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7 physics teachers in Douala

Trusted teacher: 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
Math · Physics · Computer science
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Math · Physics · Science
Trusted teacher: YKS, SAT, AP, IB, A Level and University Tutoring in Mathematics, Physics and Biology from a Physics Graduate of the Technical University of Munich (TUM). I graduated from the Technical University of Munich this summer with a good average in Physics. I am also doing a double major in Computer Engineering. As of this semester, I will start my master's degree in Computational Science and Engineering (CSE), one of the prestigious master's programs at the Technical University of Munich. WHY SHOULD YOU STUDY WITH ME? With my unique lecture technique, I give you new perspectives in both subject comprehension and question solving. Before the lesson, I make the lessons most effective by compiling level-specific course PDFs and questions appropriate to the student's level. After the lesson, I share the course materials with my students. I also shared the video recording of the lesson so that the students could repeat the lesson. You will gain speed and practicality in solving questions with the new perspectives you have acquired. I have always received positive feedback from the lessons I have given so far. We will gain new perspectives, and I am with you in achieving success with my lessons, including full lectures and question solutions. MY SUCCESSES § SAT (US College Exam) exam Full Score in Math 1 and 2, Physics and Biology § National Science Olympiad Gold Medal in Biology for 2 consecutive years § International Biology Olympiad (IBO) Bronze and Silver Medals MY EDUCATION EXPERIENCES; § I have been working as an academic lecturer in the National Science Olympiads Summer Camps organized by Tübitak (4 YEARS Experience). § I worked as an instructor at Munich Technical University for 2 semesters because I got the highest grades in Mathematics. MY LANGUAGE CERTIFICATES; § I got 108 points in Toefl. § I have Goethe German C1 certificate. I have a good command of Mathematics, Physics and Biology curricula in YKS. I can explain the underlying logic of the subjects well. I can give private lessons in AP, SAT, A level, IB exams in Mathematics, Physics and Biology. At undergraduate level ; § Calculus 1, 2 and 3 § Real Analysis § Linear and Abstract Algebra § Discrete Structures and Probability Theory § Numerical Analysis § Classical Mechanics § Electromagnetic Theory § Quantum Mechanics § Statistical Mechanics and Thermodynamics I can explain the lessons in Turkish, English and German.
Physics · Math · Biology
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CHEMISTRY and BIOLOGY (Cambridge IGCSE / O-Levels / Person Edexcel / Oxford AQA Int, GCSE / AS & A-LEVELS / IB Diploma) (Tokyo)
Benson
After my first lesson with Benson, i have felt more confidence in my skills with chemistry than i have in many years. Where I previously felt very subconscious and unable to answer questions, i have now been able to answer difficult IB exams questions with ease. Benson provided me a safe and comfortable environment which has left me excited for my next class at school to show what i have learned with a fresh confidence! I highly recommend this tutor to anyone who struggles with confidence in both themselves and their subjects.
Review by TIA
Scientific subjects (Math, Physics, Chemistry) for students of the French mission/for middle and high school students (Casablanca)
Amin
So far, I've been getting help with my IGCSE 's in Math and Computer Science with Amin. In most of the lessons I've been with him, he's been really helpful and responsible. He has also been very patient. He helps me become more confident in my answers and makes the lessons pretty fun! After my lessons with him, I do understand my topics more and am able to go to my classes in school without feeling lost. If you're ever struggling with Physics or Programming, I'm sure he can help you too :)
Review by MANIJ
Tuition Math - Physics - Chemistry - Biology (Mexico City)
Raef
I found Dr. Ralf to be a wonderful Teacher. The things that he taught me through online helped me a great deal in this class as well as in statistic level. Because of the help and attention that He provided me with, I understand and enjoy Statistics. The class was great in that he didn’t just give the answers away – he made me THINK. This was sort of frustrating, but it helped me understand the material much better. I would recommend him as a Teacher for future classes, without a doubt.
Review by AHMED