Martin Flashman's Courses
Math 106 Calculus for Business and Economics
Fall, '06
Current Assignment and Schedule
Tentative Assignments Assignments are official when a due date is assigned.
*Early or Just in time:
When two due dates are given,
the first date is for preparation and/or starting problems,
the second date is for completion of problem work
.
On-line Sensible Calculus is indicated by SC.

*Early or Just in time:
When two due dates are given,
the first date is for preparation and/or starting problems,
the second date is for completion of problem work








































Due Date
Reading for 3rd Edition   Problems CD Viewing [# minutes] Optional
*8/21,23
HW #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]


*8/25,28
HW #2
1.1 Functions and tables. 
A.5  pp A.22-24  
Solving equations 
 
A.5 1-7 odd, 13-19 odd
Functions [19]

HW # 3
8/30
1.2 Graphs  
Sensible Calculus 0.B.2 Functions
Do the reading first!
1.1: 1-5, 7,9, 12, 15, 16, 22, 23, 25, 33
1.2: 1,2,4,5 [Draw a mapping-transformation figure for each function in this problem]
[Read SC 0.B.2  to find out more about the mapping-transformation figure.]
Functions [19]

HW # 4
9/1
1.3 Linear functions 
Summary: 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
Graphing Lines [28] Try The Blackboard Practice Quiz on Functions
On-line Mapping Figure Activities
(this may be slow downloading)

HW #5
9/6
[Changed!]

1.4 Linear Models
2.1 Quadratic functions 
1.3: 37- 49 odd, 55, 57, 59
1.4: 1-9 odd
2.1: 1-9 odd, 25, 27, 33
Average Rates of Change [11]
Parabolas [22]
1.4: 49
HW #6
*9/8 ,11 [Changed!]

1.4 Linear Models.
A.5 ppA23-A25

3.1 Average Rate of Change
3.2 Pages 154-158
The Derivative: A Numerical and Graphical  Viewpoint
1.4:  12, 19, 21,22,25
3.1: 1-10, 13-16, 21, 39, 40
3.2: 1, 2, 5, 9,12
3.1.1 Rates of Change, Secants, and Tangents (Disc 1, 18:53) On-line Mapping Figure Activities-  (Again... ;)
The Two Questions of Calculus [10]

HW #7
*9/11,13
3.2 derivative estimates 
3.3 The Derivative: An Algebraic Viewpoint
3.2: 13, 16, 17, 19, 20; 23, 24 
Use  "4-step process" from class 3.3: 1, 2, 5 [Ignore the problem instruction!]
3.1.2 Finding Instantaneous Velocity (Disc 1, 19:57)

HW #8
9/13
3.2 (graphical)
3.3 The Derivative: An Algebraic Viewpoint
3.2: 33, 47, 49, 57, 58, 71, 83
3.3: 6,13 ,15,17, 23, 25 [
Use  "4-step process"]
3.1.3 The Derivative (Disc 1, 11:14)
Blackboard Practice Quiz on Slopes of Tangent Lines using 4 steps.
9/15
To replace class
Watch the videos listed- DO THIS with a partner if possible!
3.4 The Derivative:  Simple Rules
3.3 Some Special Derivatives
        3.3.1 The Derivative of the Reciprocal Function (Disc 1, 17:56)
        3.3.2 The Derivative of the Square Root Function (Disc 1, 15:19)
4.1 The Power Rule
        4.1.1 A Shortcut for Finding Derivatives (Disc 1, 14:03)
        4.1.2 A Quick Proof of the Power Rule (Disc 1, 9:48)
        4.1.3 Uses of the Power Rule (Disc 1, 19:43)



HW #9
9/18, 20
[changed!]
3.2 Derivative function graphs, interpretation
3.3 The Derivative: An Algebraic Viewpoint
3.2 :39, 41, 42, 59-64, 97,98, 109, 110
3.4:1-11 odd; 14-17; 19-21
.2.1 The Slope of a Tangent Line (Disc 1, 11:16)
3.2.3 The Equation of a Tangent Line (Disc 1, 17:53)
3.2: 73,74, 86

HW #10
9/20
[changed]
3.4 (Again) 
3.4 The Derivative:  Simple Rules
3.4: 61, 65, 67, 71, 79;
29, 37, 41, 42, 53, 55, 63, 64



9/22
Summary Weeks 3 and 4




HW #11
9/22
3.5 Marginal analysis 
Chapter 3 Summary as relevant.

4.1
Product Rule only!
pp 241-244
3.5: 1,5,6,9,11,13
3.5: 19, 21,28
4.1: 13, 15, 16, 21, 22
  4.2.1 The Product Rule (Disc 1, 20:43)
 3.2.2 Instantaneous Rate (Disc 1, 14:38)
3.2: 65

HW #12
9/25
4.1: Quotient Rule 4.1: 35, 37, 38, 43; 53, 59, 62 4.2.2 The Quotient Rule (Disc 1, 13:10)

HW #13
9/27
4.2 The Chain Rule 4.1: 63, 64, 71, 73
4.2 : 13- 17, 55
 4.3.1 An Introduction to the Chain Rule (Disc 1, 17:51)
       


HW #14
*9/29,10/2
4.2 The Chain Rule
4.4 Implicit Differentiation
(Skip Examples 2 and 3!)
4.2: 25, 26, 33, 35
4.4 :11, 12, 15, 35, 36, 47
4.3.2 Using the Chain Rule (Disc 1, 12:53)
6.1.2 Finding the Derivative Implicitly (Disc 2, 12:14)
6.1.1 An Introduction to Implicit Differentiation (Disc 2, 14:43)

HW #15
*10/2, 10/4
5.4 Related Rates Especially  Ex. 1-3 4.2: 47, 51, 53, 61, 62, 65
5.4: 9, 11, 13 (watch Ed for #11)
7.3.2 The Ladder Problem (Disc 2, 14:18) More on Instantaneous Rate [19]
4.4: 53
6.2.1 Using Implicit Differentiation (Disc 2, 22:24)

HW #16
10/4
A.2: Exponents
A.2: 15,19, 23, 39, 41, 71
7.3.3 The Baseball Problem (Disc 2, 18:21)  3.1.4 Differentiability (Disc 1, 2:35)
7.3.5 Math Anxiety (Disc 2, 5:30)

HW #17
*10/6,10/9
5.4 Related Rates
2.2: Exponential Functions
5.4 17,  21, 25
2.2 : 3,4,9,11, 7, 13, 17
5.2.1 Graphing Exponential Functions (Disc 1, 10:08)

HW #18
10/11
2 5.2.2 Derivatives of Exponential Functions (Disc 1, 23:17).2 pp94-104(middle)
exp'(x) = exp(x) Notes.
2.2: 45, 47, 51, 63, 73, 59, 61
4.3: 7,8,45,51,53,85
5.2.2 Derivatives of Exponential Functions (Disc 1, 23:17)     Sample Exam #1
Chapter 3 review: 2,3,4,5,9 
Chapter 4 review: 1(a-d), 2(a,b), 4(a,b)
Chapter 5 review: 7

Thursday
Oct. 12th

EXAMINATION  # 1 will cover material from Assignments till HW #15 and related sections of the text.


HW #19
*10/16, 18
2.3: pp. 110-116 [Logarithmic functions]
Log's Properties (on line).

4.3: Examples 1-5; pp 265-267.
Derivatives for Log's & Exponential Functions
2.3: 1-4, 19
4.3:1,2,15,17,19

2.3: 5, 7, 20, 21, 25,31, 45a, 48 a

4.3: 23, 27, 29, 33, 73
5.3.1 Evaluating Logarithmic Functions (Disc 2, 18:37)
5.3.2 The Derivative of the Natural Log Function (Disc 2, 13:24)
Sensible Calculus I.F.2

HW #20
*10/18,20
2.3  Example 3
4.4 log differentiation Ex. 3
2.3: 9, 11, 15
4.4: 31 , 32

Slide Rules!
UNDERSTAND HOW + WHY a slide works, a full explanation

HW #21
10/20
3.6: limits (numerical/graphical) 
P209-216 omit EX.3.
3.7: limits and continuity
3.8 limits and continuity (alg) pp225- 228
3.6: 19, 21(a,b), 23(a-e), 25(a-e), 26(a-e)
3.7: 13,14, 15
2.1.5 One-Sided Limits (Disc 1, 5:18)
2.1.6 Continuity and Discontinuity (Disc 1, 3:39)


HW #22
*10/23,25
The Intermediate Value Theorem
3.8 pp225- 230 middle: limits and continuity (alg)
 On-line: cont and diff.
5.1:  Maxima and Minima
3.7: 20,27, 28
3.8: 39, 41, 46, 53

7.4.1 The Connection Between Slope and Optimization (Disc 2, 27:18)
8.2.1 Critical Points (Disc 2, 17:43)
8.1.2 Three Big Theorems (Disc 2, [Begin-3.5min])
continuity and differentiablity on-line materials( A and B)

HW #23
*10/25, 27, 30!
5.1:  Maxima and Minima
5.2. Applications of Maxima and Minima
5.1: 1-7 odd, 8-10, 12, 13, 15, 21, 23, 24, 25
5.1: 35,  39, 41, 44
5.2: 5, 11, 13
7.4.2 The Fence Problem (Disc 2, 25:03)

 8.1.1 An Introduction to Curve Sketching (Disc 2, 8:44)



HW #24
10/27
5.2. Applications of Maxima and Minima
5.2:15, 21
7.4.3 The Box Problem (Disc 2, 20:38)
7.4.4 The Can Problem (Disc 2, 20:47)


HW #25
10/30
5.1:  Maxima and Minima
5.3 2nd deriv.pp317-320
Be sure to do Assignment #23
5.2: 25,  27, 29
5.3: 1-5,7,9,11,14
 7.1.1 Acceleration and the Derivative (Disc 2, 5:44)
8.2.3 The First Derivative Test (Disc 2, 2:46)  8.2.2 Regions Where a Function Increases or Decreases (Disc 2, 20:17)


HW #26
11/1
5.2 and 5.3 again! 5.3 : 17-20, 23; 25, 29,31
5.2: 33, 35, 41, 45
8.3.1 Concavity and Inflection Points (Disc 2, 13:12)
 8.3.2 Using the Second Derivative to Examine Concavity (Disc 2, 17:01)
7.2.1 Higher-Order Derivatives and Linear Approximation (Disc 2, 20:57)[first 5 minutes only!]
HW #27
*11/3, 11/6
3.6: p212-216
3.8: p229
5.3: p321-324
5.3: 35- 37,41, 63, 67
3.6: 1-11 odd
Graphs of Poly's [10]
The 2nd Deriv. test [4]
Vertical asymptotes [9] 
Horizontal asymptotes  [18]
Functions with Asymptotes and criti' pts [17]
HW #28
11/6
3.6,3.8  Review! 3.8: 15,17,21,23,33,35,37
3.6: 25, 27,29

5.3: 39, 43, 45
8.5.3 Graphing Functions with Asymptotes (Disc 2, 10:15)
8.5.4 Functions with Asymptotes and Holes (Disc 2, 3:28)


HW #29
11/8
6.1 The Indefinite Integral  p 353-358
Differential equations and integration SC IV.A

On-line tutorial for 6.1. On-Line: Linear Estimation
6.1: 1-13odd 7.2.2 Using the Tangent Line Approximation Formula (Disc 2, 24:22)
9.1.2 Antiderivatives of Powers of x (Disc 2, 17:56)
9.1.1 Antidifferentiation (Disc 2, 13:59)
On-line Problems on Linear Estimation  
L1-6; A1-5; App1-3

HW #30
11/13
6.1 Applications p 359-361 6.1: 15,17, 27, 35, 41-44,51



EXAMINATION  # 2 will cover material from Assignments HW #16 to HW #30 and related sections of the text.
For Sample Exams II see Blackboard
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)

HW #31
11/17
IV.E
6.2 Substitution pp364-367
6.3. The Definite Integral As a Sum.
p 373-376, 380
6.2: 1-6; 21,23
6.3: 1-5 odd, 15, 19, 21
9.4.1 Approximating Areas of Plane Regions (Disc 3, 9:39)
10.1.1 Antiderivatives and Motion (Disc 3, 19:51)
SC.III.AThe Differential
HW #32
Over  Break!
11/27
6.4 The Definite Integral: Area p384-386
6.5 pp392-395   
The Fundamental Theorem
6.4: 1-5 odd, 21
6.5 : 17-20; 67,68
9.2.1 Undoing the Chain Rule (Disc 3, 8:30)
9.4.2 Areas, Riemann Sums, and Definite Integrals (Disc 3, 13:40)
9.4.3 The Fundamental Theorem of Calculus, Part II (Disc 3, 16:28)
9.4.4 Illustrating the Fundamental Theorem of Calculus (Disc 3, 13:55)
9.4.5 Evaluating Definite Integrals (Disc 3, 12:53)
SC IV.E
9.2.2 Integrating Polynomials by Substitution (Disc 3, 15:24)

HW #33
*11/29, 12/1
6.5 pp 395  - 396
8.1 Functions of Several Variables. p467-471

5.5
Elasticity
and other economic
applications of the derivative
6.5: 27-30, 61,63
8.1: 1-9 odd, 19, 20, 21, 29, 39, 43

9.3.2 Integrating Composite Exponential and Rational Functions by Substitution (Disc 3, 13:30)
HW #34
*12/1,12/4
6.4  pp 384- 388
6.2 pp 368-371 Substitution
6.5 example 5
8.3 pp 490 - 492
6.2: 27-33,59, 60
6.5: 45,47,59,63,64
8.3:  1- 7 odd, 13, 41, 45
10.2.1 The Area between Two Curves (Disc 3, 9:04)

HW #35
12/6?
7.2 pp416-420 (area between curves)
7.2 p420-426 (Surplus and social gain)
7.3  pp 430-431
7.5 p 442-445 +
8.2
8.4 p498-501 Critical points

7.2:1,3,5,11, 15
7.2: 25, 37, 49
7.3: 1- 5odd, 29, 35a
7.5: 1-7
10.2.2 Limits of Integration and Area (Disc 3, 15:16)
18.1.1 Finding the Average Value of a Function (Disc 4, 8:18)
17.1.1 The First Type of Improper Integral (Disc 4, 9:42)
17.1.3 Infinite Limits of Integration, Convergence, and Divergence (Disc 4, 11:50)














5.5: 1, 3, 14









3.7, 5.3 Review p321-323 3.7: 15,17, 28-30
5.3: 47, 51, 63, 71
6.1: 53-55, 57

Cusp points &... [14]








Graphing, Technology problems from lab




SC IV.E











 






























Solution to 7.2:42 (See the student solutions manual).

8.2
8.4 p498-501 Critical points
8.3 Second order partials
8.2: 1-9 odd; 11-18; 19-25 odd;41, 49
8.4: 1-9 odd, 33, 37
8.3: 19-25 odd; 29,33,38,51, 53

The 20 minute review.







Reading
INVENTORY

Problems
INVENTORY

CD Viewing
INVENTORY

Optional
INVENTORY










 







7.5
8.4 pp 504-505

7.5: 11, 13, 17
8.4 :13, 15,17,19
The second type of ... [8]
The 20 minute review.



7.6 7.6: 1,3,13





 



7.4
Future and present value.

Common Mistakes [16]
The 20 minute review.



Future and present value.
Probability and 
DARTS 


7.4:1, 9, 21, 27




3.6: 31




3.8: 11-25 odd; 39-42

6.5  396-398
6.4:22

 


6.5: 9,11,41-45 odd, 42, 65,81






7.3:25






7.6:25, 27




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


 
Tentative Schedule of Topics  (Subject to  some major changes) 10-1-06 
 
Monday  Wednesday Friday
Week 1 8-21 Course Introduction Numbers, Variables, Algebra Review

Begin Functions.
More Algebra review. 
More functions review
The coordinate plane. 
Functions, graphs.
Week 2 8-28 Functions, graphs and models.
Points and Lines.
Especially Lines and models.
 
More Functions and Models: Linear Functions.
Slopes, rates and estimation. More linear models.

Quadratic functions.

Summary of Weeks 1&2
Due Friday 3 pm. 
 9-4 NO Class.... LABOR DAY
More Quadratics.Extremes and the tangent problem.
Average rates, and slopes of secant and tangent lines.
Instantaneous Rates.
The Derivative
More Motivation: Marginal cost, rates and slopes. The Derivative and algebra.
Week 4 (Graphing, Technology)
9-11 More on finding the derivative.
More: Finding the derivative as function.
Begin: The Derivative Calculus
Graphical Derivative as function graphs
Class Meeting  Cancelled
Watch Assigned Viewing from  Thinkwell CD.
Justification of the power rule.

Week 5 Summary of Weeks 3&4. Due Friday 3 pm.
9-18 Justify the sum rule.
Discuss Sum rule interpretations.
Constant Multiple Rule Interpretations.
 Marginal Applications.
Applications: Marginal vs. Average Cost
Start Product rule.
Justify product rule.
Start Quotient Rule.

Week 6
9-25 More on the Quotient rule.
The Chain Rule
More Chain Rule
Implicit functions.
Implicit Differentiation
More Implicit Functions and related rates.
Week 7
Summary of Week 5&6  Due Friday 3 pm.



10-2 Examples: f  does not have a derivative at a.
Begin Exponential functions
Interest and value

More on exponentials.
Derivatives of exponentials, esp'ly exp'(x)=exp(x).
Week 8 Midterm Exam #1 Self-Scheduled Thursday 10-12 10-9 Finish derivatives of esp's, etc. Logarithmic functions. Start Logarithmic functions.

 
Review for Exam #1
Derivatives of Logarithms and Exponentials

Logarithmic differentiation
More on models with exp and log equations.
Week 9
Summary of Weeks 7 and 8 
Due 4pm  Friday

10-16
Logarithmic scales.
Slide Rules!?

limits and continuity,
Continuity

More on continuity and limits.
IVT

Week 10 10-23 Begin Optimization  and  First Derivative Analysis
The fence problem.
More Optimization and Graphing.
Optimization  and IVT



First Derivative Analysis
Optimization: revenue example
Begin Second Derivatives- acceleration
Concavity and
Curves



Week 11
Summary of Weeks 
9 & 10 Due Friday
10-30
More on Concavity


Horizontal Asymptotes.
.
Vertical Asymptotes

Week 12
11-6 Linear Estimation and "Differentials."
Begin Differential equations and integration IV.A
Estimating cost changes from marginal costs.
Costs, marginal costs, and estimation. 
More DE's.
Acceleration and integration

11-10
No Class Veteran's Day Holiday.

week 13 Self Scheduled  
Exam #2 Tuesday 11-14

Lab ?

11-13 Relative error.
Differential Notation(started)
Introduction to the definite Integral.
Euler's Method.

IV.E
Start Substitution!
The Definite Integral
 

Riemann Sums  and Estimating Area .
Finding area by estimates and using anti-derivative
The definite integral and The FTofC.

 

Week 14
Fall Break- No Classes
11-20 Fall Break


 Week 15
Summary of Weeks 12-15
Due Friday
11-27 More Area and applications:  Interpreting definite integrals.
Fundamental Theorem I
Intro to functions of  2 or more.
 Functions of many variables.
Tables for 2 variables.

Geometric Area.
Average Value.

Partial derivatives. 1st order.

 Elasticity
Substitution in definite integrals
 linear estimation.
Consumer& Producer Surplus; Social Gain.
 
Week 16

12- 4 Visualizing Functions of 2 variables: level curves,
graphs of z=f(x,y)and 2nd order partial derivatives 
Extremes (Critical points)
Improper integrals I
Least Squares example
Improper Integrals I and II
Future and present value.
Applications of linear regression to other models using logarithms
DE's -Separation of variables: Growth models and exponential functions.
Probability and 
DARTS?
????
Week 17 Final Examination
Review Session  Sunday **pm Lib 56
Self Schedule for Final Examinations

    


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