Mathematics II
Code: 105038 ECTS Credits: 6| Degree | Type | Year | Semester |
|---|---|---|---|
| 2502444 Chemistry | FB | 1 | 2 |
Contact
- Name:
- Juan Carlos Cantero Guardeño
- Email:
- juancarlos.cantero@uab.cat
Teaching groups languages
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.
Prerequisites
Matemàtiques I
Objectives and Contextualisation
The course has three fundamental parts: the differential calculus, integral calculus and vector analysis.
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) Know how 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) Functions of several variables - Geometry of the plane and space. - Graph of a function, curves and level surfaces. - Directional derivatives, gradient. - Differentiality. Chain rule. Derivatives of higher order. Absolute and relative extrems. - Critical points, saddle points. Hessian criterion for the relative extrems. Lagrange multipliers for the calculation of absolute extremes. (2) Multiple integrals. - Iterated integrals. Fubini theorem. Principle of Cavalieri. - Variable change theorem. Polar, cylindrical and spherical coordinates. Calculation of masses and centers of masses. (3) Integral on curves and surfaces. - Parametric curves and surfaces. - implicitly given surfaces. Vector tangent to a curve at one point. Tangent plane and normal vector on a surface. - Length of a curve. Line integrals. - Area of a surface. Flow of a vector field.
- Green, Gauss and Stokes theorems.
Methodology
The methodology will be the standard for this type of subject with theory classes, problems and a practical session.
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.
Activities
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Problems | 22 | 0.88 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
| Seminars | 2 | 0.08 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
| Solving problems | 39 | 1.56 | 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 | |||
| Tutories | 12 | 0.48 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
| Type: Autonomous | |||
| Study | 39 | 1.56 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
Assessment
The assessment consists of a work (compulsory), which will count 10% of the semester's score, of an intersemestral exam (compulsory) that will count 40% of the semester's mark, and a final semester exam (obligatory) that will count 50% of the note of the semester. In order to pass the subject, the average of the corresponding qualifications will be greater or equal to 5, and that each one of these qualifications will be greater or equal to 3. There will be a recovery exam at the end of the course and the student will approve the subject if he / she meets the above conditions by substituting the partial and final exam grades for those obtained in the recovery exam. To participate in the recovery students must have previously been evaluated in a set of activities whose weight equals to a minimum of two thirds of the total grade of the subject.
Students who have chosen the single evaluation mode will have to take a final test consisting of an exam where block (1) of the contents will be evaluated with a weight of 40% of the total and where blocks (2) and (3) will also be evaluated with a weight of 50% of the total. Afterwards, the student will have to take an oral test where he/she will have to solve a series of exercises similar to those that have been worked on in the seminar sessions and which will have a weight of 10% of the total.
Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Final Exam | 50% | 3 | 0.12 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
| Midterm Exam | 40% | 3 | 0.12 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
| Recovery Exam | 90% | 3 | 0.12 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
| Work in group | 10% | 2 | 0.08 | 1, 2, 5, 3, 6, 4, 7, 8, 9, 10 |
Bibliography
J. E. Marsden y A.J. Tromba. Cálculo vectorial, cuarta edición. Addison-Wesley Longman, 1998.
S. L. Salas y E. Hille. Calculus, Vol. 1 y 2, tercera edición. Reverté, Barcelona, 1995 y 1994.
B. Demidovich. Problemas y ejercicios de Análisis Matemático. Ed. Paraninfo.
Software
None.