Martin Flashman's Courses
Math 106 Calculus for Business and Economics
Fall, '03 
Current Assignment and Schedule
Fall, 2003      Tentative AssignmentsBased on the 2nd Edition: Need to be updated: 9/11/03    M.FLASHMAN 
3rd Edition revised Assignments have dated blue sections! and on-line Sensible Calculus is indicated by SC.
Due Date Reading for 3rd Edition   Problems CD Viewing [# minutes] Optional
8-26
#1
 A.1 Review of Real Numbers 
A.3 Multiplying and Factoring 
1.1 pp 3-6 		 BLACKBOARD background assessment quiz.  
A.1: 1-21 odd 
A.3: 1-13 odd; 31-39 odd		 Introduction [in class] 
How to Do Math [in class]
8-28
#2
 1.1 Functions and tables. 
A.5pp A.22-24  
Solving equations 		 1.1: 1-5, 7,9, 12, 15, 16, 22, 23, 25, 33  
A.5 1-7 odd, 13-19 odd 		 Functions [19]
8-29 1.2 Graphs  
Sensible Calculus 0.B.2 Functions 		 1.2: 1,2,4,5 [Draw a mapping-transformation figure for each function in this assignment] [NO BLACKBOARD REPORT!] 
[Read SC 0.B.2  to find out more about the mapping-transformation figure.]		 Graphing Lines [28] Try Blackboard Practice Quiz on Functions
9-2
#3
 1.3 Linear functions 
 Functions and Linear Models		 1.2: 13, 17, 31  Draw a mapping figure for each function 
1.3 : 1-9 odd, 11,12,29,41,33 		 The Two Questions of Calculus [10]  On-line Mapping Figure Activities- 
(this may be slow downloading)
9-4
#4
 1.4 Linear Models.  1.3: 37- 49 odd, 55, 57, 59 
1.4: 1-9 odd		 Average Rates of Change [11]  1.4: 49
9-5
#5
 1.4 Linear Models. 1.4:  12, 19, 21,22,25

9-8(extended to 9-9)
#6
 2.1 Quadratic functions 
A.5 ppA23-A25		 2.1: 1-9 odd, 25, 27, 33  Parabolas [22]
9-11
#7
 3.1 Average Rate of Change 3.1: 1-10, 13-16, 21, 39, 40 Rates of Change, Secants and Tangents [19]
9-12
#8
 3.2 The Derivative: A Numerical and Graphical  Viewpoint 3.2: 1, 2, 5, 9,12  Finding Instantaneous Velocity [20] 
9-15
#9
 3.2 (graphical) 
3.3 The Derivative: An Algebraic Viewpoint		 3.2: 13, 16, 17, 19, 20; 23, 24 
3.3: 1, 2, 5[Use  "4-step process" from class for all]		 The Derivative [12] AND
Slope of a Tangent Line [12]  
9-16
#10
 3.2 derivative estimates 
3.3 The Derivative: An Algebraic Viewpoint		 3.2: 33, 39, 41, 42, 47, 49, 57, 58, 71, 83 
3.3: 6,13 ,15,17, 23, 25, 39 		 Equation of a Tangent Line [18] 3.2: 73,74, 86
9-18
#11
 3.2 Derivative function graphs, interpretation
3.4 The Derivative:  Simple Rules		 3.2 59-64, 97,98, 109, 110
3.4:1-11 odd; 14-17; 19-21		 Instantaneous Rate [15]
3.2:65
9-19
#12
 3.4 (Again) 
Chapter 3 Summary as relevant. 		3.4: 29, 37, 41, 42, 53, 55, 63, 64 Short Cut for Finding Derivatives [14]
9-22
#13
  3.4 (Again)
3.5 Marginal analysis 
Chapter 3 Summary as relevant.		 3.4: 61, 65, 67, 71, 79
3.5: 1,5,6,9,11,13		 Uses of The Power Rule [20] *The Derivative of  the Square Root [16]
*The Derivative of the Reciprocal Function [18]
9-23
#14
 3.5 (Again)
4.1  Product Rule only! pp 241-244 		3.5: 19, 21,28
4.1: 13, 15, 16, 21, 22 		The Product Rule [21] Differentiability [3]  
9-25
#15
 4.1: Quotient Rule 4.1: 35, 37, 38, 43; 53, 59, 62
The Quotient Rule [13]

9-26
#16
 4.1 4.1: 63, 64, 71, 73 More on Instantaneous Rate [19] 
9-29
#17
 4.2 The Chain Rule 4.2 : 13- 17, 55 Introduction to The Chain Rule [18]

9-30
#18
 		4.2 The Chain Rule 4.2: 25, 26, 33, 35; 47,51, 53, 61, 62, 65 Using the Chain Rule [13]

10-2
#19
 		4.4 Implicit Differentiation (Skip Examples 2 and 3!) 4.4 :11, 12, 15, 35, 36, 47 Finding the derivative implicitly [12] Intro to Implicit Differentiation [15]
10-3
#20
 5.4 Related Rates Especially  Ex. 1-3
A.2: Exponents		 5.4: 9, 11, 13
A.2: 15,19, 23, 39, 41, 71
2.2 : 3,4,9,11		 The Ladder Problem [14]
 4.4: 53
Using Implicit Differentiation [23]

End of material covered in Exam #1

10-6
#21
 2.2: Exponential Functions 
5.4 17,  21, 25
2.2:  7, 13, 17, 59, 61
 Exponential Functions [10] The Baseball Problem [19]
Morale Moment
Math Anxiety [6]
Review for EXAM 10-8
 Midterm Exam #1 covers  HW 1-20.

Chapter 3 review: 2,3,4,5,9 
Chapter 4 review: 1(a-d), 2(a,b), 4(a,b)
10-7
#22
 2.2: Exponential Functions 
 2.2: 45, 47, 51, 63, 73

2.3: 1-5, 7, 13
Logarithmic Functions [19]
10-10
#23
 2.3: Logarithmic functions 2.3: 1-4, 19
 Logarithmic Functions [19]
10-13
#24		   2.3: 5, 7, 20, 21, 25,31, 45a, 48 a
 Derivatives of Exp'l Functions [23]
10-14
#25
 		4.3: Derivatives for Log's & Exponential Functions
4.3:1,2,15,17,19, 23;
7,8,45,51,53,85
 		Derivative of log functions [14] Sensible Calculus I.F.2
10-16
#26
 4.3

 4.3: 27, 29, 33, 73
4.4: 31 , 32

10-17
#27
 2.3 4.4 Example 3

 2.3: 9, 11, 15

  
10-20
#28
 3.6: limits (numerical/graphical) 
P209-216 omit EX.3.
3.6: 19, 21(a,b), 23(a-e), 25(a-e), 26(a-e)
3.7: 13,14, 15		 One Sided Limits [6]
Continuity and discontinuity [4] 
Three  Big Theorems [Begin-3.5min]		 3.6: 31
10-21
#29
 3.7: limits and continuity
3.8 limits and continuity (alg) pp225- 230 middle
On-line: cont and diff.
The Intermediate Value Theorem
5.1:  Maxima and Minima
 3.7:20,27, 28
5.1: 1-7 odd, 8-10,12

 The connection between Slope and Optimization [28]
 3.8: 11-25 odd; 39-42
10-23
#30
 5.1:  Maxima and Minima 5.1: 13,15,21,23,24,25 Critical Points [18]
10-24
#31
  5.2. Applications of Maxima and Minima 5.1: 35,  39, 41, 44
5.2: 5, 11, 13
 Intro to Curve Sketching [9]    The Fence Problem[25]
10-27
#32
 5.2. Applications of Maxima and Minima
5.3 2nd deriv.pp317-320		 5.2:15, 21
5.3: 1-5,7,9,11,14		 Higher order derivatives and linear approximations.[first 5 minutes only!]
Regions where a function is increasing...[20]
The First Derivative Test [3]
Acceleration & the Derivative [6]
The Box Problem [20]
10-28
#33
 5.3
 5.2: 25,  27, 29
5.3 : 17-20, 23; 25, 29,31		 Using the second derivative [17]  
Concavity and Inflection Points[13]		 The Can Problem[21]
10-30
#34
 5.2 and 5.3 again!
 5.2: 33, 35, 41, 45
 5.3: 35- 37,41, 63, 67
 Graphs of Poly's [10]
The 2nd Deriv. test [4]		 Horizontal asymptotes  [18]
10-31
#35
 3.6: p212-216
3.8: p229
5.3: p321-324
 3.6: 1-11 odd
3.8: 15,17,21,23
5.3: 39, 43, 45		 Vertical asymptotes [9]  
Graphing ...asymptotes [10]
Functions with Asy.. and holes[ 4]
Functions with Asy..and criti' pts [17]
11-3
#36
 3.6,3.8  Review!
On-Line: Linear Estimation		 3.6: 25, 27,29
3.8: 33,35,37
On-line Problems on Linear Estimation  
L1-6; A1-5; App1-3		 Using tangent line approximations [25] Cusp points &... [14]
SC.III.AThe Differential
11-4
#37
 3.7, 5.3 Review
5.5 Elasticity and other economic applications of the derivative		 3.7: 15,17, 28-30
5.3: 47, 51, 63, 71
5.5: 1, 3		 Antidifferentiation[14]

11-6
#38
 Differential equations and integration SC IV.A 
6.1 The Indefinite Integral  p 353-358
On-line tutorial.
 6.1: 1-19 odd, 27, 35 Antiderivatives of powers of x [18]
11-7
 #39
 		6.1 Applications p321-323 6.1: 41-44,51
 		Antiderivatives and Motion [20]


End of material covered in Exam #2
Midterm Exam #2 covers Assignments 21-39
11-10
#40
6.1: 53-55, 57
 SC IV.E

Review for Exam #2: (will not be collected): p 136: 2,3,4
p288: 1(a,e,g,i),2(c,d),3a,8a
p350: 1(a,d,f),2,4a,5(a-c)
p362: 39
p407: 1(a,b)
11-11/13
#41
 6.3. The Definite Integral As a Sum. p 373-376
 6.3: 1-5 odd, 15, 19, 21 Approximating Areas of Plane regions [10] 
 SC IV.E
11-13/14
#42
 6.4 The Definite Integral: Area p384-386 6.4: 1-5 odd, 21, 23 Areas, Riemann Sums, and Definite Integrals [14]
11-17
#43
 6.5 pp392-395   
The Fundamental Theorem
 6.5 : 17-20; 67,68
 The Fundamental theorem[17]  
Illustrating the FT[14]
11-17
#44
 6.2 Substitution pp364-367  6.2: 1-6; 21,23 Undoing the chain rule.[9]  
Integrating polynomials by Substitution [15]

11-18
#45
 6.2 pp 368-371
6.5 396-398
7.2 pp416-420 (area between curves)		 6.2: 27-33,59, 60
6.5: 27-30
6.4:22		 Evaluating Definite Integrals [13]
Area between two curves [9] 
11-20
#46
 6.5 example 5
7.2 p420-426 (Surplus and social gain)
 6.5: 59,63,64
7.2:1,3,5,11, 15
7.2: 25, 37, 49
Limits of integration-Area [15]
Common Mistakes [16]		 Integrating composite exponential and rational functions by substitution [13] 
11-21
#47
 7.3  pp 430-431
8.1 Functions of Several Variables. p467-471
 8.3 pp 490 - 492
 7.3: 1-5 odd, 29, 35a
8.1: 1-9 odd, 19, 20, 21, 29, 39, 43
 8.3:  1- 7 odd, 13, 41, 45   		Finding the Average Value of a Function [8]
12-1/2
#48
 8.2 6.5: 9,11,41-45 odd, 42, 65,81
The 20 minute review.
12-4
#49
 8.3 Second order partials
8.4 p498-501 Critical points
 8.2: 1-9 odd; 11-18; 19-25 odd;41, 49
8.3: 19-25 odd; 29,33,38,51, 53
8.4: 1-9 odd, 33, 37

12-5
#50 (not on BB yet)
 7.6 7.6: 1,3,13
7.3::25		 The first type of improper integral[10] 7.6:25, 27
12-8
#51(Not on BB yet)
 7.5 p 442-445
8.4 pp 504-505
 7.5: 1-7
Infinite Limits of integration ... [12]
12-9
#52
 7.5 7.5:11, 13, 17 The second type of ... [8] 
12-11
 7.4
The 20 minute review. 7.4:1, 9, 21, 27

8.4 8.4 :13, 15,17,19

INVENTORY Reading
INVENTORY		 Problems
INVENTORY		 CD Viewing
INVENTORY		 Optional
INVENTORY








Domain restricted functions ...[11]  Three  Big Theorems [11]  
5.2: 56



Gravity and vertical motion [19] 
Solving vertical motion [12] 		Distance and Velocity [22]




8.2: 45








 

Probability and 
DARTS 
Future and present value.



2.3 2.3:1,3,4,5,7,11,13,31 The 20 minute review.







Final Examination: 

Tentative Schedule of Topics  (Subject to  some major changes) 9-11-03 
 
 Monday
Tuesday
  Thursday Friday
Week 1 8-25 Course Introduction  8-26 Numbers, Variables, Algebra Review 
The coordinate plane. 
Points and Lines. 		 8-28 More Algebra review. 
Begin Functions		 8-29 Functions, graphs.
Week 2 9-1 No Class- Labor Day 9-2  Functions, graphs and models. Especially Lines and models. 9-4 More Functions and Models: Linear Functions.  9-5  Quadratic functions. 
Slopes, rates and estimation. More linear models.
Week 3 
Summary of Weeks 1&2 Due Friday 9-12.		 9-8 Meet in Lab! technology.Quadratics. 9-9 Begin Average rates, and slopes of secant and tangent lines.  9-11The Derivative. Motivation: Marginal cost, rates and slopes. 9-12 More on the Derivative. 
Week 4  9-15  Begin the Derivative Calculus 9-16 The Derivative Calculus I  9-18   Justification of the power rule .  9-19  Marginal Applications.
Justify Constant Multiple Rule.
Week 5 Summary of Weeks 3&4 . 9-22 Justify the sum rule.
Examples: f  does not have a derivative at a.
Start Product rule.  		9-23 Justify product rule.
Start Quotient Rule.
 9-25 The Quotient rule.  Breath  9-26 The Chain Rule 
Week 6  9-29 Meet in lab: Technology: checking the chain rule and More Chain Rule
Implicit functions. Implicit Differentiation
9-30 Implicit Functions and Related rates. 10-2 More related rates.
 10-3Exponential functions
Interest and value
Week 7 
Midterm Exam #1 Self-Scheduled 10-8 
Summary of Week 5&6  Due 10-10
 10-6 More on exponentials.
Start Logarithmic functions. 		 10-7 Review for Exam #1
 10-9 Logarithmic functions. 10-10 
Week 8  10-13 Derivatives of Logarithms and Exponentials
 10-14 Finish derivatives of log's , etc.
Logarithmic differentiation. 

10-16  Models using exponentials 
 		 10-17  limits and continuity,
Begin First Derivative Analysis 
Week 9 Summary of Weeks 7 and 8  Due 10-24
 10-20 IVT?
Continuity		 10-21 Optimization 
The fence problem.		 10-23 More Optimization and Graphing. First Derivative Analysis 10-24  More optimization (revenue/profit) and IVT
Begin Second Derivatives- acceleration
Week 10 :  10-27 Concavity and
Curves
 
 10-28 More on Concavity
 10 -30 Horizontal Asymptotes.
Vertical Asymptotes

 10-31 Linear Estimation and "Differentials."
Relative error.

Week 11
Summary of Weeks 
9 & 10 Due 11-7
 11-3  Differentials
Elasticity. 

 
 11-4 Begin Differential equations and integration IV.A
 11-6 More on DE's and integration.
 11-7 Acceleration and integration.
Estimating cost changes from marginal costs.   Introduction to the definite Integral. More DE's.
Week 12 Self Scheduled  
Exam #2 11-12
11-10 Finding area by estimates and using anti-derivatives 
The definite integral. 

11-11 Riemann Sums  and Estimating Area .
  The definite integral and The FTofC. Finding Area exactly!
 IV.E?		 11-13 More Area and applications: 
FT of calculus I .
11-14 Substitution! (Guest Lecture) 
week 13 Summary of Weeks 11&12 11-17 Substitution in definite integrals Interpreting definite integrals. Geometric Area.

 11-18 More on area and substitution.
Consumer& Producer Surplus; Social Gain.
 11-20  Average Value. Intro to functions of  2 or more. Partial derivatives. 1st order.
11-21 Visualizing Functions of 2 variables: level curves, graphs of z=f(x,y)
Review of Exam #2?
Week 14 Fall Break 11-24 No Class 11-25 No Class 11-27 No Class 11-28No Class
Week 15  12-1 More on partial derivatives and linear estimation. Visualizing functions of 2 variables.

 12-2 2nd order partial derivatives 
Extremes (Critical points)
12-4 DE's -Separation of variables: Growth models and exponential functions.

12-5 Improper integrals I
 
. 
Week 16 
Summary of Weeks 13 & 15
Due 12-9
 12-8 Improper integrals II
Least Squares example
12-9 Begin  Future and present value.
Probability and 
DARTS?		 12-11 Future and present value. Applications of linear regression to other models using logarithms  12-12 ????
Week 17 Final Examination
Review Session  Sunday 3-5pm Lib 56
 12-15 12-16 12-18 12-19
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