05OHTLU

A.A. 2021/22

Course Language

Inglese

Degree programme(s)

1st degree and Bachelor-level of the Bologna process in Architettura (Architecture) - Torino

Borrow

01SUGLU

Course structure

Teaching | Hours |
---|---|

Lezioni | 50 |

Esercitazioni in aula | 30 |

Lecturers

Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
---|---|---|---|---|---|---|---|

Painter Kevin John | Professore Ordinario | MAT/07 | 50 | 30 | 0 | 0 | 4 |

Co-lectuers

Context

SSD | CFU | Activities | Area context |
---|---|---|---|

MAT/03 MAT/05 MAT/07 |
2 3 3 |
A - Di base A - Di base A - Di base |
Discipline matematiche per l'architettura Discipline matematiche per l'architettura Discipline matematiche per l'architettura |

2021/22

The course’s main objective is to convey, in a unified way, the learning of the main basic mathematical tools and of its language. It is directed at learners coming from diversified educational backgrounds. More specifically, the syllabus will deal with topics preparatory and in support of the parallel course of architectural drawing, and of the subsequent courses of building physics, real estate evaluation, as well as of the structural matters. Wherever possible, links and synergies with such disciplines, typical of the course of Architecture, will be outlined. For each of the arguments touched upon, the basic notions and the principal methods of analysis and resolution will be presented.
The course is organized with the objective to convey to the student the capacity to identify, interpret, apply and present results and problems of a mathematical character, aiming at the logic of the solution more than at the complexity of calculus, which can at a later stage be resolved with the help of appropriate software machinery

The main objective of the course is to convey, in a unified way, basic mathematical tools and language. It is directed towards students from diverse educational backgrounds. More specifically, the syllabus will consider topics that support the parallel course in architectural drawing, as well as in preparation for subsequent courses in building physics, real estate evaluation and structural matters. Wherever possible, links and synergies will be made with disciplines typical of a course in Architecture. For each of the topics explored, basic notions and principal methods of analysis and resolution will be presented. The course is organized with the objective of providing the student with the capacity to identify, interpret, apply and present results and problems of a mathematical nature, aimed more at directly solving problems than examining the complexity of calculus, and which can at a later stage be resolved with the help of appropriate software machinery

The students will acquire knowledge and skills below described, tied to the essential mathematical tools, specifically in order to be able to:
- understand
- classify
- resolve
differential calculus problems in one variable, integral calculus problems, linear algebra and geometry. As well as:
- identify
- examine
- reorganize
the mathematical concepts and objects used within the disciplinary areas provided for by the educational path. These include matrices, vectors, plane’s geometrical entities, surface area calculus, functional relations and their classifications.
Special attention will be devoted to spatial visualizations and to their mathematical description, thus the student shall prove able to:
- recognize from its graphic representation the properties of a function, as well as:
- represent in a graphic form elementary geometrical entities and functions of a single real variable.
The course will teach the students how to analyze, formalize through a mathematical model and solve simple problems of varying nature that they will encounter in their profession, while appraising the most appropriate analytical and geometrical instruments.

Students will acquire knowledge and skills as described below, linked to essential mathematical tools. At the end of the course the student should be able to:
- understand
- classify
- resolve
differential calculus problems in one variable, integral calculus problems, linear algebra and geometry. In addition, the student should be able to:
- identify
- examine
- reorganize
mathematical concepts and objects used within these disciplinary areas, and explained and defined during the course. These include matrices, vectors, geometrical entities of the plane, surface area calculus, functional relations and their classifications. Particular attention will be devoted to spatial visualizations and their mathematical description. At the end of the course the student should be able to:
- recognize from its graphic representation the properties of a function;
- and, represent in a graphic form elementary geometrical entities and functions of a single real variable.
The course will teach students how to analyze, formalize through a mathematical model, and solve simple problems of varying nature similar to those they will encounter in their profession, while appraising the most appropriate analytical and geometrical tools.

Knowledge of mathematical concepts typical of completed high school/entry stage of college is required. More specifically, the student shall know how to solve first and second degree equations and inequalities, fractional equations and inequalities, systems of inequalities, products and divisions of polynomials; he/she shall know basic concepts in goniometry and trigonometry, logarithms and exponentials; he/she shall know the main properties of powers, of the absolute value, of the plane’s Euclidean geometrical entities.

Knowledge of mathematical concepts typical of a completed high school/entry stage of college will be required. More specifically, the student should know how to solve first and second degree equations and inequalities, fractional equations and inequalities, systems of inequalities, products and divisions of polynomials. In addition, the student should understand basic concepts in geometry and trigonometry, logarithms and exponentials, the main properties of powers, of the absolute value, and of the plane’s Euclidean geometrical entities.

Linear algebra and geometry.
Matrices and their operations: addition, product with a scalar, matrix multiplication, transposition; submatrices; formulas to calculate the determinants of square matrices; rank of a matrix.
Vectors and their operations: geometric representation and representation with Cartesian orthonormal components; magnitude an direction; addition, subtraction and linear combination of vectors; scalar, cross and scalar triple products.
Linear systems: Cramer’s rule and Rouché-Capelli theorem; linear algebra applications for the study of planes and lines; basics of plane geometry.
Differential calculus.
Functions: domain, codomain and graphic representation; main symmetries; elementary functions (rational and irrational functions, exponential and logarithmic functions, trigonometric and hyperbolic functions); elementary operations between functions, reflections and translations; limits of functions and their determination in straightforward cases; indeterminate forms and examples of special limits; continuity and related theorems; derivability, computation of derivatives and related applications, also in the resolution of calculus problems; first derivative and tangent line; main theorems concerning monotonicity and concavity/convexity; behavior at the boundary of the domain; qualitative graph of a function.
Single variable integral calculus.
Single variable integral calculus: main properties; the definite integral and the surface area calculus; the indefinite integral and the search for simple primitives.

Linear algebra and geometry.
Matrices and their operations: addition, product with a scalar, matrix multiplication, transposition; submatrices; formulae to calculate the determinants of square matrices; rank of a matrix.
Vectors and their operations: geometric representation and representation with Cartesian orthonormal components; magnitude and direction; addition, subtraction and linear combination of vectors; scalar, cross and scalar triple products.
Linear systems: Cramer’s rule and Rouché-Capelli theorem; linear algebra applications for the study of planes and lines; basics of plane geometry.
Differential calculus.
Functions: domain, codomain and graphic representation; main symmetries; elementary functions (rational and irrational functions, exponential and logarithmic functions, trigonometric and hyperbolic functions); elementary operations between functions, reflections and translations; limits of functions and their determination in straightforward cases; indeterminate forms and examples of special limits; continuity and related theorems; derivability, computation of derivatives and related applications, also in the resolution of calculus problems; first derivative and tangent line; main theorems concerning monotonicity and concavity/convexity; behavior at the boundary of the domain; qualitative graph of a function.
Single variable integral calculus.
Single variable integral calculus: main properties; the definite integral and the surface area calculus; the indefinite integral and the search for simple primitives.

The course is structured in 50 hours of frontal class (theoretical) lectures and 30 hours of lectures devoted to exercises, that is a subdivision of approximately 60% and 40% of those activities.
The first part of the course will be mainly devoted to the subjects of linear algebra and geometry. The second part will be mainly devoted to the subjects of differential and integral calculus. To both parts a considerable portion of time of the course will be dedicated, although not necessarily in exactly equal proportions.

The course is structured according to 50 hours of frontal class (theoretical) lectures and 30 hours of lectures devoted to exercises; that is, a subdivision of approximately 60% and 40% between those activities. The first part of the course will be devoted to the subjects of linear algebra and geometry. The second part will be devoted to the subjects of differential and integral calculus. Both parts will receive a considerable portion of the overall course time of the course, although not necessarily in exactly equal proportions.

R. A. Adams, Calculus, a complete course, Pearson Canada
S. Lipschutz, M. Lipson, Linear Algebra, Schaum’s outlines
The teacher will make notes and/or exercises available online, on the students-teachers platform.
Materials for further readings will be communicated during class, if needed.

R. A. Adams, Calculus, a complete course, Pearson Canada
S. Lipschutz, M. Lipson, Linear Algebra, Schaum’s outlines
The teacher will also make notes and/or exercises available online, via the teaching portal.
Materials for further reading will be communicated during class, if needed.

...
The exam aims at ascertaining the acquisition of knowledge that allows one to comprehend and classify single-variable differential calculus problems, integral calculus, linear algebra and geometry, such as detailed in the syllabus; to identify matrices, vectors, the plane’s and space’s geometrical entities, surface area calculus, functional relations and their classifications. At the same time, the exam will ascertain the acquisition of the corresponding skills, such as knowing how to solve single-variable differential calculus problems, integral calculus, linear algebra and geometry. Thus, to know how to reorganize the concepts of matrix, vector, geometrical entity in the plane and in space, surface area, function. The ability to recognize the graph of a function or the skill to represent it will be verified.
The written exam consists of a series of 8 open-ended exercises, of which 2 with a maximum of 7 points available and 6 with a maximum of 3 points available. Maximum points shall be awarded to an exercise if it is complete, correct, logically sound and clearly presented. Any unanswered exercise is valued zero.
The written exam has a duration of 2 hours and it is passed with a mark of at least 18/30. Use of personal notes, textbooks, printed notes and calculator is not permitted. It is possible to use an inventory of formulas specifically prepared by the teacher, which will be rendered available online through the portal. The final grading is composed of the written exam’s mark and, upon explicit request by the student or as an option exercised by the teacher, by the mark of an additional oral examination, which can make the final grading vary in positive as well as in negative. The oral examination must be taken during the same exam period during which the written exam was passed. The oral examination is not administered following a written exam which was not passed.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

The exam aims to ascertain a depth of knowledge that allows one to comprehend and classify single-variable differential calculus problems, integral calculus, linear algebra and geometry, as detailed in the syllabus; to identify matrices, vectors, the plane’s and space’s geometrical entities, surface area calculus, functional relations and their classifications. At the same time, the exam will ascertain the acquisition of corresponding skills, such as understanding how to solve single-variable differential calculus problems, integral calculus, linear algebra and geometry. Therefore, to understand how to reorganize the concepts of matrix, vector, geometrical entity in the plane and in space, surface area, function. The ability to recognize the graph of a function and the skill to represent it will be verified.
The written exam will consist of a series of 8 open-ended exercises, of which 2 will have a maximum of 7 points and 6 will have a maximum of 3 points . Maximum points will only be awarded to an exercise if it is complete, correct, logically sound and clearly presented. Any unanswered exercise is valued zero.
The written exam will have a duration of 2 hours and is passed with a mark of at least 18/30. Use of personal notes, textbooks, printed notes or a calculator is not permitted. It will be possible to use an inventory of formulas specifically prepared by the teacher, which will be made available online through the teaching portal. The final grading will be composed of the written exam’s mark and, upon explicit request by the student or as an option exercised by the teacher, by the mark from an additional oral examination. If an oral exam is conducted then the grade from the written exam could vary positively or negatively, or remain unchanged. The oral exam will focus on a discussion and deepening of the topics proposed in the written test, and basic theoretical notions can also be required. The oral examination must be taken in the same exam period during which the written exam was passed. The oral examination is not administered following a written exam which was not passed.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.

The exam aims at ascertaining the acquisition of knowledge that allows one to comprehend and classify single-variable differential calculus problems, integral calculus, linear algebra and geometry, such as detailed in the syllabus; to identify matrices, vectors, the plane’s and space’s geometrical entities, surface area calculus, functional relations and their classifications. At the same time, the exam will ascertain the acquisition of the corresponding skills, such as knowing how to solve single-variable differential calculus problems, integral calculus, linear algebra and geometry. Thus, to know how to reorganize the concepts of matrix, vector, geometrical entity in the plane and in space, surface area, function. The ability to recognize the graph of a function or the skill to represent it will be verified.
The written exam consists of a series of 8 open-ended exercises, of which 2 with a maximum of 7 points available and 6 with a maximum of 3 points available. Maximum points shall be awarded to an exercise if it is complete, correct, logically sound and clearly presented. Any unanswered exercise is valued zero.
The written exam has a duration of 2 hours, subdivided into two parts of 1 hour + 1 hour, with handing of 4 exercises after each hour. Each part consists of three exercises of maximum 3 points and one of maximum 7 points. In case of impossibility to take the written exam in physical presence, it will consist of “prova scritta su carta e videosorveglianza”, meaning “written test with video surveillance” (with the possibility of being recorded). In such case, technical instructions on the procedure for carrying out and handing (uploading) the paperwork will be given during the course. It will be necessary to have at least one device with an online camera available (e.g. PC or smartphone). It may be necessary to have a second device available.
The written exam is passed with a mark of at least 18/30. Use of personal notes, textbooks, printed notes and calculator is not permitted. It is possible to use an inventory of formulas specifically prepared by the teacher, which will be rendered available online through the portal. The final grading is composed of the written exam’s mark and, upon explicit request by the student or as an option exercised by the teacher, by the mark of an additional oral examination, which can make the final grading vary in positive as well as in negative. The oral examination must be taken during the same exam period during which the written exam was passed. The oral examination is not administered following a written exam which was not passed.

The exam aims to ascertain a depth of knowledge that allows one to comprehend and classify single-variable differential calculus problems, integral calculus, linear algebra and geometry, as detailed in the syllabus; to identify matrices, vectors, the plane’s and space’s geometrical entities, surface area calculus, functional relations and their classifications. At the same time, the exam will ascertain the acquisition of corresponding skills, such as understanding how to solve single-variable differential calculus problems, integral calculus, linear algebra and geometry. Therefore, to understand how to reorganize the concepts of matrix, vector, geometrical entity in the plane and in space, surface area, function. The ability to recognize the graph of a function and the skill to represent it will be verified.
The written exam will consist of a series of 8 open-ended exercises, of which 2 will have a maximum of 7 points and 6 will have a maximum of 3 points . Maximum points will only be awarded to an exercise if it is complete, correct, logically sound and clearly presented. Any unanswered exercise is valued zero.
The written exam will have a duration of 2 hours and is passed with a mark of at least 18/30. Use of personal notes, textbooks, printed notes or a calculator is not permitted. It will be possible to use an inventory of formulas specifically prepared by the teacher, which will be made available online through the teaching portal. The final grading will be composed of the written exam’s mark and, upon explicit request by the student or as an option exercised by the teacher, by the mark from an additional oral examination. If an oral exam is conducted then the grade from the written exam could vary positively or negatively, or remain unchanged. The oral exam will focus on a discussion and deepening of the topics proposed in the written test, and basic theoretical notions can also be required. The oral examination must be taken in the same exam period during which the written exam was passed. The oral examination is not administered following a written exam which was not passed.

The exam aims at ascertaining the acquisition of knowledge that allows one to comprehend and classify single-variable differential calculus problems, integral calculus, linear algebra and geometry, such as detailed in the syllabus; to identify matrices, vectors, the plane’s and space’s geometrical entities, surface area calculus, functional relations and their classifications. At the same time, the exam will ascertain the acquisition of the corresponding skills, such as knowing how to solve single-variable differential calculus problems, integral calculus, linear algebra and geometry. Thus, to know how to reorganize the concepts of matrix, vector, geometrical entity in the plane and in space, surface area, function. The ability to recognize the graph of a function or the skill to represent it will be verified.
The written exam consists of a series of 8 open-ended exercises, of which 2 with a maximum of 7 points available and 6 with a maximum of 3 points available. Maximum points shall be awarded to an exercise if it is complete, correct, logically sound and clearly presented. Any unanswered exercise is valued zero.
The written exam has a duration of 2 hours, subdivided into two parts of 1 hour + 1 hour, with handing of 4 exercises after each hour. Each part consists of three exercises of maximum 3 points and one of maximum 7 points. In case of impossibility to take the written exam in physical presence, it will consist of “prova scritta su carta e videosorveglianza”, meaning “written test with video surveillance” (with the possibility of being recorded). In such case, technical instructions on the procedure for carrying out and handing (uploading) the paperwork will be given during the course. It will be necessary to have at least one device with an online camera available (e.g. PC or smartphone). It may be necessary to have a second device available.
The written exam is passed with a mark of at least 18/30. Use of personal notes, textbooks, printed notes and calculator is not permitted. It is possible to use an inventory of formulas specifically prepared by the teacher, which will be rendered available online through the portal. The final grading is composed of the written exam’s mark and, upon explicit request by the student or as an option exercised by the teacher, by the mark of an additional oral examination, which can make the final grading vary in positive as well as in negative. The oral examination must be taken during the same exam period during which the written exam was passed. The oral examination is not administered following a written exam which was not passed.

The exam aims to ascertain a depth of knowledge that allows one to comprehend and classify single-variable differential calculus problems, integral calculus, linear algebra and geometry, as detailed in the syllabus; to identify matrices, vectors, the plane’s and space’s geometrical entities, surface area calculus, functional relations and their classifications. At the same time, the exam will ascertain the acquisition of corresponding skills, such as understanding how to solve single-variable differential calculus problems, integral calculus, linear algebra and geometry. Therefore, to understand how to reorganize the concepts of matrix, vector, geometrical entity in the plane and in space, surface area, function. The ability to recognize the graph of a function and the skill to represent it will be verified.
The written exam will consist of a series of 8 open-ended exercises, of which 2 will have a maximum of 7 points and 6 will have a maximum of 3 points . Maximum points will only be awarded to an exercise if it is complete, correct, logically sound and clearly presented. Any unanswered exercise is valued zero.
The written exam will have a duration of 2 hours and is passed with a mark of at least 18/30. Use of personal notes, textbooks, printed notes or a calculator is not permitted. It will be possible to use an inventory of formulas specifically prepared by the teacher, which will be made available online through the teaching portal. The final grading will be composed of the written exam’s mark and, upon explicit request by the student or as an option exercised by the teacher, by the mark from an additional oral examination. If an oral exam is conducted then the grade from the written exam could vary positively or negatively, or remain unchanged. The oral exam will focus on a discussion and deepening of the topics proposed in the written test, and basic theoretical notions can also be required. The oral examination must be taken in the same exam period during which the written exam was passed. The oral examination is not administered following a written exam which was not passed.

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Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY