Mathematics I
Code: 105037 ECTS Credits: 6| Degree | Type | Year |
|---|---|---|
| 2502444 Chemistry | FB | 1 |
Contact
- Name:
- Juan Eugenio Mateu Bennassar
- Email:
- joan.mateu@uab.cat
Teaching groups languages
You can view this information at the end of this document.
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) Differential and Integral calculus
- Functions. Derivative. Graphical representation.
. Primitives. Fundamental calculus theorem.
- 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.
Activities and Methodology
| 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 |
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.
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.
Assessment
Continous Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Seminar qualification | 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 |
1) The day of the seminar there will be an exam for the students. It represents 20% of the mark.
2) A partial exam that will be carried out approximately in the middle of the semester. It represents 30% of the grade.
3) The final exam of all the material that will take place at the end of the semester. It represents 50% of the grade.
4) Students who do not obtain a grade bigger or equal to 5 from the three previous points will get the chance of a recovery exam. In this case, one can not obtain the maximun qualification of ``Matricula de Honor''
The students who have joined the single assessment modality will have to carry out a final test
which will consist of an exam of all the contents of the subject to be carried out on the day of the sencond test of the
students of the continuous assessment. The qualification of the student will be the grade of this test.
If the final grade does not reach 5, the student will have another opportunity to pass the subject
with the recovery exam. The qualification of the student will be the grade of this test. In this case, the student will not be eligible for the "Matricula d'Honor" qualification.
If the students have been assess for less than 25% of the subject their final grade will be non-assesssable.
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.
C. Neuhauser, Matemáticas para Ciencias, Prentice Hall, 2004, Codi biblioteca de Ciències: 00-N-04
Software
Not applicable
Language list
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (PAUL) Classroom practices | 1 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 2 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 3 | Catalan | first semester | afternoon |
| (SEM) Seminars | 1 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 2 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 3 | Catalan | first semester | afternoon |
| (SEM) Seminars | 4 | Catalan | first semester | afternoon |
| (TE) Theory | 1 | Catalan | first semester | morning-mixed |
| (TE) Theory | 2 | Catalan | first semester | afternoon |