Degree in Technical Architecture and Building Engineering La Salle Campus Barcelona URL

Degree in Technical Architecture and Building Engineering

The Degree in Technical Architecture and Building is temporarily paused for new students

Mathematics

Description
1. Subject´s facts 1.1. Code: GAE01 1.2. Kind of subject: Basic common or introductory 1.3. Duration: Yearly 1.4. ECTS Credits: 8,5 1.5. Responsible professor: Silvia Necchi, Andrea Berruezo 1.6. Language: English -Catalan - Spanish Subject´s description Linear Algebra and Mathematics Analysis are studied in this subject. Its objective is to provide students with solid knowledge for a future architect. As students learn Mathematics by doing them, the subject includes a practical part where problems and applications are solved. Besides, it also has a theoretical part where the necessary tools to think, understand and solve the problems are explained. In this way, students acquire an algebraic, geometric and analytic vision of the space from an architectonical point of view.
Type Subject
Primer - Obligatoria
Semester
Annual
Course
1
Credits
8.50

Titular Professors

Membre
Previous Knowledge

Precalculus Algebra.

Objectives

3. Competences that this subject intend to develop:

General competences:
CG5 Understanding of the problems of structural design, construction and engineering related to building projects.
CB1 Students have to demonstrate to possess and understand knowledge of an area of study that starts from the base of the general secondary education, and is usually found at a level that, although it is supported by advanced textbooks, also includes some aspects that imply previous knowledge of the vanguard of its field of study.

Instrumental competences (IS):
IS9 Problem solving

Systemic competences (CS):
CS3 Capacity to apply knowledge into practice

Specific competences:
B20. MATHEMATICAL CALCULUS. Comprehension and knowledge of numerical calculus, mathematical analysis, analytic and differential geometry and algebraic methods, as the base to understand the physical phenomenon that makes reference to systems, equipments and services of building and urbanism.

Introductory unit: applied knowledge of numerical calculus, analytic and differential geometry, and algebraic methods.

4. Learning objectives:

8. Comprehension of the problems related to the structural conception, construction and engineering linked with the building´s projects.

Contents

5. Units in which the subject is organized:

The themes that are studied in this Mathematics subject correspond to linear algebra and are explained below:

1st SEMESTER: LINEAR ALGEBRA

1. SPACE REPRESENTATION
1.1 Systems of linear equations
1.2 Linear combination and linear independence of vectors
1.3 Vector spaces and subspaces
1.4 System of generators and bases
1.5 Operations of vector sub spaces
1.6 Inner vector spaces

2. LINEAR TRANSFORMATIONS
2.1 Types of transformations
2.2 Characterization
2.3 Change of basis
2.5 Eigenvectors and eigenvalues of an endomorphism

3. RESOLUTION OF CONICS AND QUADRICS
3.1 Quadratic forms in geometry
3.2 Classification of conics and quadrics

2ND SEMESTER: CALCULUS

1. MATHEMATICAL MODELS
1.1 Real function of real variable: domain and image, growth and decrease, symmetry, periodicity, dimensions.
1.2 Reverse function and composition of functions.
1.3 Elementary functions

2. ANALYSE AND SKETCH FUNCTIONS
2.1 Domain
2.2 Intercepts
2.3 Symmetry
2.4 End-behaviour
2.5 Intervals of increasing/ decreasing
2.6 Intervals of concavity
2.7 Areas

3. INTERPRET AND SKETCH MATHEMATICAL RESULTS
3.1 Structures application
3.2 Optimization problems
3.3 Areas
3.4 Surfaces of revolution

Methodology

6. Methodological approach to achieve the objectives:
The methodology used for this subject includes two kinds of classes: theoretical classes and practical classes to exercise the knowledge acquired during the theoretical classes.
Total on-campus hours: 54% 4,5 cr. ETCS, divided in:
Lectures: (IS/CS/B) 65% (2,5 ECTS)
Practical classes: (CS/B) 35% (2 ECTS)

Total work-hours of the student: 46% 4 cr. ECTS divided in:
Supervised work: (CS/B) 37,5% (1,5 ECTS)
Non supervised work: (CS/B) 62,5% (2,5 ETCS)

YEARLY TIMING

Dedication to the subjects: 8,5 credits 26 hours/credit = 221 hours
Yearly dedication: 34 weeks (30 class + 4 exams)
Weekly dedication: 221 hours /36 weeks = 6,5 hours/week

Concept Total hours
Lectures 65
Practical classes 52
Individual study 65
Tutorship 39

Training activities:
A1 Lectures of concepts explanation. 30%
A2 Practical classes of problems, exercises solved by students with teacher assistance. 23%
A9 Work / self-study student. 29%
A11 Individual corrections. 18%

TOTAL YEARLY DEDICATION 221

Lectures
The professor teaches the theoretical concepts through lectures. In these classes the professor also solves problems that apply directly the explained concepts.

Classes dedicated to solve exercises.
In some classes the professor propose exercises to be solved by the students in that moment to help students to understand completely the topich during the class. The problems are more difficult than the ones solved during the lectures and have the objective to help students to relate the concepts of the same subject and with concepts of other subjects of the career. These exercises may be solved individually or in groups.

Exercises to solve at home
Beside the exercises to be solved in class, the student must solve other problems at home. The idea of these exercises is that students affirm the theoretical ideas so that they may apply them in practical contexts.

Evaluation

7. Evaluation the level of achievement of the objectives:

With the purpose of evaluating if the student has acquired an adequate level of the objectives proposed for this subject, several instruments are used to obtain the student´s information:

Exams (Competences: IS/CS) 60%
The students will be evaluated of all the themes studied during the subject along the course.
Exercises (Competences: IS/CS) 40%
The exercises solved in class in order to evaluate the knowledge acquired.

Evaluation Criteria
Basic Bibliography

8. Bibliography
Calculus:
Ayres F., Schaum's outline of calculus. McGraw-Hill, 1999
Larson R., Hostetler R., Edwards B., Cálculus, Houghton Mifflin Co., 2002.

Algebra:
Anton H., Elementary linear algebra, John Wiley & Sons, 2000.

Additional Material