Welcome to Iaroslav Blagouchine's official site!

## ★ Higher Mathematics (supervised practical works) ★

#### Level

1–st year students of the Saint–Petersburg State University of Architecture and Civil Engineering, the first and second semesters (5ЭБ–I, 21С–I, 3Э–I, 2САД–I).

#### Detailed Content

I. Analytic geometry in two dimensions: Cartesian coordinate system, coordinate of a point and of the various objects, distance between two points, division of a line segment, equations of a straight line, second-order curves (circle, ellipse, oval, hyperbola, parabola and their general forms, see also some exercices here, here, here, here and here). To be continued...

Note that during the final examination graphic calculators, laptops, mobile phones, tablets and even smartwatches are strictly forbidden.

## ★ Higher Mathematics (supervised practical works) ★

#### Level

1–st year students of the Saint–Petersburg State University of Architecture and Civil Engineering, the first semester (ДАС–I).

#### Detailed Content

I) Matrices, operations with them and their properties: definition, basic properties, sum & difference, scalar multiplication, matrix multiplication, matrix-vector product, properties of matrix addition and matrix multiplication, matrix determinant, matrix inverse (Gauss' and Cramer's methods), solutions of linear equations (Gauss' and Kramer's methods). Some exercices (with short explanations) may be found here, here and here), as well as in the litarature given below.

Note that during the final examination graphic calculators, laptops, mobile phones, tablets and even smartwatches are strictly forbidden.

## ★ Probability and Statistics (lectures and supervised practical works) ★

#### Level

2–nd year students of the Saint–Petersburg State University of Architecture and Civil Engineering (8С–II, 14С–II, ТТ–II, ТСБ–II).

#### Detailed Content

I) tbd

Note that during the final examination graphic calculators, laptops, mobile phones, tablets and even smartwatches are strictly forbidden.

## ★ Advanced Course of Higher Mathematics (Lectures & supervised practical works) ★

#### Level

Third–year students (CIR3 & U3) of the ISEN Engineering School.

#### Detailed Content

1. Theory of functions of a complex variable.
• Recalls of basic notions from mathematical analysis: sequences of numbers, functions of a real variable, functions of several real variables, limits, asymptotic notations (e.g. big O notation), differential calculus, Taylor and Maclaurin series, integral calculus, Riemann integral, line integrals, Green's, Stokes' & Ostrogradsky–Gauss theorems.
• Complex numbers: algebraic form, polar or trigonometric form, complex plane, elementary operations, complex conjugate, modulus and argument of a complex number, trigonometric and hyperbolic functions of a complex number, Euler's formulæ, de Moivre's formula, exponential function of a complex number, the nth roots of a complex number, logarithm of a complex number (Ln and ln functions).
• Functions of a complex variable: analytic functions (3 different points of view: Cauchy–Riemann conditions & harmonic functions, Cauchy's contour integral, Weiererstrass), classification of the singularities, Laurent series & Weiererstrass expansion theorem, Cauchy's integral formula and its applications to the evaluation of contour integrals, Cauchy's residue theorem and its numerous applications (Jordan's lemma, evaluation of integrals), Mittag–Leffler theorem and versatile methods for the summation of series.
2. Introduction to Operational Calculus and Fourier series: Laplace, Fourier and Hartley transforms and their applications,
3. Introduction to Special Functions of Mathematical Physics and to orthogonal polynomials: Gamma function and its derivatives (Digamma function and Trigamma function), Beta function, Riemann Zeta function, Bessel functions, Legendre polynomials, Hermite polynomials.
4. Introduction to probability theory and statistics: random variables, probability, stochastic processes, ergodicity, elements of the estimation theory.

Note that during the examination graphic calculators, laptops, mobile phones and tablets are strictly forbidden.

#### Recommended Literature

Do not hesitate to contact me if you have any further questions.

## ★ Laboratory Works in Probabilty ★

#### Level

Third–year students of the University of Toulon.

#### General description

There are 3 labworks in all. Duration time of each labwork is 4 hours. At the end of each labwork, students should leave a handwritten report. Final evaluation is based on the mean of these reports, as well as on the personal participations and contributions during the labworks.

Labwork descriptions in PDF, as well as all necessary *.m and *.mat files (versions of 2008). For more information, please contact me or Bernard Xerri, who designed these labworks.

## ★ University class in Signals and System (supervised practical work in classroom) ★

#### Level

Third–year students of the University of Toulon.

#### Content

Analog and digital signals, Fourier transforms, Hartley transform, Z–transform, spectrum, Parseval's theorem (signal's energy), auto– and cross–correlation functions, spectrum density, notion of systems, linear and time–invariant (LTI) systems, analog and digital filtering, convolution product, complex analysis, residus (Cauchy's theorem) and their applications in signal processing (especially, for the calculation of inverse Fourier/Hartley/Z/Laplace transforms), sampling and reconstruction of signals (first Shannon's theorem).

#### Recommended Literature

For any further information, you may contact me, or Eric Moreau, who gives lectures on Signal and Systems, as well as heads Telecommunication Department at ISITV, University of Toulon.

## ★ Laboratory Works in Signals and System ★

#### Level

Third–year students of the University of Toulon.

#### General

There are 5 labworks in all. Duration time of each labwork is 4 hours. At the end of each labwork, students should leave a handwritten report. Final evaluation is based on the mean of these reports, as well as on the personal participations and contributions during the labworks.

## ★ Laboratory Works in Image Processing ★

#### Level

Third–year students of the University of Toulon.

#### General description

There are 4 labworks in all. Duration time of each labwork is 3 hours. At the end of each labwork, students should leave a handwritten report. Final evaluation is based on the mean of these reports, as well as on the personal participations and contributions during the labworks.

## ★ Laboratory Works in Signal Processing ★

#### Level

Fourth–year students of Minatec (formely ENSERG Engineering School), which is a part of the INP Grenoble.

#### General description

There are 5 labworks in all. Duration time of each labwork is 4 hours. At the end of 5 labworks, there is a 2–hour handwritten examination. Final evaluation is based on the mean of these reports.

#### Objectives

To provide necessary technical skills in analog and digital signal processing, in use of the corresponding measurement and calibrating instruments (oscilloscope, signal generator, spectrum analyzer), and in signal processing modelling software (Matlab & Comsys).

#### Content

Analog and digital filtering, Fourier transform, spectrum analysis, analog and digital modulations, frequency conversion techniques, sampling, Shannon's theorem, digital signal transmission.

*Original document comes from this site.

## Top 6 Most Stupid Questions & Remarks That I'he Heard from my Students

1. “What is the cotangent?” – Mathieu C., 3rd–year student, ISITV.
2. “What is the geometric progression?” – 3rd–year student, ISITV.
3. After an exam on complex analysis, a 3rd–year student, who got a quite bad mark, tried to convince me that he deserved a better one by arguing: “Logarithms of negative numbers do not exist! At least, I've never heard about this...” – Mohamed Amine A.–H., ISITV.
4. “What is the decibel?” – several 4th–year students, INP Grenoble.
5. During the labworks in signal processing, two 4th–year students, having a signal generator and an oscilloscope, said that they had no idea how to measure the transfer function gain of a filter (INP Grenoble).
6. One of the basic questions of the second exam in signal and systems was: “What is the impulse response?” Despite the extreme simplicity of the question, many students did not respond to this question correctly. The “best” answers are resumed below (original answers in french are given as images that appear when the mouse is on the text; they were scanned from original exam sheets):
After I've heard this question, just for fun, I decided to include this question into the exam (question 2.1). The BIG (and the BAD) surprise was that from 20 students, there were 2 students (Hind B. & Othman K.) who did not answered this question correctly. One of them simply did not respond to the question; the other one first wrote that it was the ratio sin/cos, and then, he replaced this ingenious formula by the another one: arcsin/arccos... see the original here...
Also, some students were unable to convert linear ratios into decibel ones. Moreover, there were two 4th–year students, which have obtained the voltage output/input amplifier ratio equal to 1000. When I asked them to express this gain in dB, they replied me: “We need calculator for this...” Nota Bene: since this section of my WEB–site is under construction, some documents may be temporary unavailable.