### Mathematical Analysis 3

#### Course Description

Fourier analysis. Laplace transform. Vector analysis. Complex analysis.

#### Learning Outcomes

- Computation of Fourier series or Fourier integrals
- Apply Laplace transform to electrical circuits
- Use of basic notions of vector analysis
- Evaluate line and sufrace integrals
- Describe basic functions of complex variable
- Evaluate complex variable integral

#### Forms of Teaching

**Lectures**Lectures are held in 2 cycles, 6 hours per week

**Partial e-learning**Homeworks are available on the course web pages

#### Grading Method

Continuous Assessment | Exam | |||||
---|---|---|---|---|---|---|

Type | Threshold | Percent of Grade | Threshold | Percent of Grade | ||

Homeworks | 50 % | 0 % | 0 % | 0 % | ||

Attendance | 50 % | 0 % | 0 % | 0 % | ||

Mid Term Exam: Written | 0 % | 50 % | 0 % | |||

Final Exam: Written | 0 % | 50 % | ||||

Exam: Written | 0 % | 100 % |

##### Comment:

Regular attendance and solving of homework are the conditions for admission to the exam.

#### Week by Week Schedule

- Periodic functions; Trigonometric Fourier series, properties of Fourier series, Covergence theorems for Fourier series, Fourier integral, properties, spectral function
- Fourier transform; Frequency and time shifting; Convolution, Inverse transform; Table of transforms, Basics of Fast Fourier transform and Discrete Fourier transform
- Examples and properties of Laplace transform, Inverse transform; Convolution
- Solving differential and integral equations, Solving systems of differential equations, Impulses and delta function
- Plane and space curves; Parametrization of a curve; Tangent vector to a curve, Scalar and vector fields; Gradient; Directional derivative
- Divergence and curl, Special types of fields; Laplace operator; Properties of differential operator; Maxwell's equations
- Line integrals; Line integral of a scalar field; Arc lenght of curves, Line integral of a vector field; Green's formula; Path independence; Potential fields
- Midterm exam
- Surface integrals; Surface integral of a scalar field; Surface area
- Surface integral of a vector field; Flux of vector field, Divergence theorem; Stokes' theorem; Applications
- Regions and contours in a complex plane; Sequences and series of complex numbers, Functions of complex variable; Differentiability, Cauchy-Riemann equations; Elementary functions
- Bilinear (Möbius) transformation; Conformal mappings, Integral of function of complex variable
- Taylor series; Zeroes of analytic functions, Laurent series; Singular points and poles of analytic functions
- Residue theorem; Applications
- Final exam, Seminar

#### Study Programmes

##### University undergraduate

[FER3-EN] Electrical Engineering and Information Technology - study

(3. semester)
#### Literature

(.),

*Fourierov red i integral. Laplaceova transformacija; Neven Elezović; Element; 2010; ISBN: 978-953-197-534-6*,
(.),

*Višestruki integrali; Ilko Brnetić, Vesna Županović; Element; 2010; ISBN: 978-953-197-535-3*,
(.),

*Vektorska analiza; Tomislav Burić, Luka Korkut, Mario Krnić, Josipa Pina Milišić, Mervan Pašić; Element; 2010; ISBN: 978-953-197-538-8*,
(.),

*Funkcije kompleksne varijable; N. Elezović; Element; 2010; ISBN: 978-953-197-548-3*,
(.),

*A First Course in Complex Analysis with Applications; D. G. Zill, P. D. Shanahan; Jones and Bartlett; 2003; ISBN: 0-7637-1437-2*,
(.),

*Complex variables with Applications; A. D. Wunsch; Addison-Wesley; 1994; ISBN: 9780201088854*,#### For students

#### General

**ID**209730

Winter semester

**7**ECTS

**L0**English Level

**L2**e-Learning

**90**Lectures

**0**Seminar

**0**Exercises

**0**Laboratory exercises

**0**Project laboratory

#### Grading System

**85**Excellent

**70**Very Good

**55**Good

**45**Acceptable