Universitat Internacional de Catalunya
Mathematics
Other languages of instruction: Spanish
Teaching staff
Communication will be made through the dedicated space on the intranet.
Personal attention outside class hours is made by appointment by email:
Ravil Gizatulin - rgizatulin@uic.es
Roger Señis López - rsenis@uic.es
Josep Ramón Solé - jrsole@uic.es
Rafael Velasco Pérez - rvelasco@uic.es
The tutorials referring to doubts about the theoretical-practical contents that have been exposed in the classes will be done individually. The timetable will be, a priori, the same as that determined during the face-to-face teaching phase. If there are any changes, they will be communicated through the channels established by the UIC. These tutorials will be requested by email to the teacher. Once the time for tutoring has been set, they will be held in person.
The documentation of the subject will always be delivered through the Moodle of the subject.
The material used in the theoretical classes by the teachers will be posted on the Intranet for consultation, learning of the subject, preparation for the midterm and final exams.
Introduction
COMPULSORY SUBJECT
1st Degree in ARCHITECTURE
1st Semester
6 ECTS Credits
RESPONSIBLE TEACHER: Rafael Velasco Pérez (rvelasco@uic.es).
TEACHERS: Ravil Gizatulin (rgizatulin@uic.es), Roger Señis López (rsenis@uic.es), Josep Ramón Solé (jrsole@uic.es)
The subject to be developed in the subject of Mathematics must be understood as a subject associated with the learning of the tools that students need for their application in architecture.
The aim is for students to end up using mathematics as a work instrument linked to real problems that may be encountered in the future, mainly with the calculation of structures.
We propose more participatory and practical classes with the aim of increasing the student's work capacity in facets close to what will be their professional life.
It will be important to solve all the practical exercises proposed to the students, which will be corrected, by the teaching staff, in person or through the Moodle platform.
It is recommended to attend class with the previous notes read and studied, as well as with the necessary material to work.
Pre-course requirements
The skills required are:
- Operations with and without fractions.
- Inequalities
- Systems of equations
- Areas, perimeters and volumes
- Logarithmic relationships
- Trigonometry (sin, cos, tan)
- Vector representation in a plane
- Representation of figures in space
- Operations with vectors
- Operations with matrices and determinants
- Derivatives and application
- Graphing
- Integrals and their area of application.
Objectives
The main objective of these courses is to acquire knowledge of how to use the tools needed to address solving architectural problems.
Competences/Learning outcomes of the degree programme
- 07 - To acquire adequate knowledge and apply it to the principles of general mechanics, statics, mass geometry, vector fields and force lines of architecture and urban planning
- 08 - To aquire adequate knowledge and apply it to the principles of thermodynamics, acoustics and optics of architecture and urban planning.
- 09 - To acquire adequate knowledge and apply it to the principles of fluid mechanics, hydraulics, electricity and electromagnetism in architecture and urban planning.
- 11 - To acquire knowledge and apply it to numerical calculation, analytic and differential geometry and algebraic methods.
Learning outcomes of the subject
At the end of this subject, the student should be able to:
- Perform vector operations for application to the design of structures.
- Understanding the concepts of a linear combination of vectors and linear dependence.
- Understanding the classical concepts of vector spaces and their applications.
- Understanding the concepts of scalar product, norm and orthogonality in vector spaces.
- Understanding the concepts of vectors and eigenvalues of a matrix and its application to the diagonalization of matrices.
- Knowing how to relate linear transformation matrix transformations with issues specific to systems of linear equations.
- Understanding the definition of the various matrix operations and their application to linear transformations and systems of linear equations.
- Understanding the concept of the staggered and reduced echelon form of a matrix.
- Understanding the notion of inductive determinant.
- Knowing the properties of determinants and their applications.
- Understanding the subspaces associated with a matrix and their relation to linear transformations and systems of linear equations.
- Understanding the notion of a system of linear equations.
- Knowing how to identify each element of a linear system with a matrix-standardized method.
- Understanding and interpreting the concept of the solution set of a linear system.
- Knowing how to handle with ease the calculation of partial derivatives using different rules in an existing chain.
- Preserve the calculation of partial derivatives.
- Knowing how to calculate with ease domains and images of real functions
- Learn to study all the concepts necessary for the representation of a function.
- Understanding the concept of primitive function.
- Knowing how to calculate primitive functions easily, choosing the most appropriate method.
- Knowing how to calculate definite integrals.
Syllabus
1. Trigonometry
- Trigonometric functions of an acute triangle.
- Trigonometric functions of any triangle.
- Triangular resolution applied to architecture.
2. Matrices and Determinants
- Definition. Types of matrices (according to the shape and the elements). Operations with Matrices. Rank of a matrix (calculation methods).
- Calculation of determinants. Definition. Properties of determinants. Methods of calculation.
- Matrix equations.
3. Representation of functions in space (2D and 3D).
- Meaning of the function of a real variable.
- Continuity of a function (types of discontinuities in a function).
- Asymptotes.
- Symmetry of functions.
- Calculation of roots (cutting the x-axes), Rolle's Theorem, Newton’s Theorem and the tangent.
- Criteria bypass.
- Application of the derivative of a function: maximum, minimum, inflection points, concavity and convexity, growth and decrease ...
- Brief notions of partial derivatives.
- The meaning of geometric features.
- Optimization.
4. Systems of linear equations
- Systems of Equations: Incompatible, consistent, determined / undetermined.
- Inequalities.
- Notation matrix equations (simplified matrix / extended).
- Methods for solving equations.
- Numerically solving system equations.
5. Integral calculus.
- The meaning of analytical geometry.
- Definite and indefinite integrals.
- Properties of integrals.
- Integral Calculus.
- Double Integrals.
- Meaning and calculation.
- Application in the calculation of areas.
- Change of variable (polar), to simplify the calculation of surfaces.
- Implementation in architecture (structure, surface plots, bulk of buildings, budgets etc.).
Teaching and learning activities
In person
Different types of methodology have been applied depending on the type of teaching activity:
- Theory sessions for the presentation of concepts.
- Practical sessions to apply the most important theoretical concepts.
- Activities proposed in the Moodle University Teaching Platform
Each type of sessions, work and activities; They are designed for the development of the competencies that the student must acquire in the subject.
The most important recommendations made to the students can be summarized in the following diagram:
- Attendance at theory sessions in a participatory way.
- Complement the topics covered in these sessions with information offered in the bibliography.
- Use, at any time, tutorial sessions to resolve any doubts or problems.
- Completion of written tests throughout the semester.
- Follow the development of the internship according to the established criteria.
- When the necessary theoretical concepts have been explained, do not delay the completion of the exercises.
- Begin the completion of practical tasks individually.
- Solve difficulties encountered with classmates.
The weekly sessions are planned as follows:
1. Theoretical sessions (1/2 half of the hours per week): Master classes for the transmission of theoretical content and instrumental techniques through oral expression and the blackboard. The classes themselves will be taught in them and in them you can ask questions, doubts, comments.
2. Practical sessions (1/2 half of the weekly hours): Resolution of exercises posed in class and examples of resolution of practical classes. In these classes the proposed exercises will be collected.
3. Tutorial sessions: During these sessions, successive or prior to the schedules of workshops and lessons that each tutor will carry out with their assigned group of students, students may raise with the teachers those reasonable doubts that have not been solved during the rest of the sessions. Likewise, during this time the student may request a specific bibliography of extension, or any other type of information related to the subject.
| TRAINING ACTIVITY | COMPETENCES | ECTS CREDITS |
|---|---|---|
| Class exhibition | 07 08 09 11 | 1,5 |
| Class participation | 07 08 09 11 | 0,5 |
| Clase practice | 07 08 09 11 | 0,5 |
| Tutorials | 07 08 09 11 | 0,5 |
| Individual or group study | 07 08 09 11 | 3,0 |
Evaluation systems and criteria
In person
The course takes place in a certain number of sessions that are established in the Bachelor's Degree calendar.
Class attendance is mandatory, since the Bachelor's Degree in Architecture is face-to-face, therefore, 100% of the classes must be attended, in order to be able to monitor the subject well and a continuous evaluation. If the student does not meet 80% of the attendance, they will not be able to take the exam in the 1st call.
Whenever a student misses class, he or she must justify it; if they do not do so, a zero will be put on the activities of this day.
If the student is not in the first year, he or she must not enroll in any subject that coincides in schedule with mathematics.
During the semester, different exercises will be collected and scored that will account for 10% of the final grade.
Two midterm exams (they do not release subject) and a final exam are scheduled.
FINAL GRADE OF THE SUBJECT:
0,125*FPE_1 + 0,125*FPE_2 + 0,10*CE + 0,65*FE
To apply this criterion, the EF score must be equal to or greater than 5. Otherwise, the final grade of the subject will be the grade of the FE.
|
Test subject to evaluation |
% NOTE |
|
FPE_1 - 1st Midterm Exam |
12,5 % |
|
FPE_2 - 2nd Midterm Exam |
12,5 % |
|
CE - Class exercises |
10 % |
|
FE - Final Exam |
65 % |
|
|
100 % |
In the second call, the grade will be the one obtained in the final exam.
FINAL EXAMINATION
On the date scheduled by the School of Architecture, a test will be held as a global final exam of all the contents of the subject, presented in the theoretical classes, or applied in the practical work of sustainable building developed. It will have an assessment of 65% of the total of the subject.
Bibliography and resources
“Calculus. Una y varias variables” Vol I y Vol II - Salas, Hille & Etgen. - 4ª Ed. Editorial Reverté, 2002
“Cálculo diferencial e integral” - M. Piskunov. Editorial Utecha Noriega
“Cálculo integral” - P. Puig Adam.
“Problemas de cálculo integral” - Schaum.
“Problemas de ecuaciones diferenciales” - Schaum.