Martin Flashman's Courses
Math 109 Calculus I Summer, '04
MTWR  9:00-10:20 SH 128
Final Examination
Part I- Wednesday - 8-4 Core Material- no Books
Part II- Thursday - 8-5 "Anything goes" Open book- Notes allowed!

Items marked $$ are important for students beginning the course.




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Last updated: 5/11/04
Summer, 2004               MATH 109 : CALCULUS I         M.FLASHMAN 
Stewart's Calculus 5th ed'n. 
Assignments (Stewart-5th Edition / SC = Sensible Calculus online materials) and recommended problems(tentative- subject to change!) 
Date Due Reading Problems
Optional Viewing: Ed Berger CD Tutorial 
[# of minutes] 
* means optional
6-2
HW #1
SC 0.B2 [on-line]
1.1
rev. sheet (on-line): 1-3,6,13,15,16,18,19
1.1: 1,2,10,13,15,17,21,22,45, 47, 48, 51, 53

Introduction;  
How to Do Math
6-3
HW#2
Appendix B
SC 0.B2 [on-line]

pg. A-15: 7-10; 17-20; 21-35 odd; 62

On-line Mapping Figure Activities Functions [19]
6-7
HW#3
1.2
1.3
1.4
1-5;8,10,11
3;5; 54, 55
1,3,37
SC 0.B2 On line # 19, 20, 21
Parabolas [22]

Average Rates of Change [11]
The Two Questions of Calculus [10]
6-8
HW #4
2.1 Geom (i)1,2,4 0.C [on-line] Models and Mathematics- Probability  Slope of a Tangent Line [12] 
6-9
HW#5
2.1 Motion  (ii) 5,8
 Rates of Change, Secants and Tangents [19] 
6-10
HW #6
DO NOT Read 2.6 p119: 1(a),2(a),3,
5(a[ignore i and ii.Use 4steps as in class],b),
6(a[ignore i and ii.Use 4steps as in class],b),

Finding Instantaneous Velocity [20]
6-14
HW #7
2.6
3.1

Read Appendix D
 
Especially formulae 6-8,10,12,13
2.6: Use the 4 steps method with x or t = a when appropriate in 11,13,17-19; 15
3.1: 1,7, 13-16 Use the 4 steps method to find f '(a) 

The Derivative [12] 
The Derivative of the Reciprocal Function [18] 
6-15
HW#8
3.1
3.2
3.4 (i) p 157-159
3.1:  2,3, 8,26,29; 11,19-21,23
3.2: 1,4-7; 19-23 odd
3.4: 1-3;11 

Equation of a Tangent Line [18]
Instantaneous Rate [15]
6-16
HW #9
3.2
3.4 (ii)160-161, 164-165
3.3(i) p 145-149
3.2:35,36,41,46
3.4: 29,30
3.3: (i)1-5, 7-15 odd, 34-36,45 

Differentiability [3]
More on Instantaneous Rate [19]
Uses of The Power Rule [20] 
6-17
HW #10
3.3(ii)p 150-151
3.3: 17-20; 23-26; 57a,58(a,b),61a, 65-67,70-72

*The Derivative of  the Square Root [16]
Short Cut for Finding Derivatives [14]
The Product Rule [21]
Review of Trig[12]
6-21
HW #11
3.3 p 152-155
3.5 (i) pp169-172
3.3: 87, 22, 27-29, 51, 55, 56, 57(b,c), 60, 69
3.5: 1,2,5,9,10,13,23, 25

The Quotient Rule [13]
The derivatives of trig functions [14]
6-22
HW #12
3.5(ii)pp 172-173
(iii)p173-4. 

Read web materials on trigonometric derivatives.

3.5: 3,4,6, 15,21,27, 33
*Graphing Trig Functions[17]
Introduction to The Chain Rule [18] 
6-23
HW#13
3.5 READ Examples 4 and 5 first!
3.6 The Chain Rule 
pp176 though 178 Ex.2 only!
3.2  p 139-142
3.5: 35,36,38,39,43
3.6: 7-14 use Leibniz notation.
3.2: 35,36, 41
Read on-line  
Sens. Calc. 0.C on Probability Models
Using the Chain Rule [13]
6-24
HW #14
3.6 pp180-181
3.7 pp 184-187 
Read web materials on implicit differentiation.
3.6: 16, 17,21,29,35,39
3.7: 5-10, 15, 25, 26 

Differentiability [3]
Intro to Implicit Differentiation [15]
6-28
HW#15
3.6
3.9 Related rates pp198-201
3.8 Higher Order Derivatives 
pp190-194 
3.6: 45,51,53,55, 59, 63
3.7: 29, 41, 42, 51
3.9: 3,5,11
3.8:
1-15 odd, 21 
3.7:*36
Finding the derivative implicitly [12]
The Ladder Problem [14]
Acceleration and the derivative.[5]
6-29
HW #16
3.8
2.5 (i) pp 102-104
((ii) pp109-110
4.9  Read web materials on Newton's Method.
3.8:43,44,47,51; 35,36, 53
2.5: (i) 3,4,7,17-20 , 34,37,39
2.5: (ii) 41,43,45,48, 59
4.9: 1,3,5-7, 27
The Baseball Problem[19]or The Blimp Problem [12]

4.9:*(11,15,16,25)
Acceleration and the derivative.[5]
One Sided Limits [6]
Continuity and  discontinuity [4]

Examination #1
Covers all assignments through Tuesday, 6-29. [HW 1-16]
Sections covered: 1.1-1.4, 2.1,2.5,2.6, 3.1-3.9,4.9 
0.B2 , 0.C


7-1
HW #17
3.10 pp 205-207
Read web materials on differentials 
3.10: 5,7,9,10;15-17, 21-25 odd, 31,33

Using tangent line approximations [25]
7-6
HW #18
4.1
IVA(On-line)



The connection between Slope and Optimization [28]
7-7
HW#19
4.1 plus 
On-Line tutorial on Max/mins
IVA(On-line)
4.1:3-6, 31-41 odd,:45,47
4.7:1,2,7,9
On line IVA:1(a,d,e,f),10 

Intro to Curve Sketching [9]  
Critical Points [18] 
7-8
HW#20
IVA(on-line)
4.2
4.3 pp 240-242
IVB (On-line) Read
4.1: 11, 34, 36,51; 55
4.3: 5,6, 8(a,b), 11(a,b)
4.7: 15,17,29
IVA: 4, 5(a,b),8,11
4.4:*69
The First Derivative Test [3]
Regions where a function is increasing...[20]
Antidifferentiation[14]
7-12
HW #21
4.2
4.3 pp243-246
4.10
4.2:7,8,11,23, 25
4.3: 7,8, 11c, 17, 23,24, 27(c,d), 29(c,d), 47
4.7: 24, 34, 49, 53
4.10: 3-9 odd,  13-15, 23-25
[optional] The Box Problem [20] Using the second derivative [17] Concavity and Inflection Points[13] 
The 2nd Deriv. test [4] 
Acceleration & the Derivative [6]
7-13
HW #22
4.2
4.3
4.7
A java graph showing 
f (x)=P'(x) related for f a cubic polynomial

4.2:15, 19,33
4.10: 29-35odd; 41,53, 55, 57
4.7: 52

Antiderivatives of powers of x [18] Three  Big Theorems [11]
Antiderivatives and Motion [20]  
Graphs of Poly's [10]
7-14
HW #23
2.2 pp77-79 Vertical Asymptotes
4.4 pp 249-255
IVD (on-line)

4.10
4.7:54
4.10: 47,51,52
IV.D: 1-11 odd (online)
The connection between Slope and Optimization [28] Domain restricted functions ...[11]
Vertical asymptotes [9]
Horizontal asymptotes  [18] 
7-15
HW #24
2.2 pp77-79 Vertical Asymptotes
4.4 pp 249-255
IVE (on-line)
2.2: 8,9, 23-27odd
4.4: 3,4, 9-13 , 35-38
IV.E: 1,2
Graphing ...asymptotes [10]  
Functions with Asy.. and holes[ 4]  
Functions with Asy..and criti' pts [17]

7-19
HW #25
4.4
4.5 Read Examples 1-3!
10.2 pp628-634
IV.F READ
4.4: 43-45, 51-53, 59, 60
4.5:1-11 odd, 31, 36
10.2: 3-6, 7, 9, 19a,21,
10.2:24

7-20
HW #26
4.5
5.5 pp360-362
IVF(On line)
4.5: 27, 31, 35, 37
5.5:
1-4; 7-13 odd

IV.F: 1,3,5,13,15,17(on-line)


7-21
HW#27
VA ( On Line)
5.3: ex 5-ex 7

4.6 (i) Read Examples 1-3! 
V.A: 1,2 a (on line)
5.3:19-25 odd (Use F T of Calc)
4.6: 1,7


7-22
HW#28

VA ( On Line)
Appendix E p.A34 
Sum Notation
5.4 pp350-354
VA : 5(a,b)
pA38:1-4,11-13,17,18
5.3: 27-39 odd
5.4: 1-9 odd

Undoing the chain rule.[9]  
Integrating polynomials by Substitution [15] 
7-26
HW #29
5.5 pp363-364
5.3 pp 340-344
5.5: 17-23; 37-41
5.3: 3, 5,7,12, 13,49 

The Fundamental theorem[17]  
Illustrating the FT[14]  
Evaluating Definite Integrals [13]
7-29 Examination #2
Sample Exam Posted on Blackboard.
Covers all assignments though 7-26 (Mainly material not covered in Examination #1)Tentative sections covered: 3.10, 4.1-4.7, 4.10, 10.2, IVA, IVB, IVD, IVE, VA, 5.3, 5.4, 5.5 and Appendix E.

7-27
HW #30
5.2: pp 332-336
6.5
5.4: 45-49
5.2: 5, 17,19, 33,37, 48,49
6.5:1,3,5,13-15

Finding the Average Value of a Function [8]
7-28
HW #31
6.1 pages 371-374 
Probability and 
DARTS
6.1: 1,2,7,11,15,16
Area between two curves [9] 
Limits of integration-Area [15]
8-2
HW#32
6.1 pages 374-376
6.2 pp 382-385
6.1: 3,4,17, 19, 45

Finding volumes using cross sectional slices.
Solids of revolution
8-3
HW#33
6.2 pp 382-385, - 388
6.4 p394-395

6.1: 29,33,39,41
6.2: 1,3,4,7
6.2: 5,10,19,23, 31, 32 
6.4: 3,5,8
6.4:11, 13
Work.... 
Hooke's law
Inventory of old assignments from the 4th Edition.


   






3.9
(ii) pp201-203
(i)
(ii) 7,10,12 
(iii)16,19,31,32


(ii)






4.6 (i) Read Examples 1-3! 
(ii) Read Example 4
(i)1,7 
(ii) 10, 21
 


(i)3-6,7,9 
(ii) 19a, 21, 24
(i)*15, *17






Lab assignment from 4-7 Lab assignment 4-7


6.5 1,3,5,13-15


6.2 (i) pp 378-381  
(ii) pp 381-384 
(iii)p 385-386
(i)1,3,4,7 
(ii) 5,10,19,23, 31, 32 
(iii)  39, 40,51,52
*61,*59 (i)Finding volumes using cross sectional slices. 
Solids of revolution 
(ii)The disc method along the y-axis. 
The washer methods...

6.3 (i)1, 3, 7, 8, 28 
(ii) 9, 13, 21, 29 , 41, 43

Shells....

2.4?



5.1 3,11,13,14

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OFFICE: Library 48                                        PHONE:826-4950
Hours (Tent.): MTWR 12:30-1:40 AND BY APPOINTMENT or chance!
On-line Math chat : I will try attend my math chatroom Tuesday and Wednesday evenings at about 9:00 pm.
E-MAIL: flashman@humboldt.edu               WWW:  http://www.humboldt.edu/~mef2/
***PREREQUISITE: Math 115 or Math code 50 or permission.


Notice that only 400 or 500 of these points are from examinations, so regular participation with reality quizzes and the CD tutorals is essential to forming a good foundation for your grades as well as your learning.

In my experience students who are actively engaged in learning and participating regularly in a variety of activities will learn and understand more and retain more of what they learn. Each component of the course allows you a different way to interact with the material.

CHECKLIST FOR REVIEWING FOR THE FINAL   * indicates a "core" topic.
I. Differential Calculus: 
A. *Definition of the Derivative 
Limits / Notation 
Use to find the derivative 
Interpretation ( slope/ velocity ) 
B. The Calculus of Derivatives 
* Sums, constants, x n, polynomials 
*Product, Quotient, and Chain rules  
*Trignometric functions 
Implicit differentiation 
Higher order derivatives 
C. Applications of derivatives 
*Tangent lines 
*Velocity, acceleration, rates (related rates)  
*Max/min problems 
*Graphing: * increasing/ decreasing  
concavity / inflection 
*Extrema (local/ global)  
Asymptotes 
The differential and linear approximation  
Newton's method
D. Theory 
*Continuity (definition and implications) 
*Extreme Value Theorem /* Intermediate Value Theorem 
*Mean Value Theorem 
II. Differential Equations and Integral Calculus: 
A. Indefinite Integrals (Antiderivatives) 
*Definitions and basic theorem 
*Simple properties [ sums, constants, polynomials] 
*Substitution 
B. Euler's Method, etc. 
Euler's Method 
*Simple differential equations with applications 
Tangent (direction) fields/ Integral Curves 
C. The Definite Integral 
Euler Sums / Definition/ Estimates (endpoints/midpoints) /Simple Properties / Substitution 
*Interpretations (area / change in position) 
*THE FUNDAMENTAL THEOREM OF CALCULUS - evaluation form 
THE FUNDAMENTAL THEOREM OF CALCULUS - derivative form 
D. Applications 
*Recognizing sums as the definite integral  
*Areas (between curves).  
Volumes (cross sections- discs). Average value. Work.
 
Bonus Essay question for final:
Suppose P(t) is a positive continuous function on [a,b] that gives the velocity at time t of an object moving on a straight line. Explain using the mean value theorem why there is some number c between a and b where P(c) = 1/(b-a) òx=a x=b  P(x) dx.
Interpret this equation with either
(i) a discussion of the  velocity and position of the object with the position function given by a definite integral from time x=a to time x=t or
(ii) a discussion of the area under the graph of Y=P(x) above the X-axis from X=a to X=b and the area of a rectangle with height P(c) and width (b-a).

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