MATHEMATICAL ANALYSIS II COURSE
Course objectives
Knowledge and understanding. Good theoretical and practical knowledge of differential calculus and integration for functions of several real variables. Ability to understand these issues also in the context of other courses. Applying knowledge and understanding. Ability to use the acquired skills for solving simple problems and for their use required in other courses. Making judgements. Good ability to recognize, frame and set out the resolution of simple problems, selecting appropriately among the methods learned. Communication skills. Good presentation skills of basic concepts and techniques of Mathematical analysis. Learning skills. Good learning ability of mathematical issues in other courses, by virtue of the comprehension of the logical-deductive character of the discipline.
Channel 1
ANNALISA MALUSA
Lecturers' profile
Program - Frequency - Exams
Course program
Basic notions of R^n topology.
Parametric curves
Real functions of 2 or more real variables.
Limits and continuity.
Differential calculus in several variables: partial derivatives,
gradient and directional derivatives. Differentiability.
Partial derivatives of higher order.
Taylor's formula.
Double and triple integrals: reduction method, change of variables.
Generalized multiple integrals.
Ordinary differential equations: first order equations with separable variables, first order linear equations. Second order linear equations with constant coefficients.
Free optimization.
Constrained optimization.
Convex functions.
Examples and applications of the topics studied.
Prerequisites
Calculus; linear algebra.
Books
Any college-level textbook on real functions of several variables.
Frequency
Attendance is optional and will not be verified, but it is highly recommended.
Exam mode
The exam consists of a written test and an oral one.
To take the oral exam, it is necessary to have passed a written test.
The final evaluation results from that of both oral and written tests,
although the oral test does not receive an independent evaluation.
The examinee's preparation is assessed in each test (written or oral)
by solving exercises on the topics covered in class (prevalent modality
in the written test) and the enunciation and demonstration of theorems
illustrated in class (prevalent modality in the oral exam).
The written test may also include multiple-choice questions;
the written test will also be discussed in the oral exam.
Bibliography
Any college-level textbook on real functions of several variables.
Lesson mode
Lectures and exercises will be taught in a classroom.
ANNALISA MALUSA
Lecturers' profile
Program - Frequency - Exams
Course program
Basic notions of R^n topology.
Parametric curves.
Real functions of 2 or more real variables.
Limits and continuity.
Differential calculus in several variables: partial derivatives,
gradient and directional derivatives. Differentiability.
Partial derivatives of higher order.
Taylor's formula.
Double and triple integrals: reduction method, change of variables.
Generalized multiple integrals.
Ordinary differential equations: first order equations with separable variables, first order linear equations. Second order linear equations with constant coefficients.
Free optimization.
Constrained optimization.
Convex functions.
Examples and applications of the topics studied.
Prerequisites
Calculus; linear algebra.
Books
Any college-level textbook on real functions of several variables.
Frequency
Attendance is optional and will not be verified, but it is highly recommended.
Exam mode
The exam consists of a written test and an oral one.
To take the oral exam, it is necessary to have passed a written test.
The final evaluation results from that of both oral and written tests,
although the oral test does not receive an independent evaluation.
The examinee's preparation is assessed in each test (written or oral)
by solving exercises on the topics covered in class (prevalent modality
in the written test) and the enunciation and demonstration of theorems
illustrated in class (prevalent modality in the oral exam).
The written test may also include multiple-choice questions;
the written test will also be discussed in the oral exam.
Bibliography
Any college-level textbook on real functions of several variables.
Lesson mode
Lectures and exercises will be taught in a classroom.
- Lesson code10612163
- Academic year2024/2025
- CourseStatistics, Economics and Society
- CurriculumSingle curriculum
- Year2nd year
- Semester1st semester
- SSDMAT/05
- CFU6
- Subject areaMatematico