MTH 126 COURSE OUTLINE Spring 2003

INSTRUCTOR: K.W.NICHOLSON OFFICE HOURS: Posted On http://caccphysics1.cacc.cc.al.us
ph 256 215 4343 Email: nnicholson@cacc.cc.al.us
TEXT: Larson & Hostetler 's Calculus, Sixth Edition

TOPICS COVERED: Techniques of integration, applications of integrations, finding volumes of solids of revolution about a line, infinite series, a study of conic sections, vectors, lines & planes. (Chapters 6 - 10)

PURPOSE OF THIS COURSE:
This course continues the study of calculus, emphasizing more complex integration techniques, analytical geometry in two and three dimensions, and physical applications of calculus

1. The primary task of Calculus II is to learn to integrate.

 

2. The second task is to learn what to do with integrals. This second task will probably be the more useful to you most of the time, but you can never tell when you'll step into a theoretical quagmire and have to reason your way out of it using the first task. Albert Einstein was a pragmatic physicist with considerable disdain for mathematical theory. He was deeply shocked when he discovered he was going to have to delve deeply into theoretical mathematics in order to complete his general theory of relativity.

Task #1 Integration

Lots of things on a bicycle are nice but unnecessary. With a little basic knowledge of rotational dynamics and practice, one can even ride a bike without handlebars. But wheels are absolutely essential.


You (should) already know that factoring is to algebra what wheels are to a bicycle.

 

A particular technique in integration, called either integration by substitution or integration by changing the variable, (by substituting in equivalent expressions for the original), is the wheels that enables one to roll in integration. That is where we will begin our course.


EVALUATION:

Item

Date

Discussion

4-100 point tests

Jan 23, Feb 13, Mar. 6, April 3

No make up tests will be given. A missed test will be replaced by 1/2 of your final exam score.

1-200 pt Final Exam

May 1, 2003, 10:30 - 12:30

Final will be comprehensive.

15 Quizzes

Weekly

Collectively worth 100 pts, may be used to replace lowest test score

Homework

Due next class

Total worth 100 points. All hwk must include name, date, homework number, page and problem numbers.

Occasional Group Activities 10 pts each

Will be announced at a day in advance

Group activities will be conducted in the physics lab.

- Bonus Points 40 pts. max.

- Letters to politicians, or editors expressing your opinion about issues regarding the physical universe in which we live. 1 point each, 10 points maximum. You may send copies of the same letter to a maximum of 5 different people. You must turn in letters in stamped, addressed envelopes, along with a copy for the instructor, on the same day book reports are due.

- Assisting math or physics students 5 pts. per hour, 20 pts. max. (Must be done in the Library or Physics Lab verified in writing by either an instructor or librarian.)

- Occasional hand in bonus problems ( bonus questions on tests do not count toward this max)5 pts. each, 20 pt. max.
- Book report, 10 pts. (Book must be approved by instructor prior to reading, and reports are due on April 29, 2003)

GRADES:
The above total, excluding bonus points, is 600, (plus a few points, depending on miscellaneous assignments), and your accumulative total will be divided by that amount to calculate your final average.

90 - 100 = A, 80 - 89 = B, 70 - 79 = C, 60 - 69 = D, 0 - 59 = F

NOTES:
l. Final percentage will be rounded UP, i.e., a final percent of 79.00000001 will be rounded up to 80.
2. You should keep all returned papers. You should also keep track of the ratio (your accumulative total)/(The accumulative total possible to date) as the quarter progresses. If this ratio is below 70 at midterm (March 1, 2003), you should come for a conference with the instructor to discuss what each of us can do to retrieve you from doom.
3. Words of wisdom regarding Math homework.

I hear........ and I forget,

I see..........and I remember,

I do...........and I understand.
THE BIG PICTURE

Class time: 11:50 - 12:35* Tuesday and Thursday

Unless you want a 10 minute break, in which case class will end at 12:45

DAILY SCHEDULE

Date

Topic

Assignment

Th Jan 9

5.7 Differential Equations
5.8 Differentiating Inverse Trig Functions

Pg 376 - 83 - 86, 88
Sect. 5.8: Pg 382: 5 - 11, 19 - 29, 39, 41, 43 - 51
H1: 383-43,45,49

T 1-14

5.9 Inverse Trig Functions & Integration
NFQ 1

Sect. 5.9 Pg 390: 1 - 32
H2: 3,7,15,19,21,24Bonus

Th 1-16

6.1 Areas between curves
6.2 Volumes by Disk Method
NFQ 2

Pg 413: 1 - 15
Pg 423: 1-15
H3: 413-3,7,15; 423-13

Tu 1 -21

6.3 Volumes by Shell Method

Pg 432: 1-20 H4: 7,17, Bonus Ex 4 using shell

Th 1 - 23

Test 1

Tu 1 - 28

6.4 Arclength & Surface Area

P442: 1 - 7, 31 - 36, H5: 7,31,39

Th 1- 30

6.5 & 6.6 Work,
6.6 Center of Mass,
6.7 Pressure
NFQ3

Pg 451: 1-9 H6: 9,15,16Bonus
Pg 462: 1,3,9,13,15 H6: 13, 15, 36 Bonus
Pg 469: 1 - 9

Tu Feb 4

7.1 Basic Integration
7.2 Integration by Parts

Pg 479: 1 - 13, 19,23,27,31 H7: 7,23,33Bonus
Pg 487: 1,3,5,9,15,21,27,29,39,41,47 H7: 11,27,29

Th 2 - 6

7.4 Trig Substitution
NFQ 4

Pg 505: 1 - 4, 19,21,23,27,29,31
H8: 29,39,43

Tu 2 - 11

7.5 Partial Fractions

Pg 515 1 - 6, 7,13,19 H9: home made

Th 2 -13

Test 2

Tu 2 -18

7.7 Indeterminate Forms-L'Hopital's Rule
0 / 0 & ƒ/ ƒ
ü ƒ & ƒ - ƒ
ƒ0, 0ƒ, 00, 1ƒ
Miscellaneous

Pg 530: 11-21, 31-41, 51-55
H10: 19,37,55

Th 2 -20

7.8 Improper Integrals
8.1 Sequences
NFQ 5

Pg 540: 1 - 33, 51,53 H11: 33,53,37 Bonus
Pg 555: 1,3,7,9,13,15,23,25,27,29,31,33,35,
51,53,55 H11: 31,35,59

Tu 2 -25

8.2 Series & Convergence

Pg 564: 1,5,11,15,31,33,41-60
H12: 5,33,47

Th 2-27

8.3 Integral Test & P series
8.4 Comparison Test
NFQ6

Pg 571: 1,3,7,11,15,17,19 H13: 13bonus
Pg 578: 3,7,11,15,19,23,29-36, H13: 19,27

TuMar 4

8.5 Alternating Series
8.6 Ratio Test & Root Test

Pg 586: 1-4, 9,13-23 odd,37-51 odd
Pg 594: 13-25 odd, 33 - 37
H14: Pg 586: 21,39,51,53 Bonus

Th 3- 6

Test 3

Tu 3-11

8.7 Taylor's Polynomials & Approximations

Pg 604: 7,9,17,29,31 H15: 19,31

Th 3-13

8.8 Power Series
8.9 Representation of functions by Power Series NFQ 7

Pg 613: 1,3,7,13,15 H16: 19
Pg 620: 1,3,5,7,23,25 H16: 26

3-17 to 3-21

No School!

Tu 3-25

8.10 Taylor & Maclaurin Series

Pg 630: 1,3,5,7,11 H17: 5,1,19

Th 3-27

9.1 Conics & Calculus
9.2 Plane Curves & Parametric Equations
NFQ 8

Pg 647: 1-8, 9,13,21,23,41,45 H18: 13,21,45
Pg 659: 3,9,15,29,31 H18: 31

Tu Apr. 1

9.3 Parametric Equations & Calculus
9.4 Polar Coordinates

Pg 668: 1,5,19,21 H19: 5,21
Pg 678: 1,3,5,11,13,21,23,25 H19: 5,21

Th 4-3

Test 4

Tu 4 - 8

10.1 Vectors in the Plane

Pg 708: 1,3,5,7,9,13,15,29,21,23,29,30,31,37,41,43,45,
47,51,55

Th 4 - 10

10.2 Space Coordinates & Vectors in Space
NFQ 9

Pg 717: 1,5,13,17,25,29,33,35,37,39,45,61,65
H20: 45, 61, 65

Tu 4 - 15

10.3 Dot Products of Vectors
10.4 Cross Products of Vectors

Pg 727: 1-5, 11,13,21,23,25,35,59,61,65,67
Pg 735: 1-6, 7,11,13,15,33

Th 4 - 17

10.5 Lines & Planes in Space
NFQ 10

Pg 745: 1,3,5,9,15,23,25,29,31,41,43,63,65,67

Tu 4 - 22

10.6 Surfaces in Space

Pg 56: 1 - 13 odd

Th 4 - 24

10.7 Cylinderical & Spherical Coordinates
NFQ11

Pg 763: 1 - 31, 75-81

Tu 4 - 29

Last day of Classes: Review for Final ?

May 1

Final Exam 10:30 - 12:30