Degree | Type | Year | Semester |
---|---|---|---|
2502444 Chemistry | FB | 1 | 2 |
Matemàtiques I
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.
(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. Area of a surface. Line integrals.
- Flow of a vector field.
The methodology will be the standard for this type of subject with theory classes, problems and a practical session.
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 |
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.
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 |
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.