Archive for Tom Morley's 1509

Hello. Welcome to Math 1509 -- third quarter calculus.

• Page 851: 11,13,15,17
• Page 857: 1,3,5,7,9,17,19,33,35
• page 864: 1,3,5,9,13,15,21,23, 27,28,29
• Page 874: 1,3,5,7,15,17,
• Page 879: (This part probably requires more work than any other section of the chapter) 1,3,5,7,13,19,21,23,27,29,35,37,38

• Section 12.6 (page 828) 39,31,33,35,37,39,46,47,48,51,52,53, **59, **60,**61,**62,**63
• Section 12.2 (page 800): 1,3,5,7,11
• Section 12.3 (page 805): 1,3,5,7,9,11,13,23,25,29,31
• Section 12.4 (page 811): 1,3,5,7,17,19,21,*27,*29
• Section 12.5 (page 819): 1,3,5,7,9,36,13,15
• Page 780 (section 11.8): 9,11,15,23
• Page 786 (section 11.9): 41,43,45,49,51
• Page 793 (section 12.1)>: 9,11,13,24,27,41,43,45,47
• Page 798 (section 12.2): 7,9,11,23,35
• Page 729; 25,27,29,31,37,43,59
• Page 736: 33,35,37,39,63,73,74
• Page 742: 27,31
• Page 749: 21,23,31,33,35,46
• Page 755: 5,7,9,23,25,35
• Page 765: 1,3,5,7,25,27,35,43
• Page 722: 1,3,5,7,17,19,25,27,29,*55,*56
• Page 729; 25,27,29,31,37,43,59
• Page 736: 33,35,37,39,63,73,74
• Page 742: 27,31
• Page 749: 21,23,31,33,35,46
• Page 755: 5,7,9,23,25,35
• Page 765: 1,3,5,7,25,27,35,43
• Page 722: 1,3,5,7,17,19,25,27,29,*55,*56
• Page 616: 1,3,5,7,31,39,47,65
• Page 657 15,17,19,25
• Page 667 13,15,17,19,21,31
• Page 696: 1,3,5
• Page 704 1,3,5,22
• Page 714 1,3,5,7,16,17,19,25,35,38
• Section 9.4 Self Quiz: all
• Section 9.4 Drill 6,7,11,16,17,20,21,25
• --- and after you do the case for general a -- 1,3,5,9
• Section 9.5 Drill et al: 1,3,5,7,9,17,18,21

• Solutions to quiz number one (Postscript format)
• Hour Test Postscript Format or Mathematica 3.0 Format
• May 9 (Plain text format), (MAC Microsoft Word Bin Hex)
• Quiz May 15 (Plain text format)
• May 22 (Plain text format), (MAC Microsoft Word Bin Hex)
• Others are in construction

If you do not have Mathematica, you can read the following files with Math Reader , downloadable from Wolfram Research

16, Part I, and Chapter 18 (all)

Tuesday, May 20.

Prograqmming Hint: Since we know from today that the integral of speed is arc length, we can use this. Suppose that f[t] is a vector function giving the position of the algebraic topologist. Ferinstance:

f[t_] := {3 Cos[ .5 t] + 1.2 Cos[-2.4 t],
          3 Sin[ .5 t] + 1.2 Sin[-2.4 t] }

speed[t_] = Sqrt[f'[t] . f'[t] ] 

Integrate[speed[t],{t,0,47}]

• Section 12.2 (page 800): 1,3,5,7,11
• Section 12.3 (page 805): 1,3,5,7,9,11,13,23,25,29,31
• Section 12.4 (page 811): 1,3,5,7,17,19,21,*27,*29
• Section 12.5 (page 819): 1,3,5,7,9,36,13,15

Here is a cardiod:

 
x(t) = ((1 + cos(t)) cos(t)) i ,
y(t) = ((1 + cos(t)) sin(t)) j : 

x(t) = ((1 + cos(t)) cos(t)) i ,
y(t) = ((1 + cos(t)) sin(t)) j , 
z(t) = sin(t)  k: 

Where did the cusp go?

This quiz covers Conic Sections, Cilyndrical coordinates, curves and space curves, tangents and slopes.

Suggested problems:

• Page 780 (section 11.8): 9,11,15,23
• Page 786 (section 11.9): 41,43,45,49,51
• Page 793 (section 12.1)>: 9,11,13,24,27,41,43,45,47
• Page 798 (section 12.2): 7,9,11,23,35

Big Ideas:

• Vectors and points in 2 and three space.
• Dot products, orthogonality, angles, projections.
• Cross products, geometric and algebraic interpretations, uses
• Lines. Equational descriptions, parametric descriptions.
• Planes. Equational descriptions, parametric descriptions. The geometry that drives these formulas.
• Intercections and closest points. Applications to computer graphics.

Some problems:

• Page 729; 25,27,29,31,37,43,59
• Page 736: 33,35,37,39,63,73,74
• Page 742: 27,31
• Page 749: 21,23,31,33,35,46
• Page 755: 5,7,9,23,25,35
• Page 765: 1,3,5,7,25,27,35,43
• Page 722: 1,3,5,7,17,19,25,27,29,*55,*56

A (postscript) file of a Matheamtica 3.0 notebook that figures out trig identities . If you have access to Mathematica 3.x, here is the Mathematica Notebook