Mathematical Analysis III
Informacje ogólne
Kod przedmiotu: | 360-MS1-2AM3a |
Kod Erasmus / ISCED: |
11.102
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Nazwa przedmiotu: | Mathematical Analysis III |
Jednostka: | Wydział Matematyki |
Grupy: |
Erasmus+ sem. zimowy |
Punkty ECTS i inne: |
8.00
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Język prowadzenia: | angielski |
Rodzaj przedmiotu: | obowiązkowe |
Tryb prowadzenia przedmiotu: | w sali |
Skrócony opis: |
(tylko po angielsku) 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. |
Pełny opis: |
(tylko po angielsku) Course profile: academic Form of study: stationary Course type: obligatory Academic discipline: Mathematics, 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 |
Efekty uczenia się: |
(tylko po angielsku) 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 |
Metody i kryteria oceniania: |
(tylko po angielsku) The overall form of credit for the course: final exam |
Zajęcia w cyklu "Rok akademicki 2022/23" (w trakcie)
Okres: | 2022-10-01 - 2023-06-30 |
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Typ zajęć: |
Ćwiczenia, 90 godzin
Wykład, 60 godzin
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Koordynatorzy: | Tomasz Czyżycki, Andrew McKee, Aneta Sliżewska | |
Prowadzący grup: | Andrew McKee | |
Lista studentów: | (nie masz dostępu) | |
Zaliczenie: |
Przedmiot -
Egzamin
Ćwiczenia - Zaliczenie na ocenę |
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Rodzaj przedmiotu: | obowiązkowe |
Właścicielem praw autorskich jest Uniwersytet w Białymstoku.