PORTALE DELLA DIDATTICA

### Mathematical analysis II

02KXUTR

A.A. 2023/24

Course Language

Inglese

Course degree

1st degree and Bachelor-level of the Bologna process in Civil And Environmental Engineering - Torino

Course structure
Teaching Hours
Teachers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Teaching assistant
Context
SSD CFU Activities Area context
MAT/05 6 A - Di base Matematica, informatica e statistica
2021/22
This course first completes the theory of functions of one variable which was developed in the Mathematical Analysis I course, by introducing the student to basic concepts of numerical series, power series, Fourier series, and Laplace transform. The course then introduces basic topics in the mathematical analysis of functions of several variables including differential calculus in several variables, the theory of multiple integration, line, and surface integration.
This course first completes the theory of functions of one variable which was developed in the Mathematical Analysis I course, by introducing the student to basic concepts of numerical series, power series, Fourier series, and Laplace transform. The course then introduces basic topics in the mathematical analysis of functions of several variables including differential calculus in several variables, the theory of multiple integration, line, and surface integration.
The student should be able to understand the mathematical tools introduced in the course, to make computations with them and to apply such tools in engineering disciplines.
The student should be able to understand the mathematical tools introduced in the course, to make computations with them and to apply such tools in engineering disciplines.
The topics covered in the Mathematical Analysis I and Linear Algebra and Geometry courses. In particular, notions and properties of limits, numerical sequences, differential and integral calculus for functions of one variable, differential equations, linear algebra, geometry of curves.
The topics covered in the Mathematical Analysis I and Linear Algebra and Geometry courses. In particular, notions and properties of limits, numerical sequences, differential and integral calculus for functions of one variable, differential equations, linear algebra, geometry of curves.
- Laplace transform. (1cfu) - Review on vectors and elementary notions of topology of R^n. Functions of several variables, vector fields. Limits and continuity. Partial and directional derivatives, Jacobian matrix. Differentiability, gradient, and tangent plane. Second derivatives, Hessian matrix. Taylor polynomial. Critical points, unconstrained maxima and minima. (2cfu) - Double and triple integrals, center of mass. Length of a curve and area of the region under the graph of a function. Line and surface integrals (for graphs of functions only). Circulation and flux of a vector field. (1,5cfu) - Conservative vector fields. Green, Gauss, and Stokes theorems. (1,5cfu) - Numerical series: definition and convergence criteria. Power series and Taylor series. Fourier series. (2cfu)
- Laplace transform. (1cfu) - Review on vectors and elementary notions of topology of R^n. Functions of several variables, vector fields. Limits and continuity. Partial and directional derivatives, Jacobian matrix. Differentiability, gradient, and tangent plane. Second derivatives, Hessian matrix. Taylor polynomial. Critical points, unconstrained maxima and minima. (2cfu) - Double and triple integrals, center of mass. Length of a curve and area of the region under the graph of a function. Line and surface integrals (for graphs of functions only). Circulation and flux of a vector field. (1,5cfu) - Conservative vector fields. Green, Gauss, and Stokes theorems. (1,5cfu) - Numerical series: definition and convergence criteria. Power series and Taylor series. Fourier series. (2cfu)
The course consists in theoretical lectures and practice classes. Theoretical lectures are devoted to the presentation of the topics, with definitions, properties, introductory examples, as well as a number of selected proofs which are believed to facilitate the learning process. The practice classes are devoted to the acquisition of the abilities through guided solution of problems.
The course consists in theoretical lectures and practice classes. Theoretical lectures are devoted to the presentation of the topics, with definitions, properties, introductory examples, as well as a number of selected proofs which are believed to facilitate the learning process. The practice classes are devoted to the acquisition of the abilities through guided solution of problems.
The following textbook covers the topics of the course and will be used as a reference: - C. Canuto, A. Tabacco, "Mathematical Analysis II", Springer` Other material will be suggested in class and made avalaible thorugh the Portale della Didattica.
The following textbook covers the topics of the course and will be used as a reference: - C. Canuto, A. Tabacco, "Mathematical Analysis II", Springer` Other material will be suggested in class and made avalaible thorugh the Portale della Didattica.
Modalità di esame: Prova scritta (in aula); Prova orale facoltativa;
Exam: Written test; Optional oral exam;
... The goal of the exam is to test the knowledge of the students on the topics included in the official program of the course and to verify their computational and theoretical skills in solving problems. Marks range from 0 to 30 and the exam is successful if the mark is at least 18. The exam consists in a written part and in an optional oral part. The written part consists of 10 exercises with closed answer on the topics presented in the course. Questions cover also theoretical aspects. The aim of the exam is to certify the Expected Learning Outcomes (see above). Questions cover both computational and theoretical aspects, to evaluate the ability in building a logical sequence of arguments using the tools introduced in the course. The exam lasts 100 minutes. Marks are given according to the following rules. Each exercise assigns: 3 points if correct, 0 points if blank, -1 point if wrong. The final mark is the sum of points obtained in each exercise plus 2 extra points. A cum Laude mark is assigned only to students who give all correct answers and ask for an oral exam to confirm the 30/30 mark and possibly get the cum Laude mark. During the exam it is forbidden to use notes, books, exercise sheets and pocket calculators. The test results will be posted on the teaching portal. Students can request an optional oral part that can alter both in the positive and in the negative the mark obtained in the written part. The optional oral part can only be requested in the same exam session of the written part. Students can request the optional oral part only if the mark they obtained in the written part is at least 18/30.
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.
Exam: Written test; Optional oral exam;
The goal of the exam is to test the knowledge of the students on the topics included in the official program of the course and to verify their computational and theoretical skills in solving problems. Marks range from 0 to 30 and the exam is successful if the mark is at least 18. The exam consists in a written part and in an optional oral part. The written part consists of 10 exercises with closed answer on the topics presented in the course. Questions cover also theoretical aspects. The aim of the exam is to certify the Expected Learning Outcomes (see above). Questions cover both computational and theoretical aspects, to evaluate the ability in building a logical sequence of arguments using the tools introduced in the course. The exam lasts 100 minutes. Marks are given according to the following rules. Each exercise assigns: 3 points if correct, 0 points if blank, -1 point if wrong. The final mark is the sum of points obtained in each exercise plus 2 extra points. A cum Laude mark is assigned only to students who give all correct answers and ask for an oral exam to confirm the 30/30 mark and possibly get the cum Laude mark. During the exam it is forbidden to use notes, books, exercise sheets and pocket calculators. The test results will be posted on the teaching portal. Students can request an optional oral part that can alter both in the positive and in the negative the mark obtained in the written part. The optional oral part can only be requested in the same exam session of the written part. Students can request the optional oral part only if the mark they obtained in the written part is at least 18/30.
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.