Math 125 Course Outline Spring 2004

MTH 125 COURSE OUTLINE Spring 2004

INSTRUCTOR: K.W.NICHOLSON email: nnicholson@cacc.cc.al.us
OFFICE HOURS: POSTED ON DOOR OF RM 224 Ph 256-215-4336 or 4343
webpage located at: http://caccphysics.cacc.cc.al.us
TEXT: Larson, Hostetler & Edwards, Seventh Edition

TOPICS COVERED: Functions, derivatives, curve sketching, max & min word problems, integration of polynomial, trig and exponential functions. (Essentially, Chapters 1 through 5)

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

4-100 point tests

Jan 29, Feb 19, Mar 11, April 8

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

April 29, 10:30 - 12:30

Final will be comprehensive.

Ocassional quizzes

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 average is not above 70 by midterm, you should consider dropping the course to avoid a bad grade.

3. If you stop attending this class without obtaining a drop slip from student services the registrar will give you a grade of F in this course.

4. Words of wisdom regarding Math homework.
I hear........ and I forget,
I see..........and I remember,
I do...........and I understand. 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 ?
1
a-n = an

Special products

x2 - y2 = (x-y)(x+y)
x3 + y3 = (x+y)(x2-xy+y2)
x3 - y3 = (x-y)(x2+xy+y2)
x2 + 2ax + a2 = (x+a)2

Analytical geometry

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.

Course Overview.

1. Discuss the definition of functions and limits.

2. Discuss the true meaning of a derivative, to get an idea of its usefulness, and learn the differentiation formulas that make differentiation a powerful, easy to use tool that permeates all of science, and increasingly, business as well.

3. Practice using derivatives to graph functions, and solve applied problems.

4. Learn what an integral is, what it means, and what exactly was "the discovery of the Calculus", that made Newton and Leibniz so famous. THE BIG PICTURE

Class time: Tuesday and Thursday 10:50 - 12:35 or 10:50 - 11:50 & 12:00 - 12:45

DAILY SCHEDULE

Date

Topic

L, H, & E Homework assignment

Th Jan 8

€ Finding Limits conceptually
€ Finding Limits Graphically

Sect.1.2 Pg 54: 1,3,7,11-17, 23,25

T 1-13

€Evaluating limits analytically

Sect.1.3 Pg 65: 5,11,17, 23,25,,27,29,

Th 1-15

€ More Evaluating Limits analytically

€ Continuities & Discontinuities

Sect.1.3 Pg 65: 37,41, 43, 44, 49,51, 67,69,71,83,103,
Sect. 1.4 Pg. 76 5-9, 15,17,19,25,27,33 41, 69,71, 83?

Tu 1 -20

€Infinite Limits, Vertical and Horizontal Asymptotes

Sect. 1.5 Pg. 85: 1,3,5,11,15,17,29,31,33,35

Th 1 - 22

€ Using Secant Lines to Find Average Rate of Change
€ Using the Derivative to Find Instantaneous Rates
€ Finding Instantaneous Velocity
€ Understanding the Concept of the Derivative

Sect. 2.1 Pg : 5,7,17,25,3139,41,71-79
Sect. 2.2 Pg 113: 1 - 39

Tu 1 - 27

€Derivatives and the Tangent line to a curve
€Finding the Equation of Tangent Lines

Sect. 2.2 continued 41 - 61, 91,101

Th 1- 29

Test 1

Tu Feb 3

€Derivative formulas
€Product and Quotient Rules

Sect. 2.3 Pg. 124: 1 - 51, 63,65,67,75,83, 87,89,91

Th 2 - 5

The Chain Rule

Sect. 2.4 Pg 133: 1 - 25, 43-56, 61, 69, 71,75,79,81

Tu 2 - 10

Implicit Differentiation

Sect. 2.5 Pg 142: 1,5,7,11,15,19,21,23,27,29,35,37,39

Th 2 -12

Related Rate Problems

Sect. 2.6 Pg 149: 1,3,7,9,13,17,21,25,31,35,43

Tu 2 -17

Max and Min Problems

Sect. 3.1 Pg. 165: 1 - 31, 49-55,59

Th 2 -19

Test 2

Tu 2 -24

Increasing and decreasing functions

Sect. 3.3 Pg 181 1 - 33, 43 - 56

Th 2-26

Second Derivative Test and Concavity

Sect. 3.4 Pg. 189: 1 - 21,27 - 37, 45,46,49 55, 67,69

Tu 3 - 2

Limits at Infinity

Sect. 3.5 Pg. 199: 1 -32, 49 - 61, 69,71

Th 3- 4

Curve sketching using calculus

Sect 3.6 Pg. 208: 1-5,7-23,31, 51-55, 67- 70

Tu 3-9

Optimization Problems

Sect. 3.7 Pg. 216: 5,13,15,17,21,23,43

Th 3-11

Test 3

tu 3-16

Differentials

Sect. 3.9 Pg 233: 1,3,7,9,11-19,29,33,37

th 3-18

Integration I

Sect. 4.1 Pg 249: 1 - 47, 55-62, 65,68,71,73,77,81,84

Tu 3-25

Sigma notion
Definite Integral and Area ??

Sect. 4.2 Pg 261: 1,3,7,15,17, 49,51
Sect. 4.3 Pg 271: 1 -10, 11,15,19,21,23

Tu 3-30

The Fundamental Theorem of Calculus

Sect. 4.4 Pg. 284: 5 - 21, 27-31, 35-43, 69,73

Th 4-1

Integration by Substitution

Sect. 4.5 Pg. 297: 1 - 33 , 41-53, 57,59,65,69,75

Tu 4 - 6

Log Fct Review & Differentiation of ln u

Sect. 5.1 Pg 321: 3 -33,37,45- 59, 69,73

Th 4 - 8

Test 4

Tu 4 - 13

Ý du/u

Sect. 5.2: Pg 330: 1 - 40, 43 - 50,67

Th 4 - 15

Inverses of functions

Sect. 5.3 Pg 338: 1,3,5, 9-16,29-31

Tu 4 - 20

Exponential Functions

Sect. 5.4 : Pg 347: 1 -17, 25 - 31,39 58,65,67, 87 - 108

Th 4 - 22

Other Bases

Sect. 5.5: Pg 357: 1 - 34, 41 - 67

Tu 4 - 27

Inverse Trig Functions

Sect. 5.8: Pg 386: 5 - 11, 17 - 29, 31,33,41 - 59, 71

Th 4-29

Final Exam 10:30 - 12:30

Integraion involving Inverse Trig Functions

Sect. 5.9 Pg 393: 1 - 44

Item	Date	Discussion
4-100 point tests	Jan 29, Feb 19, Mar 11, April 8	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	April 29, 10:30 - 12:30	Final will be comprehensive.
Ocassional quizzes

Date	Topic	L, H, & E Homework assignment
Th Jan 8	€ Finding Limits conceptually € Finding Limits Graphically	Sect.1.2 Pg 54: 1,3,7,11-17, 23,25
T 1-13	€Evaluating limits analytically	Sect.1.3 Pg 65: 5,11,17, 23,25,,27,29,
Th 1-15	€ More Evaluating Limits analytically € Continuities & Discontinuities	Sect.1.3 Pg 65: 37,41, 43, 44, 49,51, 67,69,71,83,103, Sect. 1.4 Pg. 76 5-9, 15,17,19,25,27,33 41, 69,71, 83?
Tu 1 -20	€Infinite Limits, Vertical and Horizontal Asymptotes	Sect. 1.5 Pg. 85: 1,3,5,11,15,17,29,31,33,35
Th 1 - 22	€ Using Secant Lines to Find Average Rate of Change € Using the Derivative to Find Instantaneous Rates € Finding Instantaneous Velocity € Understanding the Concept of the Derivative	Sect. 2.1 Pg : 5,7,17,25,3139,41,71-79 Sect. 2.2 Pg 113: 1 - 39
Tu 1 - 27	€Derivatives and the Tangent line to a curve €Finding the Equation of Tangent Lines	Sect. 2.2 continued 41 - 61, 91,101
Th 1- 29	Test 1
Tu Feb 3	€Derivative formulas €Product and Quotient Rules	Sect. 2.3 Pg. 124: 1 - 51, 63,65,67,75,83, 87,89,91
Th 2 - 5	The Chain Rule	Sect. 2.4 Pg 133: 1 - 25, 43-56, 61, 69, 71,75,79,81
Tu 2 - 10	Implicit Differentiation	Sect. 2.5 Pg 142: 1,5,7,11,15,19,21,23,27,29,35,37,39
Th 2 -12	Related Rate Problems	Sect. 2.6 Pg 149: 1,3,7,9,13,17,21,25,31,35,43
Tu 2 -17	Max and Min Problems	Sect. 3.1 Pg. 165: 1 - 31, 49-55,59
Th 2 -19	Test 2
Tu 2 -24	Increasing and decreasing functions	Sect. 3.3 Pg 181 1 - 33, 43 - 56
Th 2-26	Second Derivative Test and Concavity	Sect. 3.4 Pg. 189: 1 - 21,27 - 37, 45,46,49 55, 67,69
Tu 3 - 2	Limits at Infinity	Sect. 3.5 Pg. 199: 1 -32, 49 - 61, 69,71
Th 3- 4	Curve sketching using calculus	Sect 3.6 Pg. 208: 1-5,7-23,31, 51-55, 67- 70
Tu 3-9	Optimization Problems	Sect. 3.7 Pg. 216: 5,13,15,17,21,23,43
Th 3-11	Test 3
tu 3-16	Differentials	Sect. 3.9 Pg 233: 1,3,7,9,11-19,29,33,37
th 3-18	Integration I	Sect. 4.1 Pg 249: 1 - 47, 55-62, 65,68,71,73,77,81,84
Tu 3-25	Sigma notion Definite Integral and Area ??	Sect. 4.2 Pg 261: 1,3,7,15,17, 49,51 Sect. 4.3 Pg 271: 1 -10, 11,15,19,21,23
Tu 3-30	The Fundamental Theorem of Calculus	Sect. 4.4 Pg. 284: 5 - 21, 27-31, 35-43, 69,73
Th 4-1	Integration by Substitution	Sect. 4.5 Pg. 297: 1 - 33 , 41-53, 57,59,65,69,75
Tu 4 - 6	Log Fct Review & Differentiation of ln u	Sect. 5.1 Pg 321: 3 -33,37,45- 59, 69,73
Th 4 - 8	Test 4
Tu 4 - 13	Ý du/u	Sect. 5.2: Pg 330: 1 - 40, 43 - 50,67
Th 4 - 15	Inverses of functions	Sect. 5.3 Pg 338: 1,3,5, 9-16,29-31
Tu 4 - 20	Exponential Functions	Sect. 5.4 : Pg 347: 1 -17, 25 - 31,39 58,65,67, 87 - 108
Th 4 - 22	Other Bases	Sect. 5.5: Pg 357: 1 - 34, 41 - 67
Tu 4 - 27	Inverse Trig Functions	Sect. 5.8: Pg 386: 5 - 11, 17 - 29, 31,33,41 - 59, 71
Th 4-29	Final Exam 10:30 - 12:30
	Integraion involving Inverse Trig Functions	Sect. 5.9 Pg 393: 1 - 44