllabus/contents
Hours	hours

Unit 1 (de 6): Introduction to Mathematical Modelling in Civil Engineering
Activities	Hours
Class Attendance (theory) [PRESENCIAL][Lectures]	2
Problem solving and/or case studies [PRESENCIAL][Project/Problem Based Learning (PBL)]	2
Study and Exam Preparation [AUTÓNOMA][Self-study]	10
On-line debates and forums [AUTÓNOMA][Online Forums]	1
Writing of reports or projects [AUTÓNOMA][Project/Problem Based Learning (PBL)]	8

Unit 2 (de 6): Introduction to Platforms for Advanced Numerical Computation: MATLAB
Activities	Hours
Class Attendance (theory) [PRESENCIAL][Lectures]	2
Problem solving and/or case studies [PRESENCIAL][Project/Problem Based Learning (PBL)]	1
Computer room practice [PRESENCIAL][Project/Problem Based Learning (PBL)]	2
Study and Exam Preparation [AUTÓNOMA][Self-study]	12
Writing of reports or projects [AUTÓNOMA][Project/Problem Based Learning (PBL)]	2

Unit 3 (de 6): Review of Basic Numerical Methods
Activities	Hours
Class Attendance (theory) [PRESENCIAL][Lectures]	9
Problem solving and/or case studies [PRESENCIAL][Project/Problem Based Learning (PBL)]	4
Computer room practice [PRESENCIAL][Project/Problem Based Learning (PBL)]	4
Practicum and practical activities report writing or preparation [AUTÓNOMA][Self-study]	5
Study and Exam Preparation [AUTÓNOMA][Self-study]	20
On-line debates and forums [AUTÓNOMA][Online Forums]	1
Writing of reports or projects [AUTÓNOMA][Project/Problem Based Learning (PBL)]	8

Unit 4 (de 6): Numerical Solution of Ordinary Differential Equations
Activities	Hours
Class Attendance (theory) [PRESENCIAL][Lectures]	6
Problem solving and/or case studies [PRESENCIAL][Project/Problem Based Learning (PBL)]	3
Computer room practice [PRESENCIAL][Project/Problem Based Learning (PBL)]	4
Practicum and practical activities report writing or preparation [AUTÓNOMA][Self-study]	5
Study and Exam Preparation [AUTÓNOMA][Self-study]	14
On-line debates and forums [AUTÓNOMA][Online Forums]	1
Writing of reports or projects [AUTÓNOMA][Project/Problem Based Learning (PBL)]	6

Unit 5 (de 6): Numerical Solution of Partial Differential Equations
Activities	Hours
Class Attendance (theory) [PRESENCIAL][Lectures]	8
Problem solving and/or case studies [PRESENCIAL][Project/Problem Based Learning (PBL)]	3
Computer room practice [PRESENCIAL][Project/Problem Based Learning (PBL)]	6
Practicum and practical activities report writing or preparation [AUTÓNOMA][Self-study]	5
Study and Exam Preparation [AUTÓNOMA][Self-study]	20
On-line debates and forums [AUTÓNOMA][Online Forums]	1
Writing of reports or projects [AUTÓNOMA][Project/Problem Based Learning (PBL)]	8

Unit 6 (de 6): Optimization Methods in Civil Engineering
Activities	Hours
Class Attendance (theory) [PRESENCIAL][Lectures]	7
Problem solving and/or case studies [PRESENCIAL][Project/Problem Based Learning (PBL)]	2
Computer room practice [PRESENCIAL][Project/Problem Based Learning (PBL)]	3
Practicum and practical activities report writing or preparation [AUTÓNOMA][Self-study]	5
Study and Exam Preparation [AUTÓNOMA][Self-study]	16
On-line debates and forums [AUTÓNOMA][Online Forums]	1
Writing of reports or projects [AUTÓNOMA][Project/Problem Based Learning (PBL)]	8

Global activity
Activities	hours

Author(s)	Title	Book/Journal	Citv	Publishing house	ISBN	Year	Description	Link	Catálogo biblioteca
Arora, J.S.	Introduction to Optimum Design			Fourth edition, Academic Press, Elsevier		2016	Lesson 6
Attaway, S.	MATLAB: A Practical Introduction to Programming and Problem Solving			Fifth edition, Elsevier	978-0-12-815479-3	2019	Lesson 2
Barnes, B., and Fulford, G.R.	Mathematical Modelling with Case Studies Using Maple and MATLAB			Third edition, CRC Press, Taylor & Francis Group		2015	Lesson 1
Bashier, E.B.M.	Practical Numerical and Scientific Computing with MATLAB and Python			CRC Press, Taylor & Francis Group	978-0-42-902198-5	2020	Lessons 3 and 4
Belegundu, A.D., and Chadrupatla, T.R.	Optimization Concepts and Applications in Engineering			Third edition, Cambridge University Press	978-1-108-42488-2	2019	Lesson 6
Bober, W	MATLAB Essentials A First Course for Engineers and Scientists			CRC Press, Taylor & Francis Group		2018	Lesson 2
Bungartz, H.-J., Zimmer, S., Buchholz, M., and Pflüger, D.	Modeling and Simulation: An Application-Oriented Introduction			Springer-Verlag		2014	Lesson 1
Burden, R.L., Faires, J.D., and Burden, A.M.	Numerical Analysis			Tenth edition, Brooks/Cole Cengage Learning		2016	Lessons 3 and 4
Butcher, J.C.	Numerical Methods for Ordinary Differential Equations			Third edition, John Wiley & Sons		2016	Lesson 4
Chapra, S.C.	Applied Numerical Methods with MATLAB for Engineers and Scientists			Fourth edition, McGraw-Hill		2017	Lesson 2
Chapra, S.C., and Canale, R.P.	Numerical Methods for Engineers			Eight edition, McGraw-Hill	978-1-260-23207-3	2021	Lessons 3, 4, 5 and 6
Chaskalovic, J.	Mathematical and Numerical Methods for Partial Differential Equations: Applications for Engineering Sciences			Springer		2014	Lesson 5
Cheney, W., and Kincaid, D.	Numerical Mathematics and Computing			Seventh edition, Cengage Learning		2013	Lessons 3, 4, 5 and 6
Eck, C., and Garcke, H., and Knabner, P.	Mathematical Modeling			Springer	978-3-319-55161-6	2017	Lesson 1
Epperson, J.F.	An Introduction to Numerical Methods and Analysis			John Wiley & Sons		2013	Lessons 3 and 4
Esfandiari, R.S.	Numerical Methods for Engineers and Scientists Using MATLAB			Second edition, CRC Press, Taylor & Francis Group	978-1-4987-7742-1	2017	Lessons 2-5
Gander, W., Gander, M.J., and Kwok, F.	Scientific Computing: An Introduction using Maple and MATLAB			Fourth edition, Springer		2014	Lessons 3, 4 and 6
Gilat, A.	MATLAB: An Introduction with Applications			Fifth edition, John Wiley & Sons		2014	Lesson 2
Giordano, F.R., Fox, W.P., and Horton, S.B.	A First Course in Mathematical Modeling			Fifth edition, Brooks/Cole Cengage Learning		2014	Lesson 1
Hahn, B.D. and Valentine, D.T.	Essential MATLAB for Engineers and Scientists			Seventh edition, Academic Press, Elsevier	978-0-08-102997-8	2019	Lesson 2
Holmes, M.H.	Introduction to Scientific Computing and Data Analysis			Springer		2016	Lessons 3, 4 and 6
Kharab, A. and Guenther, R.B..	An Introduction to Numerical Methods: A MATLAB Approach			CRC Press, Taylor & Francis Group	978-1-138-09307-2	2019	Lessons 2-6
Kiusalaas, J.	Numerical Methods in Engineering with MATLAB			Third edition, Cambridge University Press		2016	Lessons 3, 4 and 6
Kochenderfer, M.J., and Wheeler, T.A.	Algorithms for Optimization			Massachusetts Institute of Technology Press		2019	Lesson 6
Lindfield, G.R., and Penny, J.E.T.	Numerical Methods using MATLAB			Fourth Edition, Academic Press, Elsevier	978-0-12-812256-3	2019	Lessons 3 and 6
Lyche, T., and Merrien, J.-L.	Exercises in Computational Mathematics with MATLAB			Springer-Verlag		2014	Lesson 2
Miller, G.	Numerical Analysis for Engineers and Scientists			Cambridge University Press		2014	Lesson 3
Mo, J.P.T, Cheung, S.C.P., and Das, R.	Demystifying Numerical Models: Step-by-Step Modeling of Engineering Systems			Elsevier	978-0-08-100975-8	2019	Lesson 1
Pedregal, P.	Optimization and Approximation			Springer	978-3-319-64842-2	2017	Lesson 6
Quarteroni, A., Saleri, A., and Gervasio, P.	Scientific Computing with MATLAB and Octave			Fourth edition, Springer-Verlag		2014	Lessons 3 and 6
Rao, S.S.	Engineering Optimization: Theory and Practice			Fifth edition, John Wiley & Sons	978-1119454816	2019	Lesson 6
Rao, S.S.	The Finite Element Method in Engineering			Sixth edition, McGraw-Hill	978-0-12-811768-2	2018	Lesson 5
Sauer, T.	Numerical Analysis			Third edition, Pearson Education	978-0-13-469645-4	2018	Lessons 3, 4 and 5
Shankar, P.M.	Differential Equations: A Problem Solving Approach Based on MATLAB			CRC Press, Taylor & Francis Group		2018	Lesson 4
Siauw, T., and Bayen, A.M.	An Introduction to MATLAB Programming and Numerical Methods for Engineers			Academic Press, Elsevier		2015	Lesson 2
Simon, V., Weigand, B., and Gomaa, H.	Dimensional Analysis for Engineers			Springer	978-3-319-52028-5	2017	Lesson 1
Sioshansi, R., and Conejo, A.J..	Optimization in Engineering: Models and Algorithms			Springer		2017	Lesson 6
Surana, K.S.	Numerical Methods and Methods of Approximation in Science and Engineering			CRC Press, Taylor & Francis Group	978-0-367-13672-7	2019	Lessons 3 and 4
Whiteley, J.	Finite Element Methods: A Practical Guide			Springer		2017	Lesson 5
Woodford, C., and Phillips, C.	Numerical Methods with Worked Examples: MATLAB			Second edition, Springer		2012	Lessons 3 and 6
Wouver, A.V., Saucez, P., and Vilas, C.	Simulation of ODE/PDE Models with MATLAB, OCTAVE and SCÍLAB: Scientific and Engineering Applications			Springer		2014	Lessons 4 and 5
Xue, D	Differential Equation Solutions with MATLAB			De Gruyter	978-3-11-067524-5	2020	Lessons 4 and 5
Yang, X.-S.	Optimization Techniques and Applications with Examples			John Wiley & Sons		2018	Lesson 6
Zienkiewicz, O.C., Taylor, R.L., and Zhu, J.Z.	The Finite Element Method: Its Basis and Fundamentals			Seventh edition, Elsevier		2013	Lesson 5