Universitat Internacional de Catalunya
Mathematics
Other languages of instruction: Spanish
Teaching staff
The class schedule is:
Monday from 14.00 to 16.00
Tuesday from 14.00 to 16.00
If more time is needed, the student will request an appointment for the teachers by e-mail.
- María José Díez (mjdiez@uic.es)
- Pedro Casariego (pcasariego@uic.es)
- José Ramón Solé (jrsole@uic.es)
Introduction
This subject is related exclusively to learning the tools that students need for their application in the field of architecture.
It is intended that the student finishes the course using mathematics as a work tool related to real problems that they might encounter in the future, especially for the calculation of structures.
Given the current situation, a hybrid teaching modality (a mixture of face-to-face and non-face to-face) has been raised for next course 2021-22. Fifty per cent of the classes will be face-to-face in the classroom, and 50% will be teached online using the platform Teams.
Interactive and more participatory classes will be taught with the aim of increasing the student's work capacity in facets close to what their professional life will be.
The resolution of all practical exercises will be important proposed to the student, which will be graded, as soon as posible, by teacher virtually or presencially.
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
- 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 concept of the inductive factor.
- Knowing the properties of determinants and their applications.
- 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.
- Dominate 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.
- Learn compute fluently primitive functions by selecting the most appropriate method.
- Knowing how to calculate definite integrals
- Knowing how to calculate with ease double and triple integrals using iterated integrations.
Syllabus
1. 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
- Mean Value Theorem
- 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, waxing and waning, etc.
- Brief notions of partial derivatives
- The meaning of geometric features.
- Optimization
2. 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. Variable change (polar) to simplify the calculation of surfaces
- Implementation in architecture (structure, surface plots, bulk of buildings, budgets etc.)
3. 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
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
- Numerically solving system equations
5. Vector algebra
- Vectors in free space. Components of a vector (or standard length, direction, sense). Types of vectors
- Operations with vectors
- Projection of a vector and angle between vectors
- Linear dependence and independence of vectors. Linear combination
- Parallel, perpendicular (orthogonal) and geometric mean vectors
Teaching and learning activities
In blended
Based on the calendar developed by the Board of the School of Architecture for course 2021-2022, Mondays classes will be online and Tuesdays classes will be face-to-face.
Virtual classes are very participative, in where short questions will be asked to the students during the lesson. Students should have a camera and a microphone (computer) to follow the class and communicate with the rest of the students. Any case, students can communicate between them and with the teacher using the chat
Before classes students will receive some documents for personal reading and study. During the lessons, some exercises and questionnaires will be proposed virtually to the student through Moodle platform. Questions and doubts will be solved during the class. Teacher will solve some of the exercises synchronously according to the questions that the students may ask.
Last minutes of classes will be used to introduce the topic to be covered in the next session
Class attendance is compulsory
Face-to-face classes will be similar to virtual classes, but the interaction between teacher and students will be lower and teacher will cover the topics and solve exercises in the blackboard at classes. The class will not be recorded, so it is mandatory for students to come to classes.
Note: if the situation changes, and students and teacher are forced to move to virtual classes, both classes (Monday and Tuesday) will be online. In the case of students living in foreign countries with different time zone, classes will be recorded and students may follow the event on a delayed basis.| 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 blended
Assessment is continuous and class attendance is compulsory in both modalities (face-to-face and virtual). Students must attend the 100% of the classes to ensure a satisfactory comprehension of the topics covered in the subject. It is not possible to pass the subject with an unic exam.
Missed class must be clearly justify it, independently if the class is face-to-face or virtual. Not justified classes will be grade with zero in the activities of this day.
Students must not enrol in other subjects which overlap Maths classes.
During the semester, exercises solved at class by the student will be graded. Exercises not submitted will be grade with -1. The average of all the exercises solved and submitted at class, will represent the 30% of the final grade of the subject.
A partial exam is schedule on the calendar
Final grade will be obtained by means of the following criteria:
- The average of all the exercises solved and submitted at class, will represent the 30% of the final grade of the subject.
- Partial exam: 30% of the final grade
- Final exam: 40% of the final grade
Two types of grading will be considered:
|
OPTION A |
|||
|
Class Exercises |
Partial Exam ≥ 6,5 Content of 1st part of the subject |
Final Exam Content of 2nd part of the subject |
|
|
CE |
PE |
FE |
Final Grade 0,30*CE+0,35*PE+0,35*FE |
|
OPTION B |
|||
|
Class Exercises |
Partial Exam < 6,5 Control |
Final Exam Content of the full subject |
|
|
CE |
PE |
FE |
Final Grade 0,30*CE+0,30*PE+0,40*FE |
In the second call, the grade obtained by the student will be considered only if the student follows the indicated requirements according with the circumstances in which we find ourselves. If the students do not follow the requirement imposed to do the exam, the maximum grade will be 5.
Bibliography and resources
Calculus. Una y varias variables. Vol I y Vol II. Salas, Hille & Etgen. 4ª Ed. Editorial Reverté, 2002
M. Piskunov: “Cálculo diferencial e integral” ed. Utecha Noriega
P. Puig Adam. “Cálculo integral”
Schaum: “ Problemas de cálculo integral”
Schaum: “ Problemas de ecuaciones diferenciales”