Junior_9.5

Date	Activities / Objectives	Images / Home work / Assignments	Remarks / Images	References / Links
Tuesday Nov. 1 3:15 - 4:45	Collect missing registrations Call / absences : 12 students absent !!! Check exercise on Assignment #2 Handout Assignment #3 Formal definition and theorems Memo #2 Even and Odd functions Axial Symmetry / ∆ (x=a) f(a + X) = f(a - X) Central Symmetry / I (a;b) f(a + X) + f(a-X) = 2b Exercises : Assignment #3 p.2	Exercises on associated functions (Ass.#3 p.1)	Exercises on Symmetries (Proof by calcutlations) 10 students absent !	Assignment #3 MEMO / SYMMETRIES Answers / Ass.#3
Tuesday Nov. 8 3:15 - 4:45	Check Exercises from Ass.#3 p2 (Symmetries) Hand out ANSWERS of Ass.#3 p.1 & p.2 Check Attendance ! Introduction to Numerical SEQUENCES Examples Arithmetic sequences : U_n = U₀ + n.r Geometric sequences : V_n = V₀.q^r Examples of non Arith. and non Geom. Sequences: Fibonacci decimal digits of π Homographic function	Assignment # 4 Study of a non Arithm. and Non Geom Sequ. to be prepared for Tuesday Nov.15	Comparison of Arithmetic and Geometric means of two positive numbers : For the 3rd time Pb of keys to open the classroom and the lights adequately for the video projector. 19 students absent !	MEMO / SEQUENCES Arithmetic Geometric Assignment # 4 Study of a non Arithm. and Non Geom Sequ.
Tuesday Nov. 15 3:15 - 4:45	Check Attendance ! Check Exercises from Ass.#4 p.1 (Sequence) Non Geom. Non Arith. Exercises on new sequences : Ass. #5 Arithmetic Récurrent Geometric		Great Satisfactions : No absent ! One studient [于睿元] was able to formally prove and explain to the whole class that for the sequence defined by : lim u_n = +∞ New change of room ! (temporary)	Assignment # 5 Study of two sequences defined by the same function : Directly Recursively
Tuesday Nov. 22 3:15 - 4:45	Limits of arithmetic and of geometric Sequences and Series U_n = U₀ + n.r : r > 0 => lim Un = +∞ r < 0 => lim Un = -∞ r =0 => lim Un = U0 V_n = V₀. qⁿ: q > 1 and V₀ > 0 => lim Vn = +∞ q > 1 and V₀ < 0 => lim Vn = - ∞ q = 1 => lim Vn = V0 \|q\| < 1=> lim Vn = 0 Examples : Assignment # 6 Series : S_n = U₀ + U₁ + U₂ +...+U_n Lim S_n in each case : Formula Arith series Geom series Limits : Arith series Geom series Examples : Assignment # 6 Formal definition of limits of a sequence.	The original box has a diameter of 10cm Each earing is 1/10 of the box. How many boxes included inside one another can be seen until the diameter of the box is less than .5 mm. ?	Each box side is 3/4 of the previous one, what is the total area covered ? Each bar height is 1/2 of the previous one, what is the total lenght ? Five students absent for special Math competitive exam at the University of Princeton (USA)	Assignment # 6 Study of geometric Sequences & Series Assignment # 7 Recurrent Sequences defined by linear or homographic functions
Tuesday Nov. 29 3:15 - 4:45	Check Attendance ! Study of the Hanoï Towers problem M_n = Minimum Nb of moves : M_n+1 = M_n + 1 + M_n H_n+1= M_n+1 +1 = 2 (M_n + 1) = 2H_n H_n= 2ⁿ Check and complete Ass.# 7.p.1/3 (Recurrent Sequences) Complete Ass.# 7.p.2/3	M_n= 2ⁿ - 1	高宇翔(Tony) received a price at the special Math competitive exam at the University of Princeton (USA)	Assignment # 7 p.3/3 To prepare for Tuesday Dec. 6