Universitat Politècnica de Catalunya · BarcelonaTech

Differential Geometry and Differential Equations (250122) – Course 2022/23 PDF

Syllabus

Learning Objectives

Students will acquire an understanding of differential geometry (including curves and surfaces, as well as integration on manifolds and integral theorems) and partial differential equations of mathematical physics. They will also develop the skills to analyse and solve mathematical problems in engineering that involve these concepts. Upon completion of the course, students will have acquired the ability to: 1. Relate partial differential equations to engineering problems in continuous media. 2. Program complex solutions using basic software and obtain numerical solutions. 3. Develop analytical solutions to complex multidimensional boundary value and initial value problems with simple geometric conditions that allow an analysis of these solutions, including a parametric study. 4. Carry out an analytical description of curves and surfaces, calculate their properties, and perform differential and integral calculus operations on them. Basic tools in metric geometry: Ruler-and-compass constructions and demonstrations; Floor plans; Technical drawing; The conic system

Competencies

Especific

Ability to provide analytical descriptions of curves and surfaces, calculate their properties and perform differential calculus operations on them; find analytical solutions to complex contour and initial value problems in various dimensions and with simple geometrical conditions enabling an analysis, including a parametric study, to be made of these solutions

Transversal

SUSTAINABILITY AND SOCIAL COMMITMENT - Level 1. Analyzing the world¿s situation critically and systemically, while taking an interdisciplinary approach to sustainability and adhering to the principles of sustainable human development. Recognizing the social and environmental implications of a particular professional activity.

EFFICIENT ORAL AND WRITTEN COMMUNICATION - Level 1. Planning oral communication, answering questions properly and writing straightforward texts that are spelt correctly and are grammatically coherent.

EFFECTIVE USE OF INFORMATI0N RESOURCES - Level 2. Designing and executing a good strategy for advanced searches using specialized information resources, once the various parts of an academic document have been identified and bibliographical references provided. Choosing suitable information based on its relevance and quality.

SELF-DIRECTED LEARNING - Level 2: Completing set tasks based on the guidelines set by lecturers. Devoting the time needed to complete each task, including personal contributions and expanding on the recommended information sources.

Total hours of student work

Hours Percentage
Supervised Learning Large group 30h 30.30 %
Medium group 30h 30.30 %
Laboratory classes 30h 30.30 %
Guided Activities 9h 9.09 %
Self Study 126h

Teaching Methodology

The course consists of 6 hours per week of classroom to classroom (large group). They are devoted to lectures 2.5 hours largest group, the teacher presents the basic concepts and materials of matter, presents examples and exercising. It is dedicated 3.5 hours largest group, solving problems with greater interaction with the student. Practical exercises to consolidate the objectives of general and specific learning. The rest of weekly hours dedicated to evaluations. Support material is used in the form of detailed teaching plan using the virtual campus ATENEA: content, programming and evaluation activities directed learning and literature. Although most of the sessions will be given in the language indicated, sessions supported by other invited experts may be held in other languages. The language may change due to force majeure.

Grading Rules

The evaluation calendar and grading rules will be approved before the start of the course.

There will be two written exams of the subject. One in Differential Geometry area, G1, and other in Differential Equations area, E1. The dates of the two exams will be located within the period determined by the School. The exams will have the same value for the final note The final note will, NF = (G1 + E1) / 2. Criteria for re-evaluation qualification and eligibility: Students that failed the ordinary evaluation and have regularly attended all evaluation tests will have the opportunity of carrying out a re-evaluation test during the period specified in the academic calendar. Students who have already passed the test or were qualified as non-attending will not be admitted to the re-evaluation test. The maximum mark for the re-evaluation exam will be five over ten (5.0). The non-attendance of a student to the re-evaluation test, in the date specified will not grant access to further re-evaluation tests. Students unable to attend any of the continuous assessment tests due to certifiable force majeure will be ensured extraordinary evaluation periods. These tests must be authorized by the corresponding Head of Studies, at the request of the professor responsible for the course, and will be carried out within the corresponding academic period. Evaluation in the English Group The evaluation will consist of three elements. 30% of the grade will depend on activities performed during classes. These will include short evaluations of assigned reading, exercises performed individually or in group, and active participation. There will be two exams in the periods set by the Civil Engineering school for the mid-term and the final evaluations, each accounting for 35% or the grade. Students that have participated in the activities associated to the ordinary evaluation but not passing the course will be offered a re-evaluation. The maximum mark for the re-evaluation exam will be five over ten (5.0). The non-attendance of a student to the re-evaluation test, in the date specified will not grant access to further re-evaluation tests. Students unable to attend any of the continuous assessment tests due to certifiable force majeure will be ensured extraordinary evaluation periods.

Test Rules

Failure to perform a continuous assessment activity in the scheduled period will result in a mark of zero in that activity.

Office Hours

To be arranged in the course.

Bibliography

Basic

Complementary