In the event that the health authorities announce a new period of confinement due to the evolution of
the health crisis caused by COVID-19, the teaching staff will promptly communicate how this may effect
the teaching methodologies and activities as well as the assessment.
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 2020-21. Fifty per cent of the classes will be face-to-face in the classroom, and 50% will be teached online using the platform Blackboard Collaborate.
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.
Competencies
11 - To acquire knowledge and apply it to numerical calculation, analytic and differential geometry and algebraic methods.
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.
Learning outcomes
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