Mathematical Analysis III

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.

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

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

The overall form of credit for the course: final exam