facebook
favorite button
super instructor icon
Trusted teacher
This teacher has a fast response time and rate, demonstrating a high quality of service to their students.
member since icon
Since August 2021
Instructor since August 2021
Translated by GoogleSee original
Courses and homework help in Electromagnetic Compatibility
course price icon
From 31.66 C$ /h
arrow icon
Electromagnetic compatibility oriented towards electrical engineering is a very important course for many disciplines such as power electronics, electrical installations, instrumentation or transport and distribution.
This course deals with the fundamentals and applications of EMC
Location
green drop pin icon
|
Use Ctrl + wheel to zoom!
zoom in iconzoom out icon
location type icon
At student's location :
  • Around Douala, Cameroon
location type icon
Online from France
About Me
I am an engineer in Electrical Engineering and Intelligent Systems and a PhD student in Normandy (Le Havre). Furthermore, I hold a degree in fundamental physics.
I am passionate about reading, sports, especially football, tennis and Formula 1.
Education
- Scientific baccalaureate

- Bachelor's degree in fundamental physics.

- Design engineer diploma in Electrical Engineering and Intelligent Systems.

-Doctoral student in energy management.
Experience / Qualifications
I have extensive experience in tutoring.
I very often held pupils and students in several subjects including physics, mathematics, automation and power electronics.
Age
Teenagers (13-17 years old)
Adults (18-64 years old)
Seniors (65+ years old)
Student level
Beginner
Intermediate
Duration
60 minutes
The class is taught in
French
English
Reviews
Availability of a typical week
(GMT -05:00)
New York
at teacher icon
Online via webcam
at home icon
At student's home
Mon
Tue
Wed
Thu
Fri
Sat
Sun
00-04
04-08
08-12
12-16
16-20
20-24
Power Electronics is a specialty course specific to Electrical Engineering.
You have the possibility of being followed with private lessons and homework help.
All conversions are addressed
-A summary on power switches and another on classic and advanced power topologies
Read more
Stéphane, Engineer in Electrical Engineering and Intelligent Systems and PhD candidate.

Support courses and homework help in: electrical circuits
-MATLAB for Electrical Engineering

I have had the chance to teach for more than 2 years now.
Patience and Adaptability for a satisfactory result. This is my motto, because to teach you need a lot of patience because to ensure the progress of a student, you need time and a lot of pedagogy. Because you have to understand that the profiles are different and therefore it is always important to adapt well to the student you are supervising for better support.
Read more
Show more
arrow icon
Similar classes
arrow icon previousarrow icon next
verified badge
Léon
Digital suites courses

I - General
A numeric sequence is an application from N to R.
• Bounded sequence
A sequence (Un) is bounded if there exists a real A such that, for all n, Un ≤ A. We say that A is an upper bound of the series.
A sequence (Un) is reduced if there exists a real number B such that, for all n, B ≤ one. One says
that B is a lower bound of the sequence.
A sequence is said to be bounded if it is both increased and reduced, that is to say if it
exists M such that | Un | ≤ M for all n.

• Convergent suite

The sequence (Un) is convergent towards l ∈ R if:
∀ε> 0 ∃n0 ∈ N ∀n ≥ n0 | un − l | ≤ ε.
A sequence which is not convergent is said to be divergent.
When it exists, the limit of a sequence is unique.
The deletion of a finite number of terms does not modify the nature of the sequence, nor its possible limit.
Any convergent sequence is bounded. An unbounded sequence cannot therefore be convergent.

• Infinite limits

We say that the following (un) diverges

Towards + ∞ if: ∀A> 0 ∃n0∈N ∀n ≥ n0 Un≥A
Towards −∞ if: ∀A> 0 ∃n0∈N ∀n≤ n0 Un≤A.

• Known limitations

For k> 1, α> 0, β> 0


II Operations on suites

• Algebraic operations

If (un) and (vn) converge towards l and l ', then the sequences (un + vn), (λun) and (unvn) respectively converge towards l + l', ll and ll '.

If (un) tends to 0 and if (vn) is bounded, then the sequence (unvn) tends to 0.

• Order relation

If (un) and (vn) are convergent sequences such that we have a ≤ vn for n≥n0,
then we have:
Attention, no analogous theorem for strict inequalities.

• Framing theorem

If, from a certain rank, un ≤xn≤ vn and if (un) and (vn) converge towards the
same limit l, then the sequence (xn) is convergent towards l.


III monotonous suites

• Definitions

The sequence (un) is increasing if un + 1≥un for all n;
decreasing if un + 1≤un for all n;
stationary if un + 1 = one for all n.

• Convergence

Any sequence of increasing and increasing reals converges.
Any decreasing and underestimating sequence of reals converges.
If a sequence is increasing and not bounded, it diverges towards + ∞.

• Adjacent suites

The sequences (un) and (vn) are adjacent if:
(a) is increasing; (vn) is decreasing;

If two sequences are adjacent, they converge and have the same limit.

If (un) increasing, (vn) decreasing and un≤vn for all n, then they converge to
l1 and l2. It remains to show that l1 = l2 so that they are adjacent.

IV Extracted suites

• Definition and properties

- The sequence (vn) is said to be extracted from the sequence (un) if there exists a map φ of N
in N, strictly increasing, such that vn = uφ (n).
We also say that (vn) is a subsequence of (un).
- If (un) converges to l, any subsequence also converges to l.

If sequences extracted from (un) all converge to the same limit l, we can conclude that (un) converges to l if all un is a term of one of the extracted sequences studied.
For example, if (u2n) and (u2n + 1) converge to l, then (un) converges to l.

• Bolzano-Weierstrass theorem

From any bounded sequence of reals, we can extract a convergent subsequence.

V Suites de Cauchy

• Definition

A sequence (un) is Cauchy if, for any positive ε, there exists a natural integer n0 for which, whatever the integers p and q greater than or equal to n0, we have | up − uq | <ε.
Be careful, p and q are not related.

• Property

A sequence of real numbers, or of complexes, converges if, and only if, it is
Cauchy




SPECIAL SUITES

I Arithmetic and geometric sequences

• Arithmetic sequences

A sequence (un) is arithmetic of reason r if:

∀ n∈N un + 1 = un + r

General term: un = u0 + nr.

Sum of the first n terms:


• Geometric sequences

A sequence (un) is geometric of reason q ≠ 0 if:

∀ n∈N un + 1 = qun.

General term: un = u0qn

Sum of the first n terms:

II Recurring suites

• Linear recurrent sequences of order 2:

- Such a sequence is determined by a relation of the type:

(1) ∀ n∈N aUn + 2 + bUn + 1 + cUn = 0 with a ≠ 0 and c ≠ 0
and knowledge of the first two terms u0 and u1.
The set of real sequences which satisfy the relation (1) is a vector space
of dimension 2.
We seek a basis by solving the characteristic equation:

ar2 + br + c = 0 (E)
- Complex cases a, b, c
If ∆ ≠ 0, (E) has two distinct roots r1 and r2. Any sequence satisfying (1) is then
like :
where K1 and K2 are constants which we then express as a function of u0 and u1.

If ∆ = 0, (E) has a double root r0 = (- b) / 2a. Any sequence satisfying (1) is then
type:


- Case a, b, c real
If ∆> 0 or ∆ = 0, the form of the solutions is not modified.
If ∆ <0, (E) has two conjugate complex roots r1 = α + iβ and r2 = α − iβ
that we write in trigonometric form r1 = ρeiθ and r2 = ρe-iθ

Any sequence satisfying (1) is then of the type:


• Recurrent sequences un + 1 = f (un)

- To study such a sequence, we first determine an interval I containing all
the following values.
- Possible limit
If (un) converges to l and if f is continuous to l, then f (l) = l.
- Increasing case f
If f is increasing over I, then the sequence (un) is monotonic.
The comparison of u0 and u1 makes it possible to know if it is increasing or decreasing.
- Decreasing case f
If f is decreasing over I, then the sequences (u2n) and (u2n + 1) are monotonic and of
contrary




Made by LEON
message icon
Contact Stéphane
repeat students icon
1st lesson is backed
by our
Good-fit Instructor Guarantee
Similar classes
arrow icon previousarrow icon next
verified badge
Léon
Digital suites courses

I - General
A numeric sequence is an application from N to R.
• Bounded sequence
A sequence (Un) is bounded if there exists a real A such that, for all n, Un ≤ A. We say that A is an upper bound of the series.
A sequence (Un) is reduced if there exists a real number B such that, for all n, B ≤ one. One says
that B is a lower bound of the sequence.
A sequence is said to be bounded if it is both increased and reduced, that is to say if it
exists M such that | Un | ≤ M for all n.

• Convergent suite

The sequence (Un) is convergent towards l ∈ R if:
∀ε> 0 ∃n0 ∈ N ∀n ≥ n0 | un − l | ≤ ε.
A sequence which is not convergent is said to be divergent.
When it exists, the limit of a sequence is unique.
The deletion of a finite number of terms does not modify the nature of the sequence, nor its possible limit.
Any convergent sequence is bounded. An unbounded sequence cannot therefore be convergent.

• Infinite limits

We say that the following (un) diverges

Towards + ∞ if: ∀A> 0 ∃n0∈N ∀n ≥ n0 Un≥A
Towards −∞ if: ∀A> 0 ∃n0∈N ∀n≤ n0 Un≤A.

• Known limitations

For k> 1, α> 0, β> 0


II Operations on suites

• Algebraic operations

If (un) and (vn) converge towards l and l ', then the sequences (un + vn), (λun) and (unvn) respectively converge towards l + l', ll and ll '.

If (un) tends to 0 and if (vn) is bounded, then the sequence (unvn) tends to 0.

• Order relation

If (un) and (vn) are convergent sequences such that we have a ≤ vn for n≥n0,
then we have:
Attention, no analogous theorem for strict inequalities.

• Framing theorem

If, from a certain rank, un ≤xn≤ vn and if (un) and (vn) converge towards the
same limit l, then the sequence (xn) is convergent towards l.


III monotonous suites

• Definitions

The sequence (un) is increasing if un + 1≥un for all n;
decreasing if un + 1≤un for all n;
stationary if un + 1 = one for all n.

• Convergence

Any sequence of increasing and increasing reals converges.
Any decreasing and underestimating sequence of reals converges.
If a sequence is increasing and not bounded, it diverges towards + ∞.

• Adjacent suites

The sequences (un) and (vn) are adjacent if:
(a) is increasing; (vn) is decreasing;

If two sequences are adjacent, they converge and have the same limit.

If (un) increasing, (vn) decreasing and un≤vn for all n, then they converge to
l1 and l2. It remains to show that l1 = l2 so that they are adjacent.

IV Extracted suites

• Definition and properties

- The sequence (vn) is said to be extracted from the sequence (un) if there exists a map φ of N
in N, strictly increasing, such that vn = uφ (n).
We also say that (vn) is a subsequence of (un).
- If (un) converges to l, any subsequence also converges to l.

If sequences extracted from (un) all converge to the same limit l, we can conclude that (un) converges to l if all un is a term of one of the extracted sequences studied.
For example, if (u2n) and (u2n + 1) converge to l, then (un) converges to l.

• Bolzano-Weierstrass theorem

From any bounded sequence of reals, we can extract a convergent subsequence.

V Suites de Cauchy

• Definition

A sequence (un) is Cauchy if, for any positive ε, there exists a natural integer n0 for which, whatever the integers p and q greater than or equal to n0, we have | up − uq | <ε.
Be careful, p and q are not related.

• Property

A sequence of real numbers, or of complexes, converges if, and only if, it is
Cauchy




SPECIAL SUITES

I Arithmetic and geometric sequences

• Arithmetic sequences

A sequence (un) is arithmetic of reason r if:

∀ n∈N un + 1 = un + r

General term: un = u0 + nr.

Sum of the first n terms:


• Geometric sequences

A sequence (un) is geometric of reason q ≠ 0 if:

∀ n∈N un + 1 = qun.

General term: un = u0qn

Sum of the first n terms:

II Recurring suites

• Linear recurrent sequences of order 2:

- Such a sequence is determined by a relation of the type:

(1) ∀ n∈N aUn + 2 + bUn + 1 + cUn = 0 with a ≠ 0 and c ≠ 0
and knowledge of the first two terms u0 and u1.
The set of real sequences which satisfy the relation (1) is a vector space
of dimension 2.
We seek a basis by solving the characteristic equation:

ar2 + br + c = 0 (E)
- Complex cases a, b, c
If ∆ ≠ 0, (E) has two distinct roots r1 and r2. Any sequence satisfying (1) is then
like :
where K1 and K2 are constants which we then express as a function of u0 and u1.

If ∆ = 0, (E) has a double root r0 = (- b) / 2a. Any sequence satisfying (1) is then
type:


- Case a, b, c real
If ∆> 0 or ∆ = 0, the form of the solutions is not modified.
If ∆ <0, (E) has two conjugate complex roots r1 = α + iβ and r2 = α − iβ
that we write in trigonometric form r1 = ρeiθ and r2 = ρe-iθ

Any sequence satisfying (1) is then of the type:


• Recurrent sequences un + 1 = f (un)

- To study such a sequence, we first determine an interval I containing all
the following values.
- Possible limit
If (un) converges to l and if f is continuous to l, then f (l) = l.
- Increasing case f
If f is increasing over I, then the sequence (un) is monotonic.
The comparison of u0 and u1 makes it possible to know if it is increasing or decreasing.
- Decreasing case f
If f is decreasing over I, then the sequences (u2n) and (u2n + 1) are monotonic and of
contrary




Made by LEON
Good-fit Instructor Guarantee
favorite button
message icon
Contact Stéphane