Vector Calculus and Differential Equations (2500012) – Course 2025/26 PDF
Syllabus
Learning Objectives
This module presents an introduction to vector calculus and integral calculus over curves and surfaces. The approach is multidisciplinary, with the aim of developing skills in the use of basic mathematical tools for the modeling and analysis of physical problems described by partial differential equations. Contents: Integrals along curves. Integrals over surfaces. Differential operators. The integral theorems of vector analysis. Introduction and general features of PDEs. The heat, Laplace's and wave equations. Knowledge of ordinary differential equations. Basic knowledge of differential equations in partial derivatives, types, some analytical solutions in particular cases of special interest in engineering. 1 Ability to relate ordinary differential equations with engineering problems. 2 Ability to program simple solutions through basic software and to obtain numerical solutions. 3 Ability to develop solutions to these problems under simple conditions that allow an analysis of these solutions, including a parametric study.
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 | 30h | 50.00 % | |
| Medium group | 30h | 50.00 % | ||
| Self Study | 90h | |||
Teaching Methodology
The course consists of 2 hours per week of classroom activity (large size group) and 2 hours weekly with half the students (medium size group). The 2 hours in the large size groups are devoted to theoretical lectures, in which the teacher presents the basic concepts and topics of the subject, shows examples and solves exercises. The 2 hours in the medium size groups is devoted to solving practical problems with greater interaction with the students. The objective of these practical exercises is to consolidate the general and specific learning objectives. Support material in the form of a detailed teaching plan is provided using the virtual campus ATENEA: content, program of learning and assessment activities conducted and literature. Although most of the sessions will be given in the language indicated, sessions supported by other occasional guest experts may be held in other languages.
Grading Rules
The evaluation calendar and grading rules will be approved before the start of the course.
The grade for the subject is the highest of two modalities: Continuous / Discontinuous. The discontinuous modality consists of two partial exams (50%+50%). The continuous modality incorporates the partial exams (37.5%+37.5%) and adds several activities (25%), both individual and group, of incremental training, carried out during the module, both inside and outside the classroom. The final grade will be calculated as follows: max( 0.25*AC + 0.375*EX1 + 0.375*EX2 , 0.5*EX1 + 0.5*EX2 ), where - EX1: Written exam on the first part of the module - EX2: Written exam on the second part of the module - AC: activities in or outside the classroom. The assessment tests consist of questions on concepts associated with learning objectives integrated into a set of application exercises.
Test Rules
The assignments must be sent through ATENEA respecting the announced deadline. Late submissions or assignments submitted by other means will not be accepted and will be graded 0. Assignments must be completed individually: students are encouraged to confront each other over issues, but submitted work must be the result of their own efforts of each students. Plagiarism in homework will be penalized with a 0 in the class work grade. The exams must be taken individually and books or class notes will not be accepted. Plagiarism during exams will be penalized with a 0 in the final grade for the subject. Students who fail the ordinary exams will have the option to take a reassessment test within the period set by the academic calendar. Students who have already passed the subject will not be able to take the reassessment test. The maximum grade in the case of taking the reassessment exam will be five (5.0). The non-attendance of a student summoned to the reassessment test, held within the set period, may not lead to another test at a later date.
Office Hours
Upon appointment by email.
Bibliography
Basic
- Marsden, J.E.; Tromba, A.J. Vector calculus. 6th ed., int. ed. New York: WH Freeman, 2012. ISBN 9781429224048.
- Haberman, R. Applied partial differential equations with Fourier series and boundary value problems. Fifth ed. Boston: Pearson, 2019. ISBN 9780134995434.