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This teacher has a fast response time and rate, demonstrating a high quality of service to their students.
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Since November 2022
Instructor since November 2022
Available tutor for Chemistry, Physics, Biology and Math for all levels
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From 11.5 £ /h
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This Course is intended for all those who have nightmares when approaching a Mathematics, Physics, Chemistry or Science assignment at different levels in English from the Douala Cameroon.
This course is intended for pupils of primary, secondary and 1st university year.
My goal is to advance the student through practice by treating for each student the method that corresponds to him to better understand.
Response guaranteed in a few minutes up to 10 hours maximum.
Extra information
Have your writing materials with you.
Location
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At student's location :
  • Around Dizangué, Cameroon
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At teacher's location :
  • Bonabéri, Cameroon
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Online from Cameroon
About Me
I can describe myself as friendly, enthusiastic and respectful tutor. As a tutor, i can easily get respect from my students if they would feel respected first. First, English is a language and not a basis of intelligence. I might be better than my students when it comes to speaking and understanding English but they might be more intelligent and talented than me.I am enthusiastic because i want my students to feel that i am highly spirited and faithful that i can teach them well, they can adopt it and they will become better when it comes to verbal, written and comprehension of the language. I am friendly because i want to make my students feel that speaking English can empower them to share ideas and do business outside their nation and through it, the opportunities that they can get are limitless.
Education
Bachelor's degree in Biochemistry and Molecular Biology at the University of Buea.
GCE A- level at Government Bilingual high school Mambanda- Bonaberi
120-Hour TEFL certificate obtained.
Experience / Qualifications
I taught as an English and French online tutor for 3 months. I honestly enjoyed this experience and learned a lot from each of my student.I felt like understanding each student better and better as we progressed every day. This experience helped me to understand that teaching was a right choice for me, and now I am motivated to teach, and to put into practice everything I learned. Of course, I know I still have a lot to learn, and hope to continue my studies while teaching. Also,I've applied to be a home tutor for elementary school students for 6 months. It was difficult at first, because I found it hard to cope with the discipline issues. However, after few weeks I got into the groove, and learned what worked with the children, and how to keep the discipline at a reasonable level at least. It was an extraordinary time, and to be honest, I still miss the children. Further, I am a certified English tutor, with a 120-hour TEFL certificate.
Age
Preschool children (4-6 years old)
Children (7-12 years old)
Teenagers (13-17 years old)
Adults (18-64 years old)
Student level
Beginner
Intermediate
Advanced
Duration
60 minutes
90 minutes
120 minutes
The class is taught in
English
French
Availability of a typical week
(GMT -05:00)
New York
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At teacher's location and via webcam
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At student's home
Mon
Tue
Wed
Thu
Fri
Sat
Sun
00-04
04-08
08-12
12-16
16-20
20-24
Filling comfortable having conversation with other in another language, which is not our mother tongue is very important and sometimes you have no confident speaking in public. Just boook a lesson with me and build the confidence you need.

During our conversation classes, i will help you improve your pronunciation, how to start conversation, build your confidence in communicating in public and increase your fluency in the language. Further, one of my hobbies is to discover new cultures, so i hope you will love sharing your culture with me.

During our vocabulary classes, we would explored different words, designate a word of the week with a challenge to use it creatively in that week's work and also use jokes and audios to add engagement to word studies, especially those with multiple meanings.
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Similar classes
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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




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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




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