Calculus (2500005) – Course 2025/26 PDF
Syllabus
Learning Objectives
Knowledge of differential calculus of functions of several variables; Riemann multiple Integral; Successions and series of functions; and ordinary differential equations 1 Ability to relate ordinary differential equations to engineering problems. Ability to solve ODEs in simple conditions and conduct analysis such as parametric studies. 2 Ability to solve engineering problems that require minimization, integration and analysis of functions of several variables. Knowledge of differential calculation of functions of various variables. Knowledge of integral calculation of various variables, including representation integral of functions, integral dependent on parameters. Directional derivatives. Gradient vector. Chain rule. Tangent plane. Inverse function theorem. Implicit functions. Higher order partial derivatives. Taylor's formula. Free extrema. Conditional extrema. Knowledge of the existence of serial development and its application to problems in civil engineering.
Competencies
Especific
Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge about: linear algebra; geometry; differential geometry; differential and integral calculation; differential equations and partial derivatives; numerical methods; numerical algorithmic; Statistics and optimization. (Basic training module)
Total hours of student work
| Hours | Percentage | |||
|---|---|---|---|---|
| Supervised Learning | Large group | 20h | 33.33 % | |
| Medium group | 30h | 50.00 % | ||
| Laboratory classes | 10h | 16.67 % | ||
| Self Study | 90h | |||
Teaching Methodology
The subject consists of 4 hours a week of face-to-face classes in the classroom and 2 hours a week of voluntary workshop. In face-to-face classes, the teaching staff presents the basic concepts and materials of the subject, presents examples and carries out exercises. The volunteer workshop hours are mostly devoted to consolidating concepts previous to entering university and solving problems, always having a great deal of interaction with the students. Support material is used in the form of a detailed teaching plan through the ATENEA virtual campus: contents, schedule of assessment and directed learning activities and bibliography. Although the majority of sessions will be held in the language indicated in the guide, sessions supported by other guest experts from time to time may be held in another language.
Grading Rules
The evaluation calendar and grading rules will be approved before the start of the course.
The subject's grade is obtained from the continuous assessment grades and the corresponding laboratory and/or computer lab grades. There will be a global test with 50% of the weight of the assessment and the remaining 50% will be continuous assessment tests. The continuous assessment consists of doing different activities, both individual and group, of an additive and formative nature, carried out during the course (inside and outside the classroom). The assessment tests consist of a part with questions about concepts associated with the learning objectives of the subject in terms of knowledge or understanding, and a set of application exercises. Criteria for qualification and admission to the re-evaluation: Students suspended from the ordinary evaluation who have appeared regularly in the evaluation tests of the suspended subject will have the option to take a re-evaluation test in the period set in the academic calendar Students who have already passed it, or students classified as not present, will not be able to take the revaluation test of a subject. The maximum grade in the case of taking the reassessment exam will be five (5.0). The non-attendance of a student called to the re-evaluation test, held in the fixed period, cannot give rise to the completion of another test with a later date. Extraordinary assessments will be carried out for those students who, due to accredited force, have not been able to take any of the continuous assessment tests. These tests must be authorized by the corresponding head of studies, at the request of the teacher responsible for the subject, and will be carried out within the corresponding teaching period.
Office Hours
To be agreed with the teachers of the subject
Bibliography
Basic
- Estela, M.R.; Saà, J. Cálculo con soporte interactivo en Moodle. Madrid: Pearson Educación, 2008. ISBN 9788483224809.
- Estela, M. R.; Serra, A. Cálculo: ejercicios resueltos. Madrid: Pearson Educación, 2008. ISBN 9788483224816.
- Edwards, C.H.; Penney, D.E. Ecuaciones diferenciales y problemas con valores en la frontera: cómputo y modelado. 4a ed. México: Prentice Hall Hispanoamericana, 2009. ISBN 9789702612858.