### Mathematical Analysis 3

#### Course Description

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

#### Learning Outcomes

1. Computation of Fourier series or Fourier integrals
2. Apply Laplace transform to electrical circuits
3. Use of basic notions of vector analysis
4. Evaluate line and sufrace integrals
5. Describe basic functions of complex variable
6. 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

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

1. Periodic functions; Trigonometric Fourier series, properties of Fourier series, Covergence theorems for Fourier series, Fourier integral, properties, spectral function
2. Fourier transform; Frequency and time shifting; Convolution, Inverse transform; Table of transforms, Basics of Fast Fourier transform and Discrete Fourier transform
3. Examples and properties of Laplace transform, Inverse transform; Convolution
4. Solving differential and integral equations, Solving systems of differential equations, Impulses and delta function
5. Plane and space curves; Parametrization of a curve; Tangent vector to a curve, Scalar and vector fields; Gradient; Directional derivative
6. Divergence and curl, Special types of fields; Laplace operator; Properties of differential operator; Maxwell's equations
7. 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
8. Midterm exam
9. Surface integrals; Surface integral of a scalar field; Surface area
10. Surface integral of a vector field; Flux of vector field, Divergence theorem; Stokes' theorem; Applications
11. Regions and contours in a complex plane; Sequences and series of complex numbers, Functions of complex variable; Differentiability, Cauchy-Riemann equations; Elementary functions
12. Bilinear (Möbius) transformation; Conformal mappings, Integral of function of complex variable
13. Taylor series; Zeroes of analytic functions, Laurent series; Singular points and poles of analytic functions
14. Residue theorem; Applications
15. Final exam, Seminar

#### Study Programmes

[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,

#### 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