Autumn 2010
Notes for Math 151H: Honors Calculus

 Homework due Wednesday, December 1:
 Section 5.2  27,30,32,34, 38,40,41, 52.
 Section 5.3  9,12, 14,17,19, 21,24, 45,46,47.
 Section 5.5  1, 5, 7, 9, 13, 17, 19.

 TEST THURSDAY 18 NOVEMBER
  This will cover sections 3.6--3.8, 3.10--3.12, 4.1--4.4, 4.6.
 Homework due Wednesday, November 17:
 Section 4.2  15,17, 20,21,24, 28,30.
 Section 4.3  11,12,13, 33,34, 44,45, 75,78,80, 84.
 Section 4.4  3,6, 15,16, 23,28, 39,40,44, 49,51, 63,65.
 Section 4.6  2,14,15,20, 34, 38, 46, 54, 65.

 TEST THURSDAY 18 NOVEMBER
 Homework due Wednesday, November 17:
 Section 4.2  15,17, 20,21,24, 28,30.
 Section 4.3  11,12,13, 33,34, 44,45, 75,78,80, 84.

 Homework due Wednesday, November 10:
 Section 3.10 1, 8, 9, 10, 13, 18, 24, 26, 27, 29, 33.
 Section 3.11 3, 10, 18,20,22,24, 28,33,34.
 Section 3.12 9,10.
 Section 4.1  15,18,19,22, 29,30,37,38, 46.

 Handed back tests.  The average was 64.29, which was a bit low, due to
 my miscalibration.

 The topic today was the end of implicit differentiation and derivatives 
 of vector-valued functions. 

 Homework due Wednesday, November 3:
 Section 3.6 2,4,7,8,10,16,21,23,28ab,30,32,34,40.
 Section 3.7 2,3,6,8,13,14,18.
 Section 3.8 10,18,23,30,36,40,46,47,49,51,53,66.

 Tests will be graded and handed back on Thursday, 28 October.
 We passed out copies of Flatland.  Discussion later in November.

 The topic today was implicit differentiation.

 We completed Section 3.4 today.
 The test will cover Sections 1.1, 1.2, 1.3, 2.1--2.5, 3.1--3.4.

 To help you prepare for the test, here is homework due Wednesday, October 27:
 Section 3.2 14,22,31,37,40,46,51,53,60,73.
 Section 3.3 7,9,10,15,27.
 Section 3.4 2,9,10,20,25,39,44,46,47.

 Homework due Wednesday, 13 October
 Section 2.5  4,5,10,11,13,16,21,26,28,35,39,46,49,56,58,59.
 Section 3.1  5,9,10,14,20,23,26,28,34,35.

• State the ε - δ definition of "The function f approaches the limit l near a".
• Find a number δ such that |f(x) - l| <ε for all x satisfying 0<|x-a|<δ for the function f(x)=x^1/2,
  where a and ε are both positive numbers, and l=a^1/2. (See hint on problem 31 of page 111.)
  You may find it useful to do some of the homework due Wedensday first.

  Homework due Wednesday, 29 September.
  Section 1.3 2,6,7,8,12,21,40.
  Section 2.4 2,11,12,18,23,26.
  Section 2.3 2,3,12,13,14.

  Homework due Wednesday, 22 September.
  Section 1.1 6,11,12,14,19,23,31,32.
  Section 1.2 1,14,15,22,23,29,35,36,41,53.

There are 14 ways to associate 5 summands
  (((a+b)+c)+d)+e    a+(b+(c+(d+e)))
  ((a+(b+c))+d)+e    a+(b+((c+d)+e))
  (a+((b+c)+d))+e    a+((b+(c+d))+e)
  (a+(b+(c+d)))+e    a+(((b+c)+d)+e)
  ((a+b)+(c+d))+e    a+((b+c)+(d+e))
 (((a+b)+c)+(d+e)) ((a+b)+((c+d)+e))
 ((a+b)+(c+(d+e))) ((a+(b+c))+(d+e))

  This sequence (of ways to associate n summands) is 1,1,2,5,14,.....
  A google search reveals this as the Catalan numbers.  It is well-worth perusing
  descriptions of the Catalan numbers.

1) As far as I know, we are supposed to have a (real, human) grader 
     for this course.  YOU DO NOT NEED TO BUY ACCESS TO WEBASSIGN!
     DO not waste your money and cause all of us some grief.
(2)  Here is a clarification from yesterday:
     (When I derived the quadratic formula)
Here are the manipulations

Starting with,
  ax^2 + bx + c = 0
we get
  a( x^2 + (b/a)x     )  =  -c
Now, complete the square to get in the parentheses
   ( x^2 + (b/a)x + (b/2a)^2 )
But this adds  (b^2/4a) to the left hand side
(multiply it out) which must also be added to the
right hand side.

This gives
   a( x^2 + (b/a)x + (b/2a)^2 )  =  -c + b^2/4a
Now divide by a and recognise the square on the left
  (x + b/2a)^2 = -c/a + b^2/4a^2 = (b^2-4ac)/4a^2
Take square roots and solve for x.