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Mathematical Analysis III

General data

Course ID: 360-MS1-2AM3a
Erasmus code / ISCED: 11.102 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title: Mathematical Analysis III
Name in Polish: Mathematical Analysis III
Organizational unit: Faculty of Mathematics
Course groups:
ECTS credit allocation (and other scores): 8.00 Basic information on ECTS credits allocation principles:
  • the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS;
  • the student’s weekly hourly workload is 45 h;
  • 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes;
  • weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS;
  • work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load.

view allocation of credits
Language: English
Type of course:

obligatory courses

Mode:

(in Polish) w sali

Short description:

Course objectives: Knowledge of material related to presented contents:

a) understanding introduced notions and theorems

b) knowledge of presented proofs

c) giving appropriate examples

d) solving computational problems

Euclidean space is a simple and useful model of the space we live in. This course is a mathematical exploration of this space: we define distance, shapes including boxes and balls, and extend the notion of convergence from single-variable analysis.

The next step is to study functions on Euclidean space, aiming to understand continuous functions. We discuss how the main results from single-variable analysis can be extended to the multi-variable case.

We move to derivatives of multi-variable functions, aiming to replicate both the geometric meaning (slope of tangents) and the formalism from the single-variable case, as well as developing a theory which is useful for applications.

In the final part of the course we achieve similar goals with integration.

Full description:

Course profile: academic

Form of study: stationary

Course type: obligatory

Academic discipline: science and natural science, field of study in the arts and science: mathematics

Year: 2, semester: 3

Prerequisities: Mathematical Analysis II, Linear Algebra II

lecture 60 h. exercise class 90 h.

Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups.

ECTS credits: 8

Balance of student workload:

attending lectures15x4h = 60h

attending exercise classes 30x3h = 90h

preparation for classes 7x3h = 21h

completing notes after exercises and lectures 7x2h = 14h

consultations 5x1h = 5h

home works: solving exercises 45h = 45h

the final examination: preparation.and take 12h + 4h = 16h

Quantitative description

Direct interaction with the teacher: 150 h., 5 ECTS

Practical exercises: 145 h., 5 ECTS

Learning outcomes:

Learning outcomes:

Can integrate function of several variables.K_U07, K_U10, K_U11, K_U13, K_U14, K_W02, K_W04, K_W05, K_W07

Knows Stokes theorem, can apply it and understands vector versions of this theorem.K_U12, K_U13, K_U14, K_U18, K_U24, K_W02,

K_W04, K_W05, K_W07

Knows definitions and basic properties of operators such as gradient, rotation and divergence.K_U16, K_U17, K_W02, K_W04, K_W05

Knows and can apply differential calculus of functions of several variables: knows basic theorems in this topic.K_U12, K_W02, K_W04,

K_W05, K_W07

Possesses basic knowledge on the spaces of continuous linear and multilinear maps.K_U16, K_U17, K_W02, K_W04, K_W05

Assessment methods and assessment criteria:

The overall form of credit for the course: final exam

Classes in period "Academic year 2022/2023" (past)

Time span: 2022-10-01 - 2023-06-30
Selected timetable range:
Navigate to timetable
Type of class:
Class, 90 hours more information
Lecture, 60 hours more information
Coordinators: Tomasz Czyżycki, Andrew McKee, Aneta Sliżewska
Group instructors: Andrew McKee
Students list: (inaccessible to you)
Examination: Course - Examination
Class - Grading
Type of course:

obligatory courses

Course descriptions are protected by copyright.
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