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B006517 - MATHEMATICAL ANALYSIS II
Main information
Teaching Language
Course Content
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Sustainable Development Goals 2030
Academic Year 2023-24
Coorte 2022 - 3-years First Cycle Degree (DM 270/04) in CIVIL, BUILDING AND ENVIRONMENTAL ENGINEERING
Course year
Second year - First Semester
Belonging Department
Civil and Environmental Engineering (DICEA)
Course Type
Single education field course
Scientific Area
MAT/05 - MATHEMATICAL ANALYSIS
Credits
9
Teaching Hours
81
Teaching Term
11/09/2023 ⇒ 15/12/2023
Attendance required
No
Type of Evaluation
Final Grade
Course Content
show
Lectureship
Teaching Language
Italian
Course Content
The n-dimensional Euclidean space. Curves in parametric form, line integrals.
Differential calculus for (real valued) functions of several variables.
*[Unconstrained and constrained optimization problems.]
Differential calculus for vector valued functions of several variables; parametric surfaces.
Multiple integrals.
Vector fields, corresponding line integrals. Surface and flow integrals.
Function spaces. Sequences of functions, function and power series. Fourier series.
Differential calculus for (real valued) functions of several variables.
*[Unconstrained and constrained optimization problems.]
Differential calculus for vector valued functions of several variables; parametric surfaces.
Multiple integrals.
Vector fields, corresponding line integrals. Surface and flow integrals.
Function spaces. Sequences of functions, function and power series. Fourier series.
Learning Objectives
Knowledge acquired: fundamental elements of differential and integral calculus in several variables; curves and surfaces. Sequences and series of functions, Fourier series.
Skills: understanding of problems relating to the listed topics (see Knowledge), autonomy in proposing and rigorously supporting arguments for their resolution. Confident usage of symbols and results; good control of errors.
Abilities: setting up an analytical framework for simple physical/mechanical problems; strenghtened communication skills in written and oral presentations; autonomy within the individual study and active participation in a group.
Skills: understanding of problems relating to the listed topics (see Knowledge), autonomy in proposing and rigorously supporting arguments for their resolution. Confident usage of symbols and results; good control of errors.
Abilities: setting up an analytical framework for simple physical/mechanical problems; strenghtened communication skills in written and oral presentations; autonomy within the individual study and active participation in a group.
Prerequisites
Differential and integral calculus for functions of one variable
Sequences and numerical series. Ordinary Differential Equations.
Linear algebra and analytic geometry.
Prerequisite (formal): course "Analisi Matematica I"
Recommended: course "Geometria"
Sequences and numerical series. Ordinary Differential Equations.
Linear algebra and analytic geometry.
Prerequisite (formal): course "Analisi Matematica I"
Recommended: course "Geometria"
Teaching Methods
Lessons (in the classroom), in the absence of rigid separation between theory and practice. The discussion of assigned exercises/ problems and possibly of some proofs is part of the course.
Flipped classroom.
Flipped classroom.
Further information
Course duration: 13 nominal weeks, from Sept. 18 to Dec. 15, 2023, excluding Nov. 1 and Dec. 8 (National holidays); 81 hours
Schedule (at the Centro Didattico Morgagni):
Tue.
Wed.
Thu.
Schedule (at the Centro Didattico Morgagni):
Tue.
Wed.
Thu.
Type of Assessment
The exam includes (i) a written part (equivalently, two partial tests during the course) and (ii) an oral part.
(i) The written exam, focused on the topics of the course, comprises both elementary questions and problems (the solutions of the latter need to be supplemented with explanations); some examples can be found on Moodle. (A discussion of the paper with the instructor should be foreseen.)
Two written exams will be organized in the middle and at the end of the course, respectively. An evaluation of no less than 12 in the first exam allows access to the second one; passing the complex of the partial tests (with an average of no less than 15) exempts from taking the written exam.
(ii) The oral exam - compulsory for those who have obtained an evaluation not higher than 20 in the written exam - concerns definitions, overviews, statements of theorems, some proofs (specified in Moodle). Themes for oral presentations will be provided by the instructor, along with bibliographic references (posted in Moodle).
Note:
a) An evaluation higher than 20 in the written exam exempts from the oral exam.
b) Please note that the "Appelli" are distinct from each other: the oral exam cannot be postponed to a subsequent appello (possible exceptions decided by the instructor).
(i) The written exam, focused on the topics of the course, comprises both elementary questions and problems (the solutions of the latter need to be supplemented with explanations); some examples can be found on Moodle. (A discussion of the paper with the instructor should be foreseen.)
Two written exams will be organized in the middle and at the end of the course, respectively. An evaluation of no less than 12 in the first exam allows access to the second one; passing the complex of the partial tests (with an average of no less than 15) exempts from taking the written exam.
(ii) The oral exam - compulsory for those who have obtained an evaluation not higher than 20 in the written exam - concerns definitions, overviews, statements of theorems, some proofs (specified in Moodle). Themes for oral presentations will be provided by the instructor, along with bibliographic references (posted in Moodle).
Note:
a) An evaluation higher than 20 in the written exam exempts from the oral exam.
b) Please note that the "Appelli" are distinct from each other: the oral exam cannot be postponed to a subsequent appello (possible exceptions decided by the instructor).
Sustainable Development Goals 2030
17. Partnership for the goals