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
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 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 use software platforms to numerically address problems arising in the field of civil engineering.
Students can use estimation techniques for quantities and associated errors.
Students mathematically formulate and quantitatively solve a problem involving (ordinary and/or partial) differential equations using analytical techniques and/or numerical methods.
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	R	Description *
Class Attendance (theory) [ON-SITE]	Lectures	AFC1 CB06 CB07 CB09 CB10 G01 G17 G18 G19 G21 G25 G27 G28 G29	1.28	32	N	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	0.56	14	Y	N	N	Following every lecture (with a typical duration of an hour), problem sets will be proposed to the students to be solved during the class. These sessions are at the heart of the course since they will provide the necessary skills in order to assimilate the contents of the course. Students are encouraged to actively participate in these sessions by presenting to the class partial/full solutions to the attempted problems.
Computer room practice [ON-SITE]	Project/Problem Based Learning (PBL)	AFC1 CB06 CB07 CB09 CB10 G01 G17 G18 G19 G21 G25 G27 G28 G29	0.72	18	Y	Y	N	Another key aspect of this course is learning to develop both small and medium-size programs to solve computational problems using the studied numerical methods. Students may bring their own laptops to the computer sessions, which will take place after completing each lesson (the specific dates will be announced in advance). Students will learn how to use at least one programming environment: preferentially MATLAB. Open source environments, such as Python, 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 will be proposed. This problem will be solved either individually or in small teams (the modality will be announced in advance). The students are expected to significantly contribute to the solution and to interact with the professor.
Final test [ON-SITE]	Assessment tests	CB06 CB07 CB09 G01 G17 G18 G19 G21 G25 G27 G28 G29	0.16	4	Y	Y	Y	Students will have two opportunities to pass the course: the Ordinary and the Extraordinary calls. The exam, in any of these calls, will have the same structure: it will consist of a questionnaire, with short problems to be chosen by the student, 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. Since the exams will involve problem solving skills it is advised that students attend regularly to the problem solving sessions during the course.
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	2.4	60	N	N	N
Study and Exam Preparation [OFF-SITE]	Self-study	AFC1 CB06 CB07 CB09 CB10 G01 G17 G18 G19 G21 G25 G27 G28 G29	3.6	90	N	N	N
On-line debates and forums [OFF-SITE]	Online Forums	CB06 CB07 CB09 G01 G17 G18 G19 G27 G28 G29	0.28	7	N	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
R: Rescheduling training activity

	Grading System
Evaluation System	Face-to-Face	Self-Study Student	Description
Final test	50.00%	0.00%	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 problem solving and/or case studies	15.00%	0.00%	All students are encouraged and expected to actively participate in the problem solving sessions that will follow every lecture. Problem sets to be solved during class will be proposed to the students. Those providing and presenting to the rest of the class partial/full detailed answers will receive credit for their work in accordance with the difficulty level of the problem. Every student should furnish at least two such solutions (either partial/full) during the course to obtain a grade in this evaluation part.
Assessment of activities done in the computer labs	35.00%	0.00%	Computational problems will be posed to the students (to be solved individually or in a team). Most computational problems will have to be completed during the class. Students will have to submit their developed programs (via web upload through the Campus Virtual) for each assigned problem. The time allotted to solve these computational problems as well as their modality (individual/team) will be announced in advance. These sessions will not be repeated so that for every session missed by the student no credit will be given.
Total:	100.00%	0.00%

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)]	1
Study and Exam Preparation [AUTÓNOMA][Self-study]	6
On-line debates and forums [AUTÓNOMA][Online Forums]	2

Unit 2 (de 6): Introduction to Platforms for Advanced Numerical Computation: MATLAB
Activities	Hours
Class Attendance (theory) [PRESENCIAL][Lectures]	1
Computer room practice [PRESENCIAL][Project/Problem Based Learning (PBL)]	4
Study and Exam Preparation [AUTÓNOMA][Self-study]	6

Unit 3 (de 6): Review of Basic Numerical Methods
Activities	Hours
Class Attendance (theory) [PRESENCIAL][Lectures]	8
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]	18
Study and Exam Preparation [AUTÓNOMA][Self-study]	18
On-line debates and forums [AUTÓNOMA][Online Forums]	1

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)]	2
Computer room practice [PRESENCIAL][Project/Problem Based Learning (PBL)]	3
Practicum and practical activities report writing or preparation [AUTÓNOMA][Self-study]	12
Study and Exam Preparation [AUTÓNOMA][Self-study]	12
On-line debates and forums [AUTÓNOMA][Online Forums]	1

Unit 5 (de 6): Numerical Solution of Partial Differential Equations
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]	18
Study and Exam Preparation [AUTÓNOMA][Self-study]	24
On-line debates and forums [AUTÓNOMA][Online Forums]	1

Unit 6 (de 6): Optimization Methods in Civil Engineering
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)]	3
Final test [PRESENCIAL][Assessment tests]	4
Practicum and practical activities report writing or preparation [AUTÓNOMA][Self-study]	12
Study and Exam Preparation [AUTÓNOMA][Self-study]	24
On-line debates and forums [AUTÓNOMA][Online Forums]	2

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			Fourth edition, Elsevier		2017	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
Belegundu, A.D., and Chadrupatla, T.R.	Optimization Concepts and Applications in Engineering			Second edition, Cambridge University Press		2011	Lesson 6
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
Chapman, S.J.	MATLAB Programming with Applications for Engineers			Cengage Learning		2013	Lesson 2
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			Seventh edition, McGraw-Hill		2015	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
Christensen, P.W., and Klarbring, A.	An Introduction to Structural Optimization			Springer		2009	Lesson 6
Epperson, J.F.	An Introduction to Numerical Methods and Analysis			John Wiley & Sons		2013	Lessons 3 and 4
Forst, W., and Hoffmann, D.	Optimization: Theory and Practice			Springer		2010	Lesson 6
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
Griffiths, D.F., and Higham, D.J.	Numerical Methods for Ordinary Differential Equations: Initial Value Problems			Springer-Verlag		2010	Lesson 4
Heinz, S.	Mathematical Modeling			Springer-Verlag		2011	Lesson 1
Holmes, M.H.	Introduction to Scientific Computing and Data Analysis			Springer		2016	Lessons 3, 4 and 6
Hritonenko, N., and Yatsenko, Y.	Mathematical Modeling in Economics, Ecology and the Environment			Springer		2013	Lesson 1
Imboden, D.M., and Pfenninger, S.	Introduction to Systems Analysis: Mathematical Modeling Natural Systems			Springer-Verlag		2013	Lesson 1
Khennane, A.	Introduction to Finite Element Analysis using MATLAB and Abaqus			CRC Press, Taylor & Francis Group		2013	Lesson 5
Kiusalaas, J.	Numerical Methods in Engineering with MATLAB			Third edition, Cambridge University Press		2016	Lessons 3, 4 and 6
Lindfield, G.R., and Penny, J.E.T.	Numerical Methods using MATLAB			Third Edition, Elsevier		2012	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
Moore, H.	MATLAB for Engineers			Third edition, Pearson Education		2012	Lesson 2
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			Fourth edition, John Wiley & Sons		2013	Lesson 6
Rao, S.S.	The Finite Element Method in Engineering			Fifth edition, McGraw-Hill		2011	Lesson 5
Sauer, T.	Numerical Analysis for Engineers and Scientists			Pearson Education		2012	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
Sioshansi, R., and Conejo, A.J..	Optimization in Engineering: Models and Algorithms			Springer		2017	Lesson 6
Smith, D.M.	Engineering Computation with MATLAB			Second edition, Addison-Wesley		2010	Lesson 2
Tan, Q.-M.	Dimensional Analysis with Case Studies in Mechanics			Springer-Verlag		2011	Lesson 1
Trangenstein, J.A.	Numerical Solution of Elliptic and Parabolic Partial Differential Equations			Cambridge University Press		2013	Lesson 5
Tveito, A., Langtangen, H.P., Nielsen, B.F., and Cai, X.	Elements of Scientific Computing			Springer-Verlag		2010	Lessons 3, 4 and 5
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
Yang, X.-S.	Engineering Optimization: An Introduction with Metaheuristic Applications			John Wiley & Sons		2010	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