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Type A
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Code |
Competences Specific | | | A1.1 |
Consistently apply knowledge of basic, scientific and technological subjects pertaining to engineering |
| | A3.1 |
Ability to solve a wide range of mathematical problems in engineering. Ability to apply the knowledge of linear algebra, geometry, differential geometry, differential and integral calculus, differential equations and partial differential equations, numerical methods, numerical algorithmics, statistics and optimisation (FB1)
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Type B
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Code |
Competences Transversal |
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Type C
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Code |
Competences Nuclear |
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Type A
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Code |
Learning outcomes |
| | A1.1 |
Aplica correctament els principis matemàtics que puguin plantejar-se en l’enginyeria, àlgebra lineal, geometria, geometria diferencial, càlcul diferencial i integral, equacions diferencials i en derivades parcials, mètodes numèrics, algorítmica numèrica, estadística i optimització.
| | | A3.1 |
Adquireix les tècniques més elementals del càlcul numèric i aplicar-les, amb l’ajuda d’un llenguatge de programació estructurat d’alt nivell a models matemàtics relacionats amb l’enginyeria.
Compren el concepte i adquirir les tècniques analítiques i numèriques mes habituals relacionades amb la resolució d’equacions diferencials i aplicar-les, amb l’ajuda d’un llenguatge de programació, a models matemàtics relacionats amb l’enginyeria.
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Type B
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Code |
Learning outcomes |
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Type C
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Code |
Learning outcomes |
| Topic |
Sub-topic |
| First order ordinary differential equations. |
Analysis of critical points. Derivatives field. Numerical methods to solve odes: Euler, Runge-Kutta, predictor-corrector and multistep methods. Stiff type problems. Implicit Euler's method. MATLAB "ode suite" solvers |
| Systems of first order ordinary differential equations. |
Solution of homogeneous linear ode systems with constant coefficients. Non-homogeneous systems: method of variation of constants. Solution by Laplace transform. Stability analysis of planar autonomous systems. Linear stability criterion for non-linear systems. Solving with MATLAB |
| Second and higher order ordinary differential equations |
Analytical solution. Initial value problems: numerical solution of the equivalent system of odes. Boundary problems: shooting method, MATLAB solvers and finite difference method. |
| Laplace transform |
Definition, properties. Inverse Laplace transform. Application to the resolution of initial value problems of linear differential equations. |
| Partial differential equations. |
Introduction and types of partial differential equations. Separation of variables. Example: linear diffusion problems.
Stationary and non-stationary problems. Diffusion, convection, evolution and propagation terms. Finite difference solution. Solving with MATLAB. |
| Methodologies :: Tests |
| |
Competences |
(*) Class hours
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Hours outside the classroom
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(**) Total hours |
| Introductory activities |
|
1 |
0 |
1 |
| Lecture |
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18 |
30 |
48 |
| IT-based practicals in computer rooms |
|
28 |
24 |
52 |
| Problem solving, exercises in the classroom |
|
9 |
14 |
23 |
| Personal attention |
|
1 |
0 |
1 |
| |
| Extended-answer tests |
|
2 |
0 |
2 |
| Practical tests |
|
0 |
22 |
22 |
| Practical tests |
|
0 |
1 |
1 |
| |
(*) On e-learning, hours of virtual attendance of the teacher.
(**) The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. |
Methodologies
| |
Description |
| Introductory activities |
Introduction to the subject and general planning: sources of information, schedule of tests and activities, standards required for following the subject satisfactorily. |
| Lecture |
Introduction of basic concepts, proofs and examples |
| IT-based practicals in computer rooms |
Writing of numerical routines and scripts, based on the list of course problems, using MATLAB. |
| Problem solving, exercises in the classroom |
Master class on examples which will serve as the basis for the the MATLAB lab |
| Personal attention |
To make it easier for the student to profitably follow the subject, individual feedback will be given through the exercises corrected in moodle and the resolution of doubts. |
|
Description |
|
To advise the student in his work, consultation hours will be held in person or online, at the convenience of both parties. Appointments must be made in advance via moodle. Questions will not be resolved by email. For teachers' availability times, consult the subject's moodle |
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Methodologies |
Competences
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Description |
Weight |
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| Practical tests |
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Deliverables: Problems solved outside the classroom and delivered individually through moodle. They are weekly exercises to assess the understanding of the subject taught in class (see note 1 below) |
40% |
| Extended-answer tests |
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Global individual test at the end of the academic period (see note 2 below) |
50% |
| Others |
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Nota de la tasca de l'API2 de Matemàtiques III (veure nota 3 a baix) |
10% NAC |
| |
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Other comments and second exam session |
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(1) The practical tests are individual tests to assess programming skills and use of the procedures practiced in class. Therefore, a computer with MATLAB will be necessary. This should be the student's own laptop. (2) MINIMUM GRADE for averaging with deliverables: 3.5/10. Access to the internet is expressly prohibited during the final exam, as well as the use of any other electronic device. (3) If there is no API2 mark, the missing 10% will be the average mark of the deliverables of the course. So, in this case the final grade will be 50% (deliverables) and 50% (final exam) In the second call, the exam will be worth 80% and the deliverables will count for the remaining 20%. The API2 assignment will no contribute to the grade. . |
| Basic |
Dennis G. Zill, Michael R. Cullen, Ecuaciones diferenciales con problemas de valores en la frontera, ,
C. H. Edwards, David E. Penney, Ecuaciones diferenciales elementales y problemas con condiciones en la frontera , ,
José Gaspar González Montiel, Ecuaciones en derivadas parciales : teoría y problemas, ,
Haberman, Richard, Ecuaciones en derivadas parciales con series de Fourier y problemas de contorno, ,
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| Complementary |
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| Subjects that it is recommended to have taken before |
| MATHEMATICS II/20204006 | | MATHEMATICS I/20204005 |
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(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation. |
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