Home tutorial classes for both students in the first cycle and second cycle. - Dibombari - Private lessons

Home tutorial classes for both students in the first cycle and second cycle.

From 8 $ /h

Biology, chemistry, physic, mathematic.

I know this subjects may look difficult to students but with my expert teaching methods I assure you (student) that it's going to be your best subject. I believe there's a brilliant capacity in every child out there which just need an expert teaching method to bring it out.

Extra information

Pen, chalk, book

Location

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At student's location :

Around Dibombari, Cameroon

About Me

*Description:*

As a seasoned science tutor, excels in simplifying complex concepts and fostering a deep understanding of physics, chemistry, and biology. With a strong educational background and extensive teaching experience, I THEODORE provides personalized guidance to students of various skill levels.

*Key Strengths:*

- Expertise in physics, chemistry, and biology
- Effective communication and teaching methods
- Patient and encouraging approach
- Ability to break down complex concepts into manageable parts
- Strong problem-solving skills

*Tutoring Style:*

- Interactive and engaging lessons
- Customized learning plans tailored to individual needs
- Emphasis on conceptual understanding and practical applications
- Regular assessments and progress tracking
- Supportive and motivating environment

*Qualifications:*

- Level 3 pharmacy student in FMPS UD

- 4 years of tutoring experience

*Availability:*

- Online or in-person tutoring options

Education

Year 3 Pharmacy student in FMPS UD (Faculty of medicine and pharmaceutical science University of Douala).

A grade in the above subjects and teaching in both first cycle and second cycle.

Experience / Qualifications

4 years of experience in tutoring home classes, high level of education I obtain in FMPS UD and also from high school, also worked with other educational cooperations e.g Universe Cooperation, Big Dreams academy etc

Age

Children (7-12 years old)

Teenagers (13-17 years old)

Adults (18-64 years old)

Seniors (65+ years old)

Student level

Intermediate

Advanced

Duration

120 minutes

The class is taught in

English

Skills

Availability of a typical week

(GMT -05:00)

New York

At student's home

Mon

Tue

Wed

Thu

Fri

Sat

Sun

00-04

04-08

08-12

12-16

16-20

20-24

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

I specialize in tutoring math, computer science and physics for ordinary level students and preparing them to obtain excellent result in GCE Ordinary Level exams. My goal is to keep students challenged, but not overwhelmed. I assign homework after every lesson and provide periodic progress reports. I also apply different methods of teaching.

A spherical lens is a transparent medium bounded by two spherical caps or by a spherical cap and a plane.
There are two types of lenses: thin-edged (converging) lenses and thick-edged lenses.

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

I specialize in tutoring math, computer science and physics for ordinary level students and preparing them to obtain excellent result in GCE Ordinary Level exams. My goal is to keep students challenged, but not overwhelmed. I assign homework after every lesson and provide periodic progress reports. I also apply different methods of teaching.

A spherical lens is a transparent medium bounded by two spherical caps or by a spherical cap and a plane.
There are two types of lenses: thin-edged (converging) lenses and thick-edged lenses.

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Contact Theodore