MTH 125 COURSE OUTLINE Fall 98
INSTRUCTOR: K.W.NICHOLSON OFFICE HOURS: POSTED ON DOOR OF RM 224.
TEXT: Riddle's Calculus, Alternate Edition
TOPICS COVERED: Functions, derivatives, curve sketching, max & min word problems, integration of polynomial, trig and exponential functions.
PURPOSE OF THIS COURSE:
Til now most of your math has dealt with static situations and functions. Calculus introduces the math of dynamic situations. This course will develop the symbols and language of math that will enable you to solve some really interesting problems. Your objective should be to become familiar enough with differentiation and integration that it becomes part of your vocabulary and your thinking.
EVALUATION:
|
Item |
Date |
Discussion |
|
3-100 point tests |
Sept. 21, Oct. 26, and Nov. 23 |
No make up tests will be given. A missed test will be replaced by 1/2 of your final exam score. |
|
1-200 point Final Exam |
Dec. 14, 15, 16, or 17 |
Final will be comprehensive. |
|
1-40 point written report |
Dec 2, 1998 |
May consist of synopsis of 4 magazine articles, or a book
report. |
|
Miscellaneous hand-in problems and quizes |
Due on date specified |
Priced as marked. |
|
Ocassional Group Activities 10 pts each |
Will be announced at a day in advance |
Group activities will be conducted in the physics lab. |
- 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 project reports are due.
- Assisting math or physics students 5pts. 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 Dec 2, 1998)
GRADES:
The above total, excluding bonus points, is 1065, (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 (Feb 11, 1998), you should come for a conference with the
instructor to discuss what each of us can do to retrieve you from
doom.
3. WRITTEN REPORTS WILL BE GRADED EITHER ACCEPTABLE OR REDO FROM
START.
4. If you have more than two excused absences you will be dropped
from the course, as required by the college admission policies.
5. 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: 11:30 - 1:10 Monday and Wednesday .
1. Review some basic essentials in Algebra.
(a + b)n is never equal to an + bn for any n, so (a + b)2 = a2
+ 2ab + b2, not a2 + b2.
And since nˆa = (a)1/n, = (a + b)1/n, so
= (a + b)1/2 is never a1/2 + b1/2 .
Never cancel the same thing from top and bottom of a fraction. Instead you divide numerator and denominator by the same factor, thereby reducing that factor to 1 on both top and bottom.
|
Rules for exponents. anam = am+n, so 32·34 = 36, not 96. (ab)n = anbn so (x3y4)2 = x6y8, but what is (x3 + y4)2
? |
Special products x2 - y2 = (x-y)(x+y) |
Points in the xy plane, distance and midpoint formulas.
A line and its essential components.
Slopes of parallel and perpendicular lines.
A circle and its essential components.
There are essentially two aspects of Calculus: Techniques and Concepts. You need to learn both. We will try to divide the week into two parts, working on Techniques on Tuesdays and Concepts on Thrusdays. Occassionally, however, Techniques will run over two days and so will Concepts.
Course Overview.
1. Discuss the definition of functions and limits.
|
Date |
Topic |
Assignment Due date or Discussion date |
|
8- 24 |
Techniques 1: Lines, circles, domains, ranges & functions. |
Pg. 32: 1-25, Pg 51 1-10, find domains only for 11 - 26, find D & R for 31 - 38, and pg 39, 1 - 35, 36B & 40 (5 points Bonus, due next class at beginning of period.) |
|
8-26 |
Concept 1: Words to Graphs to Equations |
Do the Next Time Problems, |
|
8-31 |
Techniques 2: Function Notation-comp orientation |
Pg 57 : 1-22 Hand in NTP 1 |
|
9-2 |
Concept 2- Exp 1: Measurement |
Meet in the physics lab. |
|
9-9 |
Concept 3: Limits |
68: 1-31 |
|
9-14 |
Technique 3: Infinite Limits |
Pg 82: 1-34 |
|
9-16 |
Concept 4: Instantaneous Rate of Change |
Pg 108 1-22 odd |
|
9-21 |
Test 1 First hour |
|
|
9-23 |
Technique 4: Drill on Derivatives I |
Pg 116 1 - 43 odd, Pg 122 1 - 31 odd |
|
9-28 |
Technique5: Drill on Derivatives II |
Pg 133 1 - 37 odd; Pg 138 1 - 35 odd; |
|
9-30 |
Technique 6: Drill on Derivatives III More Trig fcts |
Pg 146 1-28 odd |
|
10-5 |
Technique 7&7a Curve Sketching w/o & w Calculus |
Page 82: Graph 11 - 24, Page 172: 1 - 22, 27 &
28; |
|
10-7 |
Concept 5: Max & Min Apps, Optimization probs |
Page 203 1 - 8, 13, 14, 17, 19 |
|
10-12 |
Concept 6: Max & Min Apps with Calculus |
Page 223 : 1,3,5,8,9,11,12,21,22,23,30,33,37, 38,40,42, and as many of the "C" problems as you please for 5 Points Bonus each !! |
|
10-14 |
Technique 8a: Implicit Differentiation, |
Page 151 1 - 36 odd, |
|
10-19 |
Concept 7: The Differential, |
Page 240, do 4,10,15,16; Assign: 1 - 15 |
|
10-21 |
Concept 8 continued |
5 Pts Bonus: 33. 10 Pts Bonus: 34 |
|
10-26 |
Test 2 First hour |
Page 284: 1-18 odd, 19 - 37 every other odd, 51, 52 |
|
10-28 |
Technque 10: Integration by Substitution |
Pg 294: 1 - 37 odd, Pg 356: 1 - 39 odd |
|
11-2 |
Concept 9: Area under Curves |
Page 278 in Riddle: 8-18 odd, |
|
11-4 |
Concept 10: Area between Curves |
Page 303 1 - 24 odd |
|
11-9 |
Technique 10a: Log & Exponential Functions |
Page 365 1 - 38 , |
|
11-16 |
Technique 10b: Diff & Integ log & exp functions |
Page 373 1 - 44 |
|
11-18 |
Concept 11: Applications of Integration |
Pg 311 1,2,3,5,8,9,11,15,19, |
|
11-23 |
Test 3 First hour, |
Assign: Page 348, 1 - 36 odd. |
|
11-30 |
Technique 12: Derivatives of Inverse Trig Function |
Page 354, 1 - 28 odd |
|
12-2 |
Technique 13: Integration of the above derivatives |
|
|
12-7 |
Review for Final |
|
|
12-9 |
Review for Final |
|
|
12-? |
Final Exam |
We also need to consider ....
We need to move onto the next step...
Let's come back to that if we have time.
Skeptic:
Devil's advocate
Helps avoid quick agreement, (which can be disastrous)
asks questions that will lead to understanding
pushes members to explore all possibilities
-- to accomplish this, use phrases like:
...What else could we say about this?
Are there other possibilities here?
Before we agree, maybe we should consider...
Checker/Recorder:
Checks for consensus among group members
Obtains members consent upon completion of each step
Writes group solution
Turns in completed problem -- to accomplish this, use phrases
like:
Can you explain how we got this?
Let's summarize what we have decided...
Introduction to Mac Computers
Turning on and off
Open & Close folders
Create your own folder
Start & quit programs
Close file ‚ quit program Show Finder & About this Macintosh
under the Apple
Demo Wordperfect
Open Phy files, open Lab 1 write-up, save it in your own folder
Discuss the difference between an experiment and the write up. Don't
turn in the experiment with a lab write-up.
Demo Excel?? Sure
Web orientation.
Show'm their own web pages and how to change them.
Show'em where games are
Game Rules: No games during class
No games during break (what break?)
Always quit a game when you leave the computer.
Tell'em to stay out of the HD