Martin Flashman's Courses
Math 106 Calculus for Business and Economics
Fall, '04
CHECKLIST FOR REVIEWING FOR THE FINAL
Current Assignment and Schedule
Fall, 2004      Tentative Assignments    M.FLASHMAN 
On-line Sensible Calculus is indicated by SC.
Due Date Reading for 3rd Edition   Problems CD Viewing [# minutes] Optional
HW #1   8-26
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]

HW #2      8-27 1.1 Functions and tables. 
A.5  pp 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]
HW # [NONE]
8-30
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 The Blackboard Practice Quiz on Functions
HW #3
8-31

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)

HW #4
9-2
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
HW #5
9-3
1.4 Linear Models. 1.4:  12, 19, 21,22,25
On-line Mapping Figure Activities-  (Again... ;)
HW #6
9- 9
2.1 Quadratic functions 
A.5 ppA23-A25
2.1: 1-9 odd, 25, 27, 33 Parabolas [22]
HW #7
9-10
3.1 Average Rate of Change 3.1: 1-10, 13-16, 21, 39, 40 Rates of Change, Secants and Tangents [19]
HW #8
9-13
3.2 Pages 154-158
The Derivative: A Numerical and Graphical  Viewpoint
3.2: 1, 2, 5, 9,12


HW #9
9-14
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]
Finding Instantaneous Velocity [20]
HW #10
9-16
3.2 derivative estimates 
3.3 The Derivative: An Algebraic Viewpoint
3.2: 33, 47, 49, 57, 58, 71, 83
3.3: 6,13 ,15,17, 23, 25
The Derivative [12]
HW #11
9-17
3.2 Derivative function graphs, interpretation
3.3 The Derivative: An Algebraic Viewpoint
3.2 :39, 41, 42, 59-64, 97,98, 109, 110
Blackboard Practice Quiz on Slopes of Tangent Lines using 4 steps.
Slope of a Tangent Line [12]
Equation of a Tangent Line [18]
3.2: 73,74, 86
HW #12
9-20
3.4 The Derivative:  Simple Rules 3.4:1-11 odd; 14-17; 19-21 Short Cut for Finding Derivatives [14]
HW #13
9-21
3.4 (Again) 
Chapter 3 Summary as relevant.
3.4: 29, 37, 41, 42, 53, 55, 63, 64
3.4: 61, 65, 67, 71, 79
Uses of The Power Rule [20]  *The Derivative of  the Square Root [16]
*The Derivative of the Reciprocal Function [18]

3.2: 65
HW #14
9-23
3.5 Marginal analysis 
Chapter 3 Summary as relevant.

3.5: 1,5,6,9,11,13
 


HW #15
9-24
Summary of Weeks 3&4. Due Friday 9-24
4.1
Product Rule only! pp 241-244
3.5: 19, 21,28
4.1: 13, 15, 16, 21, 22
The Product Rule [21] Instantaneous Rate [15]
HW #16
9-27
4.1: Quotient Rule 4.1: 35, 37, 38, 43; 53, 59, 62 The Quotient Rule [13]
HW #17
9-28
4.2 The Chain Rule
4.1: 63, 64, 71, 73
4.2 : 13- 17, 55
Introduction to The Chain Rule [18]
Differentiability [3] 
HW #18
9-30
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
Using the Chain Rule [13]
Finding the derivative implicitly [12]
Intro to Implicit Differentiation [15]
More on Instantaneous Rate [19]
HW #19
10-1
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)

The Ladder Problem [14] 4.4: 53
Using Implicit Differentiation [23]

HW #20
10-4
The third Summary is due by 4:00 pm.
A.2: Exponents
5.4 Related Rates
A.2: 15,19, 23, 39, 41, 71
5.4 17,  21, 25

The Baseball Problem [19]
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
Morale Moment Math Anxiety [6]





#21
10-5
Midterm Exam #1 covers  HW #1-#20.
2.2: Exponential Functions
2.2 : 3,4,9,11, 7, 13, 17 Exponential Functions [10]
#22
10-8
2.2 pp94-104(middle)

2.2: 45, 47, 51, 63, 73, 59, 61 Logarithmic Functions [19] (Preparation for Friday class)

#23
10-11
exp'(x) = exp(x) Notes.
4.3: 7,8,45,51,53,85 Derivatives of Exp'l Functions [23] Sensible Calculus I.F.2
#24 (note changed due to error-10-12)
10-13!
2.3: pp. 110-113 [Logarithmic functions]
4.3: Example 1,3; pp 265-267.
Derivatives for Log's & Exponential Functions

2.3: 1-4, 19
4.3:1,2,15,17,19

Derivative of log functions [14]

#25
10-14
2.3:pp112-116 Logarithmic functions
Log's Properties (on line).
4.3  Examples 1-5.
2.3: 5, 7, 20, 21, 25,31, 45a, 48 a
4.3: 23,
27, 29, 33, 73


#26
10-15
2.3  Example 3
2.3: 9, 11, 15


#27
10-18
4.4 log differentiation Ex. 3 4.4: 31 , 32
Slide Rules!
UNDERSTAND HOW + WHY a slide works, a full explanation
#28
10-19(20)
The Fourth Summary is due by 4:00 pm.

10-19!
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
One Sided Limits [6]
Continuity and discontinuity [4]
Three  Big Theorems [Begin-3.5min]
#29
10-21

3.8
pp225- 230 middle: limits and continuity (alg)
3.7: 20,27, 28
3.8: 39, 41, 46, 53


continuity and differentiablity on-line materials( A and B)
#30
10-22 and 25!
On-line: cont and diff.
5.1:  Maxima and Minima
5.1: 1-7 odd, 8-10, 12, 13, 15, 21, 23, 24, 25 The connection between Slope and Optimization [28]
Critical Points [18]
The Fence Problem[25]
#31
10-26

5.1:  Maxima and Minima
The Intermediate Value Theorem
5.1: 35,  39, 41, 44 Intro to Curve Sketching [9]
#32
10-28
5.2. Applications of Maxima and Minima 5.2: 5, 11, 13 Regions where a function is increasing...[20]
The First Derivative Test [3]
The Box Problem [20]
#33
10-29
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!]
Acceleration & the Derivative [6]

#34
11-1
5.5 Elasticity and other economic applications of the derivative
5.5: 1, 3, 14

#35
11-2
5.2 and 5.3 again! 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]
#36
11-4
3.6: p212-216
3.8: p229
5.3: p321-324
5.2: 33, 35, 41, 45
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 Asy..and criti' pts [17]
#37
11-5
3.6,3.8  Review!
6.1 The Indefinite Integral  p 353-358
On-line tutorial for 6.1.
On-Line: Linear Estimation
3.8: 15,17,21,23,33,35,37
5.3: 39, 43, 45
3.6: 25, 27,29

6.1: 1-13odd
Graphing ...asymptotes [10]
Functions with Asy.. and holes[ 4]
Antidifferentiation[14]
On-line Problems on Linear Estimation  
L1-6; A1-5; App1-3
#38
11-7
Differential equations and integration SC IV.A
6.1 Applications p 359-361
6.1: 15,17, 27, 35, 41-44,51 Using tangent line approximations [25]
Antiderivatives of powers of x [18]
Cusp points &... [14]
Antiderivatives and Motion [20]
SC.III.AThe Differential
End of material covered in Exam #2
Midterm Exam #2 covers Assignments 21 - 38
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)


Sample Exam II see Blackboard
#39
11-8
3.7, 5.3 Review p321-323 3.7: 15,17, 28-30
5.3: 47, 51, 63, 71
6.1: 53-55, 57

 SC IV.E
#40
11-12

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
#41
11-15
6.4 The Definite Integral: Area p384-386
6.4: 1-5 odd, 21, 23
Areas, Riemann Sums, and Definite Integrals [14]
The Fundamental theorem[17] 

#42
11-16
6.5 pp392-395   
The Fundamental Theorem
6.5 : 17-20; 67,68
Illustrating the FT[14]
Evaluating Definite Integrals [13]

#43
11-18

6.2 Substitution pp364-367
6.4  pp 384- 388
6.2: 1-6; 21,23
6.5: 63
Undoing the chain rule.[9]  
Integrating polynomials by Substitution [15]

#44
11-19/29
6.5 pp 395  - 396
6.2 pp 368-371 Substitution
6.5 example 5
7.2 pp416-420 (area between curves)
6.5: 27-30, 61
6.2: 27-33,59, 60

6.5: 45,47,59,63,64
7.2:1,3,5,11, 15
Area between two curves [9] Integrating composite exponential and rational functions by substitution [13]
#45
11-29
7.2 p420-426 (Surplus and social gain)
7.2: 25, 37, 49
Limits of integration-Area [15]

#46
11-30
7.3  pp 430-431
8.1 Functions of Several Variables. p467-471
8.3 pp 490 - 492
7.3: 1- 5odd, 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]
#47
12-2/3
8.2
8.2: 1-9 odd; 11-18; 19-25 odd;41, 49

Solution to 7.2:42 (See the student solutions manual).
#48
12-6/7
8.4 p498-501 Critical points
7.5 p 442-445 +
8.4: 1-9 odd, 33, 37
7.5: 1-7
The first type of improper integral[10]
Infinite Limits of integration ... [12]
The second type of ... [8]

#49
12-7
 8.3 Second order partials

8.3: 19-25 odd; 29,33,38,51, 53


The 20 minute review.
#50
7.5
8.4 pp 504-505


7.5: 11, 13, 17
8.4 :13, 15,17,19
The 20 minute review.

Reading
INVENTORY
Problems
INVENTORY
CD Viewing
INVENTORY
Optional
INVENTORY






7.6 7.6: 1,3,13

#54


 

#55
7.4
Future and present value.

Common Mistakes [16]
The 20 minute review.

Optional Last assignment
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

2.3 2.3:1,3,4,5,7,11,13,31



Final Examination: 



Math 106 CHECKLIST FOR REVIEWING FOR THE FINAL     M. Flashman                    * indicates a "core" topic.
         I.  Differential Calculus:

           A. *Definition of the Derivative
                Limits / Notation
                Use to find the derivative
                Interpretation ( slope/ velocity/ Marginal  cost-revenue-profit )

           B. The Calculus of Derivatives
               * Sums, constants, x n, polynomials
                *Product, Quotient, and  Chain rules 
                *logarithmic and exponential functions
                              *basic information about these functions and their use in applications
                              such as compund interest

                Implicit differentiation
                Higher order derivatives

           C. Applications of derivatives
                 *Tangent lines
                 *Velocity, acceleration, marginal rates (related rates) 
                 *Max/min problems
                 *Graphing: * increasing/ decreasing 
                           concavity / inflection
                           *Extrema  (local/ global) 
                 Asymptotes
                Linear approximation 

         

      D. Theory
                *Continuity  (definition and implications)
                *Extreme Value Theorem 
                *Intermediate Value Theorem
      E. Several Variable Functions
                  Partial derivatives. (first and second order)
                  Max/Min's and critical points.

II. Differential Equations and Integral Calculus:

           A. Indefinite Integrals (Antiderivatives)
                *Definitions and basic theorem about constants.
                *Simple properties [ sums, constants, polynomials]
                *Substitution
        *Simple differential equations with applications

             B. The Definite Integral
                 Definition/ Estimates/ Simple Properties / Substitution
                *Interpretations  (area / change in position/ Net cost-revenues-profit)
                *THE FUNDAMENTAL THEOREM OF CALCULUS -
                                                 evaluation form
                Infinite integrals 

           C. Applications
                *Recognizing sums as the definite integral 
        *Areas (between curves). 
               Average value of a function. 
               Consumer Savings.     


 
Tentative Schedule of Topics  (Subject to  some major changes) 9-24-04 
 
Monday
Tuesday
 Thursday Friday
Week 1 8-22 Course Introduction  Numbers, Variables, Algebra Review 

Begin Functions.
More Algebra review. 
More functions review
The coordinate plane. 
Functions, graphs.
Week 2 8-29 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. 
 9-6 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)
9-13 More on finding the derivative.
More: Finding the derivative as function.
Begin: The Derivative Calculus I
Graphical Derivative as function graphs
Justification of the power rule.

Week 5 Summary of Weeks 3&4. Due Friday 3 pm.
9-20 Justify the sum rule.
Discuss Sum rule interpretations.

Marginal Applications.
Constant Multiple Rule Interpretations. 

 
Applications: Marginal vs. Average Cost
Start Product rule.
Justify product rule.
Start Quotient Rule.

Week 6  9-27 More on the Quotient rule.
The Chain Rule
More Chain Rule
Implicit functions.
Implicit Differentiation
More Implicit Functions and related rates.
More Implicit Functions and related rates.
Week 7
Summary of Week 5&6  Due.
Midterm Exam #1 Self-Scheduled
Wednesday 10-6
8:00- 12:30 NHE Room 102
5:00 - 8:30pm Lib 56

10-4 Examples: f  does not have a derivative at a.
Begin Exponential functions
Interest and value

 
Review for Exam #1
More on exponentials.
Derivatives of exponentials, esp'ly exp'(x)=exp(x).
Week 8 Makeup For Exam #1
Wed. 10-13.
 8 or 9 a.m. Lib 56
See BB Announcements.
10-11 Start Logarithmic functions.
Derivatives of Logarithms and Exponentials
 
Finish derivatives of log's, etc. Logarithmic functions.
More on models with exp and log equations.
Logarithmic differentiation
Logarithmic scales.
  Slide Rules!
Week 9
Summary of Weeks 7 and 8 
Due 4pm  Tuesday 10-19

10-18
limits and continuity,
Continuity

More on continuity and limits.
IVT
Begin Optimization  and  First Derivative Analysis
The fence problem.

More Optimization and Graphing.  
Week 10 10-25 Optimization  and IVT
First Derivative Analysis
More on first derivative
Optimization: revenue example
Begin Second Derivatives- acceleration
Concavity and
Curves


Elasticity. (Guest Lecture)


Week 11
Summary of Weeks 
9 & 10 Due Friday Nov. 5
11-1More on Concavity
Horizontal Asymptotes.
Vertical Asymptotes

Linear Estimation and "Differentials."
Begin Differential equations and integration IV.A.
Acceleration and integration.
Estimating cost changes from marginal costs.  More DE's.
Relative error.
Differentials
Week 12 Self Scheduled  
Exam #2 Wednesday
11-10

11-8 Costs, marginal costs, and estimation. Introduction to the definite Integral. Euler's Method.
Differential Notation(started)

The Definite Integral

Riemann Sums  and Estimating Area . Finding area by estimates and using anti-derivatives.
week 13 Lab ? Summary of Weeks 11&12

11-15 The definite integral and The FTofC.
 IV.E

Start Substitution!
More Area and applications:  Interpreting definite integrals. Geometric Area.


Substitution in definite integrals
More Area
Intro to functions of  2 or more. Partial derivatives. 1st order.

Consumer& Producer Surplus; Social Gain.

Week 14
Fall Break- No Classes
11-22 Fall Break



 Week 15 11-29 Fundamental Theorem I
Average Value.

Functions of many variables.
Tables for 2 variables.
Partial derivatives.
Visualizing Functions of 2 variables: level curves, graphs of z=f(x,y)and linear estimation.
 Improper integrals I
 
Week 16
Summary of Weeks 13 & 15
Due Tuesday 4 pm.
12- 6 2nd order partial derivatives 
Extremes (Critical points)
Improper integrals I
 
Improper Integrals I and II
Least Squares example
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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