Curves in Engineering and Arquitecture/ Las Curvas en Ingeniería y Arquitectura

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The course deals with a cross-cutting theme in engineering and architecture – curves – approached from the point of view of mathematics and linked to other subjects: construction, industrial design and production, and road safety.
The course combines rigorous training with the excitement that comes from posing a problem, together with the discovery of its solution and practical applications.
*General introductory videos and introductory videos for each of the three parts of the course are available in both English and Spanish.

Taught by:
Universidad Politécnica de Madrid

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Puedes ver la versión en español de este vídeo en el siguiente URL: https://youtu.be/WfWQQ_LKlK4

The course deals with a cross-cutting theme in engineering and architecture – curves – approached from the point of view of mathematics and linked to other subjects: construction, industrial design and production, and road safety.
The course combines rigorous training with the excitement that comes from posing a problem, together with the discovery of its solution and practical applications.

Course registration allows you to view the content free of charge and complete the assessment activities.
The acquisition of the Certificate of Completion is optional and will be available within the course.

Duration: 45 hours of study

Start: Immediately

Target audience: 

  • Graduate and postgraduate students, researchers and professionals of different sectors. Knowledge of high school Mathematics and Physics is recommended.

Learning goals

  • To know basic notions about curves in connection with practical applications in engineering and architecture.
  • Understand mathematical, physical and graphic representation concepts and procedures, fundamental in the field of science and technology.
  • Develop the ability to model reality, applying problem-solving methods and computational techniques useful in their training process and in their future professional activity.
  • Develops the ability to work reflexively, creatively and effectively to solve real problems.
  • To introduce the mathematical definition of curves, to work with several types of parametrizations and to study the notion of differentiability.
  • To study the curves locally, the concept of length of a curve and the notions of curvature for plane and space curves and the torsion for space curves.
  • To introduce the concept of surface.
  • To study in depth three mathematical concepts that will help the student to solve the problem posed in the course.
  • To learn more about transition curves and other relevant issues in geometric design of roads.
  • To introduce the student to the knowledge of Bézier curves, a family of curves particularly suitable for design.
  • To explain the polar shape (also known as flower) of B-spline curves, a tool that relates the points of the curve to its control polygon.

 

Contents

The course is structured in three parts that can each be studied independently:

  • Part I: Curves in construction and architecture.
  • Part II: Curves in road safety.
  • Part III: Curves in industrial design and manufacturing.

Each part consists of three modules with the following structure:

  • #1. The first, introductory, module describes the practical setting and a real world example or problem whose study involves curves.
  • #2. The second module presents the materials, ideas, and methods that will be used.
  • #3. The third module serves to deepen understanding and describe connections with related topics.

Teachers:

Jesús María Alonso Trigueros
PhD in Civil Engineering from the Polytechnic University of Madrid. Road Safety Auditor accredited by the Ministry of Public Works of the Spanish Government. With more than 20 years of experience in teaching, research and collaboration with companies in the Civil Engineering sector, I am currently University Professor in the area of Graphic Expression in Engineering at the Polytechnic University of Madrid, Department of Engineering and Land Morphology.
Alicia Cantón Pire
Alicia Cantón graduated in Mathematics at the Universidad Autónoma de Madrid (Madrid, Spain) where she also obtained her PhD. She was a visiting scholar at the University of Washington (Seattle, WA (USA)) and at the Universidad Autónoma de Barcelona (Barcelona, Spain). Currently she is a professor at the Universidad Politécnica de Madrid (Madrid, Spain). Her research interests lie on Geometric Function Theory and Computer Aided Geometric Design.
Marco Castrillon López
Degree in Mathematics and Degree in Physics. PhD in Mathematics. Currently, Professor at the Faculty of Mathematics at the Complutense University of Madrid. Mathematics at the Complutense University of Madrid. My field of research focuses on Differential Geometry and its applications, mainly in Theoretical Physics. In addition, I participate in the Estalmat programme for the detection and stimulation of mathematical talent (of the Royal Academy of Sciences of Spain) and I am a member of the Mathematical Olympics Commission of the Spanish Royal Mathematical Society.
Daniel Fox
I am a mathematician studying differential geometry. See my personal web page for more information.
María Jesús Vázquez
María-Jesús Vázquez-Gallo graduated in Mathematics at the Universidad Autónoma de Madrid (Madrid, Spain) where she also obtained her PhD. Her research interests are Algebraic Geometry, from the beginning, and, more recently, Applied Mathematics. After more than 20 years teaching and doing research, currently she is a professor at the Universidad Politécnica de Madrid (Madrid, Spain) in the area of Applied Mathematics. Moreover, she takes part in the program ESTALMAT of stimulus of mathematical talent of the Spanish Real Academia de Ciencias.

Información adicional

Disponibilidad

3 meses

Modalidad

MOOC

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