| Date |
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Home
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Monday Sept. 20 14:25 -15:05 15:15 -15:55 |
Review of elementary functions(Part 1)
Examples - Equations - Graphs - Exercises
Use
of
Mathematical
software.a) Linear functions vs Affine functions what does LINEARITY mean ? (i)
Additivity
:
f(x1+x2)
= f(x1) +
f(x2)
(ii)
Homogeneity :
f(k.x) = k.f(x)
c) General
equation of a straight line in the plane coordinates :ax + by + c = 0
b) Graphing inequalities : ax + by + c ≤ 0
How is the plane divided
in two parts ?
c) Graphing linear systems of inequalities  Examples : see next column |
 Correction of Ex.1 (Assignement #1)  |
Nature of the Linear functions in R Let's prove that the only real functions which meet the two properties of Additivity and Homogeneity, are the functions defined by f(x) = ax. (the reciproqual is quite trivial and has been shown in class). In fact it depends only of (ii) : let f(1) = a, then for any x we have from (ii) : f(x) = f(x.1) = x.f(1) = x.a = ax ========= QUERY (1) Explain why the two lines defined by 2x - y + 4 = 0 2x - y - 4 = 0 are symetrical through the Origin O. QUERY (2) Explain why the two lines defined by 2x - y + 4 = 0 2x + y + 4 = 0 are symetrical through the Ox Axis. |
我很高 兴还来北京景山学校。 可能你 们知道我在Paris 和 NYC 教数学 很都年, 和去年 我在景山。 都你们 知道我用英语教数学 我的汉 语不流利。 如果我 说英语太快你们高速我。 Registration formPlanning Project 1st semester Exercises in class Assignment #1 Glossary (to be completed after each class) |
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Monday
Sept. 27 14:25 -15:05 15:15 -15:55 |
Collection of the
registration sheets with pictures.
and of the assignment #1 Correction of the
3 exercises on Assigment # 1 :
|
Kinematics
  Assignment #2 to be returned after the National day vacation on Monday October 11th |
Glossary |