Martin Flashman's Courses
Math 109 Calculus I Summer, '05
MTWR  13:00-14:20 SH 128
Final Examination
Part I- Wednesday - 8-3
Core Material- no Books or calculators.
Part II- Thursday - 8-4 
Approved Summary Notes and calculators allowed!

Items marked $$ are important for students beginning the course.
This page is subject to change. [6-1-05]





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Last updated: 7/31/05
Summer, 2005              MATH 109 : CALCULUS I         M.FLASHMAN 
Stewart's Calculus 5th ed'n. 
Tentative Assignments-This will be revised further! [7-31-05]
(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
6-1
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
SC 0.B1 Numbers [on-line]
Introduction;  
How to Do Math
6-1and 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]
6-6
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
Mechanical universe (Television program)
VIDEO1364  Derivatives
VIDEO1366 Integration
Parabolas [22]

Average Rates of Change [11]
The Two Questions of Calculus [10]
6-7
2.1 Geom (i)1,2,4 0.C [on-line] Models and Mathematics- Probability  Slope of a Tangent Line [12] 
6-7 and 6-8
2.1 Motion  (ii) 5,8
 Rates of Change, Secants and Tangents [19] 
6-8
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]
Equation of a Tangent Line [18]
6-8 and 9
2.6
3.1

2.6: Use the 4 steps method with x or t = a when appropriate in 11,13,17-19; 15
3.1: 1,7 Use the 4 steps method to find f '(a) 

The Derivative [12] 
The Derivative of the Reciprocal Function [18] 
6-9
3.1
3.2 pp134-138

3.4 pp 157-159
3.1:  2,3, 8, 26,29; 19-21,23
3.2: 1,4-7; 19-23 odd

3.4: 1-3
3.1:11
3.4:11
Instantaneous Rate [15]
Uses of The Power Rule [20] 
6-13 and 14
3.3 pp 145-149
Read Appendix D 
Especially formulae 6-8,10,12,13

3.3: 1-5, 7-15 odd, 34-36,45
3.3: 17-20; 23-26; 57a,58(a,b),61a, 65-67,70-72
Read 3.4 pp160-161, 164-165
3.4: 29,30

*The Derivative of  the Square Root [16]
More on Instantaneous Rate [19]
Short Cut for Finding Derivatives [14]

The Product Rule [21]

Review of Trig[12]
6-14 and 15
Summary #1 Due by 4:00 pm
3.3pp 150-155
3.5 (i) pp169-172
Read web materials on trigonometric derivatives.
3.5: 1,2,5,9,10,13,23, 25
3.3: 87, 22, 27-29, 51, 55, 56, 57(b,c), 60, 69

The Quotient Rule [13]
The derivatives of trig functions [14]
6-16
3.5(ii)pp 172-173   3.5: 3,4,6, 15,21,27, 33
*Graphing Trig Functions[17]
Differentiability [3] 
6-20
3.2 pp 139-142
3.5 p173-4.READ Examples 4 and 5!
 
3.2:35,36,41,46
3.5: 35,36,38,39,43

Read on-line  
Sens. Calc. 0.C on Probability Models

6-21
3.6 The Chain Rule 
pp176 though 178 Ex.2 only!

3.6 pp180-181
3.6: 7-14 use Leibniz notation.
3.6: 16, 17,21,29,35,39

Introduction to The Chain Rule [18]
Using the Chain Rule [13]

6-22
3.6
3.7 pp 184-187 
Read web materials on implicit differentiation.

3.6: 45,51,53,55, 59, 63
3.7: 5-10, 15, 25, 26

3.7: 29, 41, 42, 51
3.7:*36
Intro to Implicit Differentiation [15]
Finding the derivative implicitly [12]
The Ladder Problem [14]
Acceleration and the derivative.[5]
6-23
3.9 Related rates pp198-201
3.8 Higher Order Derivatives 
pp190-194
3.8
2.5 (i) pp 102-104
((ii) pp109-110
3.9: 3,5,11
3.8:
1-15 odd, 21
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

The Baseball Problem[19]or The Blimp Problem [12]

Acceleration and the derivative.[5]
One Sided Limits [6]
Continuity and  discontinuity [4]
6-28 and 29
Summary 2.
4.9  Read web materials on Newton's Method.
3.10 pp 205-207
Read web materials on differentials 
4.9: 1,3,5-7, 27
3.10: 5,7,9,10;
for
4.9:*(11,15,16,25) Using tangent line approximations [25]
6-27
Examination #1
Covers all assignments through that assigned for 6-28.
Sections covered: 1.1-1.4, 2.1,2.5,2.6, 3.1-3.9
0.B2 , 0.C


6-30 3.10
4.1
3.10:15-17, 21-25 odd, 31,33 SC IVA(On-line) The connection between Slope and Optimization [28]
7-5
4.1 plus 
On-Line tutorial on Max/mins
SC IVA(On-line)
4.1:3-6, 31-41 odd,:45,47
On line IVA:1(a,d,e,f),10 

Intro to Curve Sketching [9]  
Critical Points [18] 
7-6
SC IVA(on-line)
More 4.1
SC IVB (On-line) Read
4.1: 11, 34, 36,51; 55
4.7:1,2,7,9
4.7: 15,17,29
IVA: 4, 5(a,b),8,11
4.4:*69 Antidifferentiation[14]
7-7
4.2
4.10
4.2: 7,8,11,23, 25
4.7: 24, 34, 49, 53
4.10: 3-9 odd,  13-15, 23-25
[optional] The Box Problem [20] Three  Big Theorems [11]
Acceleration & the Derivative [6]
7-11
4.2
4.3 pp 240-242
4.7
A java graph showing 
f (x)=P'(x) related for f a cubic polynomial

4.2:15, 19,33
4.3: 5,6, 8(a,b), 11(a,b)

4.10: 29-35odd; 41,53, 55, 57
4.7: 52

Antiderivatives of powers of x [18] The First Derivative Test [3]
Regions where a function is increasing...[20]

Antiderivatives and Motion [20]  
Graphs of Poly's [10]
7-12
4.3 pp243-246
4.4 pp 249-255
SC IVD (on-line)

4.10
4.3: 7,8, 11c, 17, 23,24, 27(c,d), 29(c,d), 47
4.7:54
4.10: 47,51,52
IV.D: 1-11 odd (online)
The connection between Slope and Optimization [28] Using the second derivative [17] Concavity and Inflection Points[13] 
The 2nd Deriv. test [4] 
Domain restricted functions ...[11]
7-13
2.2 pp77-79 Vertical Asymptotes
4.4 pp 249-255
SC 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]
Horizontal asymptotes  [18]
7-14 and 18
4.4
4.5 Read Examples 1-3!
10.2 pp628-634
SC 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
Vertical asymptotes [9]
7-18
Summary # 3 due by 4pm.
4.5
SC IVF(On line)
4.5: 27, 31, 35, 37
IV.F: 1,3,5,13,15,17(on-line)


7-19
SC VA ( On Line)
4.6 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

The Fundamental theorem[17]  Illustrating the FT[14]  
Evaluating Definite Integrals [13]
7-20
SC VA ( On Line)
5.5 pp360-362
5.3: ex 5-ex 7
Appendix E p.A34 
Sum Notation
5.4 pp350-354
VA : 5(a,b)
5.5: 1-4; 7-13 odd
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] 
7-21
5.5 pp363-364
5.3 pp 340-344
5.5: 17-23; 37-41
5.3: 3, 5,7,12, 13,49 

 
7-25
Examination #2
Sample Exam Posted on Blackboard.
Covers all assignments though *** (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.

7-26
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]
7-27
6.1 pages 371-374 

6.1: 1,2,7,11,15,16
Area between two curves [9] 
Limits of integration-Area [15]
7-28 and 8-1
6.1 pages 374-376
6.2 pp 382-385 
6.1: 3,4,17, 19, 45
6.2: 1,3,4,7

Finding volumes using cross sectional slices.
Solids of revolution
8-1 and 8-2
6.2 pp 382-385, - 388

6.1: 29,33,39,41
6.2: 5,10,19,23, 31, 32 


The disc method along the y-axis. 
The washer methods...
8-2
6.3
6.4 p394-395

Probability and
 
DARTS
6.3: 1, 3, 7, 8, 28
6.4: 3,5,8
6.4:11, 13 Work.... 
Hooke's law
Shells....
8-3!



The 20 minute review.
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


6.2 (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

6.3
6.3: 9, 13, 21, 29 , 41, 43


2.4?



5.1 3,11,13,14

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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, trig] 
*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 Part II:
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. Using the mean value theorem, explain  why there is some number c between a and b where P(c) = 1/(b-a) Sx=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).




OFFICE: Library 48    (and soon to be Library 1)                                 PHONE:826-4950
Hours (Tent.): MTWR 10:00-10:45 AND BY APPOINTMENT or chance!
I will try attend the Blackboard 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.

 
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