2023/2024

Degree | Type | Year | Semester |
---|---|---|---|

2503740 Computational Mathematics and Data Analytics | OB | 2 | 1 |

- Name:
- Silvia Cuadrado Gavilan
- Email:
- silvia.cuadrado@uab.cat

You can check it through this link. To consult the language you will need to enter the CODE of the subject. Please note that this information is provisional until 30 November 2023.

- Joan Torregrosa Arus

It is very convenient for the student to have achieved a good knowledge of the contents in Calculus in one variable, Linear algebra and Numerical analysis of the first course.

The objective of the subject is to present differential equations as a quantitative deterministic modeling tool for many processes of physics, chemistry, biology, etc. Also, the study of the solutions of these differential equations when they can be obtained in a closed form, when qualitative analysis is convenient and when approximate numerical computation turns out to be indispensable.

- Apply basic knowledge on the structure, use and programming of computers, operating systems and computer programs to solve problems in different areas.
- Calculate and reproduce certain mathematical routines and processes with ease.
- Design, develop and evaluate efficient algorithmic solutions to computational problems in accordance with the established requirements.
- Formulate hypotheses and think up strategies to confirm or refute them.
- Make effective use of bibliographical resources and electronic resources to obtain information.
- Relate new mathematical objects with other known objects and deduce their properties.
- Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
- Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
- Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.
- Use computer applications for statistical analysis, numerical and symbolic computation, graphic visualisation, optimisation and other to experiment and solve problems.
- Using criteria of quality, critically evaluate the work carried out.

- Contrast, if possible, the use of calculation with the use of abstraction in solving a problem.
- Describe the concepts and mathematical objects pertaining to the subject.
- Develop autonomous strategies for solving problems such as identifying the ambit of problems within the course, discriminate routine from non-routine problems, design an a priori strategy to solve a problem, evaluate this strategy.
- Evaluate and analyse the complexity of computational algorithmic solutions in order to develop and implement that which guarantees best performance.
- Evaluate the advantages and disadvantages of using calculation and abstraction.
- Handle specific scientific software for the application of numerical algorithms or the automatic realisation of symbolic calculations aimed at solving particular problems.
- Identify the essential ideas in the demonstration of ceratin basic theorems and know how to adapt these to obtain other results.
- Make effective use of bibliographical resources and electronic resources to obtain information.
- Numerically integrate ordinary differential equations and partial differential equations.
- Programme mathematical-calculation algorithms.
- Select and use algorithmic structures and the representation of appropriate data to solve a problem.
- Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
- Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
- Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.
- Understand the internal functioning of computers and be critical of the results that they provide.
- Using criteria of quality, critically evaluate the work carried out.
- Verify and ensure the correct operation of an algorithmic solution in accordance with the requirements of the problem to be resolved.

Ordinary differential equations

1. Differential equations as a modeling tool. The initial value problem. Existence and uniqueness and dependence on initial conditions and parameters.

2. The scalar differential equations. Autonomous differential equations. Asymptotic behavior. Examples and applications: the balance of matter and population dynamics.

4. Systems of nonlinear differential equations. Lyapunov stability. Linearization. Phase plane. Applications to mechanics, ecology and chemical kinetics.

Two hours of theory class per week correspond to this subject. In addition, 11 hours of seminar will be held where students will solve exercises raised by the teacher, both with conventional tools and using a symbolic manipulator. There will also be 12 hours of practical classes that will be devoted mainly to the approximate calculation of solutions of differential equations. It is essential that students have at their disposal the software that teachers recommend during the course. The Virtual Campus of the subject will provide all the material and all the information related to this subject that is necessary for the student.

**Annotation**: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|

Type: Directed | |||

Theory classes | 27 | 1.08 | 16, 5, 4, 1, 2, 7, 9, 10, 14, 13, 12, 8, 17 |

Type: Supervised | |||

Practical classes | 12 | 0.48 | 16, 4, 15, 3, 7, 9, 6, 10, 12, 11, 8, 17 |

Seminars | 10 | 0.4 | 5, 4, 1, 15, 3, 7, 9, 6, 10, 14, 13, 12, 11, 17 |

Type: Autonomous | |||

Personal study | 65 | 2.6 | 16, 5, 4, 1, 15, 2, 3, 7, 9, 6, 10, 14, 12, 11, 8, 17 |

Program design and report writing | 30 | 1.2 | 16, 5, 4, 1, 15, 3, 7, 9, 6, 10, 14, 13, 12, 11, 8, 17 |

The assessment of the course will be carried out mainly from four activities:

Evaluable seminars (SEM), Practices (PR), Partial exam (EP): exam of part of the subject, with theoretical questions and problems. Final exam (EF): exam of the whole subject, with theoretical questions and problems.

In addition, students will be able to submit to a recovery exam (ER).

The final grade of the subject will be

max( 0.1*SEM+0.1*PR+0.3*EP+0.5*EF, 0.1*SEM+0.1*PR+0.8*EF,ER)

as long as, if the maximum is attained at one of the first two numbers, **EF>=3.5 **must hold** **(otherwise the subject is not passed and the student must take the recovery exam.

Students who have taken the single assessment modality must take the subject's final exam (EF) on the same date as students taking the continuous assessment. This test will account for 80% of the grade (as long as EF >=3.5). On this same date, the student will have to deliver the seminar and practice project and, if the teacher requires it, an oral evaluation of it will take place. This evaluation will account for 20% of the final grade. If the grade is lower than 5 (or EF<3.5), the student can take the recovery exam (ER).

The "matrícula de honor" will be awarded to the first complete evaluation of the subject. Later achievements will not be considered for this purpose.

Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|

Final exam | 50% | 3 | 0.12 | 16, 5, 1, 15, 2, 3, 7, 14, 13, 12, 11 |

Partial exam | 30% | 3 | 0.12 | 16, 5, 1, 2, 3, 7, 14, 13, 12, 11 |

Practices | 10% | 0 | 0 | 16, 5, 4, 1, 15, 3, 9, 6, 10, 13, 11, 8, 17 |

Seminars evaluation | 10% | 0 | 0 | 16, 5, 4, 1, 15, 2, 3, 7, 9, 6, 14, 13, 12, 11, 8, 17 |

Borrelli, R., Coleman C.S. *Ecuaciones diferenciales. **Una perspectiva de modelación*. Oxford University Press (2002)

Lynch, Stephen *Dynamical Systems with applications using Python*. Birkhauser, 2018

**Lynch, Stephen Dynamical Systems with applications using Mathematica. Birkhauser, 2007 [Recurs electrònic]**

Martínez, R. *Models amb Equacions Diferencials*, Materials de la UAB no. 149. Bellaterra, 2004

**Noonburg, V. W. Differential Equations: From Calculus to Dynamical Systems. AMS, 2019 [Recurs electrònic]**

Perelló, C*. Càlcul Infinitesimal amb M**ètodes Numèrics i Aplicacions*, Enciclopèdia Catalana, 1994

Zill, Dennis G. *Ecuaciones diferenciales con aplicacions de modelado*. Cengage Learning, 2015

**Zill, Dennis G. A First Course in Differential Equations with Modeling Applications, International Metric Edition, 2017 [Recurs electrònic]**

There are no software requirements. The student will be able to use what he knows, in particular algebraic manipulation tools such as Maxima, Sage, Maple, etc., as well as numerical computation languages such as C. The use of one of the symbolic manipulators of open source could be mandatory.