Mathematics I
Code: 105037 ECTS Credits: 6| Degree | Type | Year | Semester |
|---|---|---|---|
| 2502444 Chemistry | FB | 1 | 1 |
Contact
- Name:
- Silvia Cuadrado Gavilán
- Email:
- Silvia.Cuadrado@uab.cat
Use of Languages
- Principal working language:
- catalan (cat)
- Some groups entirely in English:
- No
- Some groups entirely in Catalan:
- Yes
- Some groups entirely in Spanish:
- No
Teachers
- Jaume Aguadé Bover
- Bogdan Vasile Crintea
- Clara Cufí Cabré
- David Marín Pérez
Prerequisites
It is convenient to know the contents of mathematics that allow you to pass the exam of Mathematics in the Selectivity [exam to enter at the University] without problems.
Objectives and Contextualisation
This course consists of a brief introduction to complex numbers, linear algebra and differential equations.
The objectives of the course are:
(i) Understand the basics in each of these parts. These concepts include both the definitions of the mathematical objects that are introduced and their interrelation.
(ii) To be able to apply the concepts studied coherently to the approach and resolution of problems.
(iii) Acquire skills in mathematical writing and in calculus.
Competences
- Adapt to new situations.
- Communicate orally and in writing in one’s own language.
- Learn autonomously.
- Manage, analyse and synthesise information.
- Obtain information, including by digital means.
- Propose creative ideas and solutions.
- Reason in a critical manner
- Recognise and analyse chemical problems and propose suitable answers or studies to resolve them.
- Resolve problems and make decisions.
- Show an understanding of the basic concepts, principles, theories and facts of the different areas of chemistry.
Learning Outcomes
- Adapt to new situations.
- Apply the suitable mathematical tools to deal with and resolve chemistry problems.
- Communicate orally and in writing in one’s own language.
- Interpret mathematical language to deal with chemistry problems.
- Learn autonomously.
- Manage, analyse and synthesise information.
- Obtain information, including by digital means.
- Propose creative ideas and solutions.
- Reason in a critical manner
- Resolve problems and make decisions.
Content
(1) Complex numbers
- Definition and elementary operations.
- Polar form.
- n-th root of complex numbers.
- Factoritzation of polynomials.
(2) Linear algebra
- Sistems of linear equations. The Gauss methode.
- Matrices and determinants.
- Vectorial spaces: linear dependence, basis and dimension.
- Eigenvalues and eigenvectors. Diagonalisation.
(3) Calculus of primitives
- Change of variable. Integration by parts.
- Primitives of rational functions.
(4) Diferential equations of first order
- Diferential equations: Definition and geometrical interpretatioon. Examples.
- Equations of separated variables.
- Linear equations of first order.
- Linear equations of greatest order.
- Linear equations of second order with constants coefficients.
- Systems of diferential equations.
Methodology
The standard methodology in this type of subject: theory classes where the definitions, the first results and examples are given, accompanied by problems classes where these examples are dealt with and where the students should try to solve these problems by themselves before coming to class.
Activities
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Problems | 22 | 0.88 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
| Seminars | 3 | 0.12 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
| Theory | 25 | 1 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
| Type: Supervised | |||
| Tutorial | 6 | 0.24 | 1, 2, 5, 3, 6, 4, 8, 9, 10 |
| Type: Autonomous | |||
| Problem solving | 40 | 1.6 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
| Study | 42 | 1.68 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
Assessment
1) A work consisting of delivering some problems proposed by the teachers that will have to be explained orally in case the teacher requires it. It represents 10% of the note.
2) A partial exam that will be carried out approximately in the middle of the semester. It represents 40% of the note.
3) The final exam of all the material that will take place at the end of the semester. It represents 50% of the note.
4) Students who do not pass the subject from the three previous points may be presented to a recovery exam if they have been evaluated at least in two of the three previous activities (delivery of problems, partial and final exams). The final mark is then the 10% corresponding to the presentation of problems (this note can not be recovered) plus 90% correspomnding ot the recovery exam.
In this case, you can not obtain the maximun qualification of ``Matricula de Honor''
Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Delivery problems | 20% | 4 | 0.16 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
| final exam | 50% | 4 | 0.16 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
| midterm exam | 30% | 4 | 0.16 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
Bibliography
M. Moreno, Una introducción al álgebra lineal elemental, UAB, 1990. Codi biblioteca de Ciències: 15-M-9; 512.64 Mor.
S. I. Grossman, Álgebra lineal, McGraw Hill, 1996. Codi biblioteca de Ciències: 15- G.19; 512.64 Gro.
F. Carreras, M. Dalmau, F. Albeniz, M. Moreno, Ecuaciones diferenciales, UAB, 1987. Codi biblioteca de Ciències: 34-E-16; 34-E-17; 517.9 Ecu.
Dennis G. Zill, Ecuaciones diferencials con aplicaciones de modelado, Thomson Editors, 1997. Codi biblioteca de Ciències: 34-Z-5; 517.9 Zil.