1. General information
Course:
NONLINEAR ANALYSIS AND DIFFERENTIAL EQUATIONS
Code:
310938
Type:
ELECTIVE
ECTS credits:
6
Degree:
2351 - MASTER DEGREE PROGRAMME IN PHYSICS AND MATHEMATICS-FISYMAT
Academic year:
2019-20
Center:
602 - E.T.S. INDUSTRIAL ENGINEERING OF C. REAL
Group(s):
20
Year:
1
Duration:
C2
Main language:
Spanish
Second language:
English
Use of additional languages:
English Friendly:
Y
Web site:
Bilingual:
N
Lecturer:
ALBERTO DONOSO BELLON
- Group(s):
20
Building/Office
Department
Phone number
Email
Office hours
Edificio Politécnico/2-B17
MATEMÁTICAS
926295251
alberto.donoso@uclm.es
Se informará a comienzo del curso
2. Pre-Requisites
Previous knowledge of multivariable calculus, linear algebra, and ordinary and partial differential equations is required
3. Justification in the curriculum, relation to other subjects and to the profession
This course pretends to be a first contact to the field of optimization through mathamatical programming, calculus of variations and optimal control. It will be of great help not only for students with mathematical background but also for physicians and engineers interested in modeling some problems as optimization ones.
4. Degree competences achieved in this course
| Course competences | |
|---|---|
| Code | Description |
| 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 |
| CB08 | Be able to integrate knowledge and face the complexity of making judgments based on information that, being incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of knowledge and judgments |
| 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 |
| CE03 | Have the ability to build and develop advanced mathematical reasoning, and delve into the different fields of mathematics |
| CG05 | Gain the ability to develop a scientific research work independently and in its entirety. Be able to search and assimilate scientific literature, formulate hypotheses, raise and develop problems and draw conclusions from the obtained results |
| CT03 | Develop critical reasoning and the ability to criticize and self-criticize |
5. Objectives or Learning Outcomes
| Course learning outcomes | |
|---|---|
| Description | |
| Be able to apply the acquired knowledge to treat different non-linear differential equations | |
| To conceive the need for weak derivation in the environment of Sobolev spaces | |
| Become familiar with the different techniques of Nonlinear Analysis | |
| Additional outcomes | |
| Not established. |
6. Units / Contents
-
Unit 1: Linear programming
-
Unit 2: Non-linear programming
-
Unit 3: Calculus of Variations
-
Unit 4: Optimal control
-
Unit 5: Variational methods for non-linear analysis
7. Activities, Units/Modules and Methodology
| Training Activity | Methodology | Related Competences (only degrees before RD 822/2021) | ECTS | Hours | As | Com | R | Description * |
| Class Attendance (theory) [ON-SITE] | Lectures | 3 | 75 | N | N | N | ||
| Writing of reports or projects [OFF-SITE] | Assessment tests | 3 | 75 | Y | Y | Y | ||
| Total: | 6 | 150 | ||||||
| Total credits of in-class work: 3 | Total class time hours: 75 | |||||||
| Total credits of out of class work: 3 | Total hours of out of class work: 75 | |||||||
As: Assessable training activity Com: Training activity of compulsory overcoming R: Rescheduling training activity
8. Evaluation criteria and Grading System
| Grading System | |||
| Evaluation System | Face-to-Face | Self-Study Student | Description |
| Assessment of problem solving and/or case studies | 15.00% | 15.00% | Exercises to support the main concepts |
| Theoretical papers assessment | 70.00% | 70.00% | Oral presentation of a case study |
| Progress Tests | 15.00% | 15.00% | Regular tests |
| Total: | 100.00% | 100.00% | |
Evaluation criteria for the final exam:
Evaluation criteria not defined
Specifications for the resit/retake exam:
Evaluation criteria not defined
Specifications for the second resit / retake exam:
Evaluation criteria not defined
9. Assignments, course calendar and important dates
| Not related to the syllabus/contents | |
|---|---|
| Hours | hours |
| Writing of reports or projects [AUTÓNOMA][Assessment tests] | 75 |
| Unit 1 (de 5): Linear programming | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 15 |
| Unit 2 (de 5): Non-linear programming | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 15 |
| Unit 3 (de 5): Calculus of Variations | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 15 |
| Unit 4 (de 5): Optimal control | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 15 |
| Unit 5 (de 5): Variational methods for non-linear analysis | |
|---|---|
| Activities | Hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 15 |
| Global activity | |
|---|---|
| Activities | hours |
