北京 景山学校 数学系
Calculus ++ @ MATHEMATICS @ Senior 2.4  。2010-11
jiguanglaoshi@gmail.com

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[5] March
[updated : 2011/03/20]
Date
 Activities / Objectives
  Images / Home work / Assignments
 Remarks / Images
 References / Links

Tuesday

March 08

3:15 - 3:55
  • Re-Introduction of the semester course :
    • new rythm : two periods separated by two days :
      • one class of lecture
      • one class of exercises
    •  new topics mostly Differentials Sequences, Series and Integrals.
  • Review of the list of the main topics studied during the first semester :
    • Limits and Asymptotes
    • Derivatives and Tangent lines
    • Applications to the variations of f.
    • Singular points
    • Graphs
  • Example : study of a function :
    •  f : x --> x3 - 3x + 1
    • first and second derivatives
    • variations and graphs
    • Tangent at x = 0
    • Inflexion point
f : x --> x3 - 3x + 1
3edeg
f '(x) = 3x2 - 3
f "(x) = 6x





I have been told by the administration not to give too heavy Home Work, because the students already have too many subjects to prepare for their final exams ... beside Maths !

Most of the topics are relevant to
the Maths textbook A 2.2
for 高二






Friday

March 11

3:15 - 3:55
  • Derivative vs  Differential

    • formal defintion of dydx

    • Illustration of the definition

    • Exercises of calculations
      • f : x --> x3 - 3x + 1 
        • @ x= 0 for dx = + 0.05
        • @ x = 2 for dx = - 0.01

      • small variations of the period of a simple pendulum :
                 T
        Find dT for dl = .02 and l = 1
diff
dy = f ‘(5).dx = 0.51 x 0.5 ≈ 0.25
=> ∆y  ≈ 0.25, <=>  f(5.5) – f(5) ≈ 0.25
=>  f(5.5) ≈ f(5) + 0.29 ≈ 5.05 + 0.25 = 5.30.







Exercises / Differentials


Memo / Derivative vs Differential












Tuesday

March 15

3:15 - 3:55
  • Handout Memo on Differentials
  • Composite derivatives :
    • demo of the formula :
      F’(x) = f ’[u(x)].u’(x)

    • Example :
      dc

  • Derivative of the reciproqual functions
    • demo of the formula :
      f-1
    • Example : derivative of ln :
      dl

  • Exercises on composite derivatives :
    to be prepared for next Wednesday 18 th.
derInv

Illustration of the formula
f-1
 y = f-1(x) <==> x = f(y)
M(x;y) and M'(y;x)
are symmetrical / 1st Bisector
the slope  a/b of the tangent line in M(x;y)
is the inverse of the slope b/a
of the tangent line on M'(y;x)



Visit of

吴鹏老师

Suggestion :
slow down the rythm
 by sending students
to the black board
(Many students
have difficulties of
undersanding English)




Memo / Derivative vs Differential






Memo-Exercises
Composite Derivatives

Friday

March 18

3:15 - 3:55
  • Review of the demos of the previous class
    (students to the board)

  • Correction of exercises on Composite derivatives
    • Formulas (1) to (4)
    • Exercise (1) to (4)

Exercicise (5) & (6) to be prepared
for next week
Next class
of
Tuesday
22
March

CANCELLED
(General meeting of the students)

Memo-Exercises
Composite Derivatives


Tuesday

March 22

3:15 - 3:55
  • Correction of exercises on Composite derivatives

  • Exercises (2) to (4)
    •


Study of the sign of the derivative of
the functions (5) and (6) :
Using an auxiliairy function.


Class eventually NOT cancelled !

Memo-Exercises
Composite Derivatives

Friday

March 25

3:15 - 3:55
  • Correction of exercises on Composite derivatives

    • Exercise (5)


  • Study of the sign of the derivative of
    the functions (5)
    Using an auxiliairy function.
Study of the endecided forms
with Exp and ln will be shown
next Friday April 1st

No Class on Tuesday March 29
[Jingshan Mid term exam]