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Etusivu > Ajankohtaiset koulutukset > Energy Technology (ETE) > 2024 > Vuosi 3 > Real Analysis (IT00BL30)

# Real Analysis

Rakennetyyppi: Opintojakso IT00BL30 ETE 2024 Insinööri (AMK) 3 (2026) Syksy 5 op Mäkelä, Jarmo Englanti

## Osaamistavoitteet

In the Real Analysis course the student learns to differentiate and integrate multivariable functions. The general theory of series is also briefly discussed. The central topic in the course is vector analysis, where vector fields are differentiated and integrated. Vector fields include, for instance, electric-, and magnetic fields, and the velocity field of a fluid. Hence vector analysis has plenty of applications, among other things, in electromagnetism and fluid dynamics.

## Opiskelijan työmäärä

135 h, including 50 h of scheduled contact studies.

## Edeltävät opinnot / Suositellut valinnaiset opinnot

Follow-up Course in Technical Mathematics.

## Sisältö

1) A brief summary of the differentiation and integration of single-variable functions,
2) Optimization of multivariable functions,
3) Vectors and vector fields,
4) Differentiation of vector fields with respect to a parameter,
5) Line integrals of vector fields,
7) Potential of the vector field,
8) Surface integral,
9) Green’s theorem,
10) Change of variables in surface integrals: The Jacobi determinant,
11) Flux of the vector field,
12) Stokes’ theorem,
13) Volume integral,
14) Change of variables in volume integrals,
15) Gauss’ theorem,
16) Differentiation of vector fields in curvilinear coordinates,
17) Convergence and divergence of series,
18) Taylor series,
19) Power series solution of differential equations,
20) Calculus of variations (if there is time).

## Opiskelumateriaali

E. Kreyszig: Advanced Engineering Mathematics (Wiley).

## Opetusmuoto / Opetusmenetelmät

Lectures and exercises.

## Arviointikriteerit

The general criteria of VAMK.

## Arviointimenetelmät

Exercise activity and a course examination.