Martin Flashman's Courses
Math 106 Calculus for Business and Economics
Spring, '04 
Current Assignment and Schedule
CHECKLIST FOR REVIEWING FOR THE FINAL

Spring, 2004      Tentative Assignments    M.FLASHMAN 
On-line Sensible Calculus is indicated by SC.
Due Date Reading for 3rd Edition   Problems CD Viewing [# minutes] Optional
1-22
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]

1-23
HW #2
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]
1-26
HW # [NONE]

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
1-27
HW #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)
1-29
HW #4
1.4 Linear Models 1.3: 37- 49 odd, 55, 57, 59 
1.4: 1-9 odd

1.4: 49
1-30
HW #5
1.4 Linear Models. 1.4:  12, 19, 21,22,25 Average Rates of Change [11]  On-line Mapping Figure Activities
(this may be slow downloading)
2-2
HW #6
2.1 Quadratic functions 
A.5 ppA23-A25
2.1: 1-9 odd, 25, 27, 33
Parabolas [22]
2-3
HW #7
3.1 Average Rate of Change 3.1: 1-10, 13-16, 21, 39, 40 Rates of Change, Secants and Tangents [19]
2-5
HW #8
3.2 The Derivative: A Numerical and Graphical  Viewpoint 3.2: 1, 2, 5, 9,12 

2-6
HW #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]
Finding Instantaneous Velocity [20]
2-9
HW #10
3.2 derivative estimates 
3.3 The Derivative: An Algebraic Viewpoint
3.2: 33, 39, 41, 42, 47, 49, 57, 58, 71, 83  The Derivative [12]
2-10
HW #11

3.2 Derivative function graphs, interpretation
3.3 The Derivative: An Algebraic Viewpoint
3.2 59-64, 97,98, 109, 110
3.3: 6,13 ,15,17, 23, 25, 39
Slope of a Tangent Line [12]
Equation of a Tangent Line [18]
3.2: 73,74, 86
2-12
HW #12
3.4 The Derivative:  Simple Rules 3.4:1-11 odd; 14-17; 19-21
Blackboard Practice Quiz on Slopes of Tangent Lines using 4 steps.
Instantaneous Rate [15] 3.2: 65
2-13
HW #13
3.4 (Again) 
Chapter 3 Summary as relevant.
3.4: 29, 37, 41, 42, 53, 55, 63, 64 Short Cut for Finding Derivatives [14]
2-16
HW #14
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]
2-17
HW #15
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]

2-19
HW #16
4.1: Quotient Rule 4.1: 35, 37, 38, 43; 53, 59, 62 The Quotient Rule [13] Summary of Weeks 3&4. Due Friday 2-20
2-20
HW #17
 4.1 4.1: 63, 64, 71, 73 More on Instantaneous Rate [19]
Differentiability [3] 
2-23
#18
4.2 The Chain Rule 4.2 : 13- 17, 55 Introduction to The Chain Rule [18]
2-24
#19
4.2 The Chain Rule 4.2: 25, 26, 33, 35; 47, 51, 53, 61, 62, 65 Using the Chain Rule [13]
2-26
#20
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]
2-27
#21
5.4 Related Rates Especially  Ex. 1-3
A.2: Exponents
5.4: 9, 11, 13
A.2: 15,19, 23, 39, 41, 71
The Ladder Problem [14] 4.4: 53
Using Implicit Differentiation [23]
3-1
#22
2.2: Exponential Functions 
5.4 17,  21, 25
2.2 : 3,4,9,11

2.2:  7, 13, 17, 59, 61
Exponential Functions [10]
The third Summary is due by 4:00 pm.

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


Midterm Exam #1 covers  HW #1-#21.


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
3-2
#23
2.2: Exponential Functions
2.2: 45, 47, 51, 63, 73

3-4
#24
2.3: Logarithmic functions 2.3: 1-4, 19 Logarithmic Functions [19]
3-5
#25
2.3: Logarithmic functions 2.3: 5, 7, 20, 21, 25,31, 45a, 48 a

3-9
#26
2.3 Log's Properties on line.
4.3: Derivatives for Log's & Exponential Functions
4.3:7,8,45,51,53,85 Derivatives of Exp'l Functions [23]
3-11
#27
4.3: Derivatives for Log's & Exponential Functions 4.3:1,2,15,17,19, 23; 27, 29, 33, 73 Derivative of log functions [14] Sensible Calculus I.F.2
exp'(x) = exp(x) Notes.
3-12
#28
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
3-22,23
#29

3.6: limits (numerical/graphical) 
P209-216 omit EX.3.

3.7: limits and continuity
3.8 limits and continuity (alg) pp225- 228
On-line: cont and diff.
The Intermediate Value Theorem

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]
3-23,25
#30
3.8 pp225- 230 middle: limits and continuity (alg)
5.1:  Maxima and Minima
3.7: 20,27, 28
3.8: 39, 41, 46, 53
5.1: 1-7 odd, 8-10,12
The connection between Slope and Optimization [28] continuity and differentiablity on-line materials( A and B)
3-25
#31
5.1:  Maxima and Minima 5.1: 13,15,21,23,24,25 Critical Points [18]
3-26
#32
 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]
3-29
#33
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]
3-30
#34
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]
4-1
#35
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]
4-2
#36
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]
4-6
#37
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
4-8
#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 Antidifferentiation[14]
4-9
#39
6.1 Applications p 359-361

6.1: 41-44,51 Antiderivatives of powers of x [18] Antiderivatives and Motion [20]
4-9
#40
5.5 Elasticity and other economic applications of the derivative 5.5: 1, 3

4-12
#41
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
4-12
End of material covered in Exam #2
Midterm Exam #2 covers Assignments 22 - 41
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)


4-13
#42
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
4-15
#43
6.4 The Definite Integral: Area p384-386 6.4: 1-5 odd, 21, 23 Areas, Riemann Sums, and Definite Integrals [14]
4-16
#44
6.5 pp392-395   
The Fundamental Theorem
6.5 : 17-20; 67,68 The Fundamental theorem[17]  
Illustrating the FT[14]

4-19
#45
6.5 pp 395  - 396
6.2 Substitution pp364-367
6.2: 1-6; 21,23
6.5: 27-30, 61, 63
Undoing the chain rule.[9]  
Integrating polynomials by Substitution [15]

4-20(22)
#46
6.2 pp 368-371 Substitution
6.5 example 5
7.2 pp416-420 (area between curves)
6.2: 27-33,59, 60
6.5: 45,47,59,63,64
7.2:1,3,5,11, 15
Evaluating Definite Integrals [13]
Area between two curves [9]

4-22
#47
7.2 p420-426 (Surplus and social gain) 7.2: 25, 37, 49 Limits of integration-Area [15] Integrating composite exponential and rational functions by substitution [13]
4-23
#48
7.3  pp 430-431 7.3: 1-5 odd, 29, 35a Finding the Average Value of a Function [8]
4-26
#49
8.1 Functions of Several Variables. p467-471
8.3 pp 490 - 492
8.1: 1-9 odd, 19, 20, 21, 29, 39, 43
8.3:  1- 7 odd, 13, 41, 45


4-27
#50
8.2 8.2: 1-9 odd; 11-18; 19-25 odd;41, 49

4-29
#51
8.3 Second order partials
8.4 p498-501 Critical points
8.3: 19-25 odd; 29,33,38,51, 53
8.4: 1-9 odd, 33, 37


4-30
#52
7.6 7.6: 1,3,13


5-3
#53
7.5 p 442-445 7.5: 1-7 The first type of improper integral[10]
Infinite Limits of integration ... [12]

5-4
#54
7.5
8.4 pp 504-505
7.5: 11, 13, 17
8.4 :13, 15,17,19
The second type of ... [8]

5-6
#55
7.4
Future and present value.

Common Mistakes [16]
The 20 minute review.

Optional Last assignment
Future and present value.
Probability and 
DARTS 

The 20 minute review. 7.4:1, 9, 21, 27

Reading
INVENTORY

Problems
INVENTORY

CD Viewing
INVENTORY

Optional
INVENTORY





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 The 20 minute review.


Final Examination: 


Tentative Schedule of Topics  (Subject to  some major changes) 2-19-04 
 
Monday
Tuesday
 Thursday Friday
Week 1  1-19 No Class- MLK Day  1-20 Course Introduction 
1-22 Numbers, Variables, Algebra Review 
1-23 The coordinate plane. 
Points and Lines. 
Begin Functions.
More Algebra review. 
Week 2 1-26 Functions, graphs.
Especially Lines and models.
1-27 Functions, graphs and models. 1-29 More Functions and Models: Linear Functions.  1-30 Quadratic functions. 
Slopes, rates and estimation. More linear models.
Quadratics.
Week 3 
Summary of Weeks 1&2 Due Friday, 2-6.
2-2 Quadratics.
Begin Average rates, and slopes of secant and tangent lines.
2- 3 Average rates, and slopes of secant and tangent lines.
Instantaneous Rates & The Derivative.
2-5  More Motivation: Marginal cost, rates and slopes. the Derivative and algebra. 2-6 Graphing, Technology,
Meet in SH 119.
More on the Derivative. and
Week 4  2-9 More on finding the derivative.
Begin the Derivative Calculus
2-10  The Derivative Calculus I

2-12 Justification of the power rule. 
2-13 Marginal Applications.
Justify the sum rule.
Week 5 Summary of Weeks 3&4. Due Friday 2-20
2-16 Discuss Sum rule interpretations.
Start Product rule. 
2-17 Justify Constant Multiple Rule.
Start Quotient Rule.
Justify product rule.
2-19
More on the Quotient rule.
Applications: Marginal vs. Average Cost
Breath 
2-20
Discuss Constant Multiple Rule.
Examples: f  does not have a derivative at a.
The Chain Rule 
Week 6  2-23 More Chain Rule
Implicit functions. Implicit Differentiation
2-24 Implicit Functions and Related rates. 2-26 More Implicit Functions and related rates.
2-27 Exponential functions
Interest and value
Week 7
Summary of Week 5&6  Due 3-1.
Midterm Exam #1 Self-Scheduled
Wednesday  3-3
 8:00-11:30am; 5:00 - 8:30pm Lib 56

3-1 More on exponentials.
Start Logarithmic functions. 
3-2 Review for Exam #1
3-4 Logarithmic functions. 3-5 Models using exponentials
Week 8  3-8 Derivatives of Logarithms and Exponentials
 
3-9 Finish derivatives of log's, etc.

3-11 Logarithmic differentiation

  Slide Rules!
3-12 limits and continuity,
Continuity
Spring break week
3-15 No Class
3-16 No Class 3-18 No Class
3-19 No Class
Week 9 Summary of Weeks 7 and 8  Due
3-22 IVT
Optimization  and  First Derivative Analysis
3-23 More Optimization and Graphing.  3-25 The fence problem.
First Derivative Analysis
More optimization  and IVT
3-26 Optimization: revenue&profit Begin Second Derivatives- acceleration
Concavity and
Curves
Week 10 3-29 More on Concavity
 3-30 Horizontal Asymptotes. 4-1 Vertical Asymptotes
4-2  Linear Estimation and "Differentials."
Relative error.

Week 11
Summary of Weeks 
9 & 10 Due 4-5.
4-5 Differentials
Begin Differential equations and integration IV.A

 
4-6 More on DE's and integration. 4-8 Elasticity.  4-9 Acceleration and integration.
Estimating cost changes from marginal costs.  More DE's.
Week 12 Self Scheduled  
Exam #2 Wed. 4-14

4-12 Costs, marginal costs, and estimation. Introduction to the definite Integral.. 4-13 Riemann Sums  and Estimating Area .Finding area by estimates and using anti-derivatives 
The definite integral and The FTofC. Finding Area exactly!
 IV.E?
4-15 More Area and applications: 
FT of calculus I .
4-16 Substitution! 
week 13 Summary of Weeks 11&12
Due 4-22
4-19 Substitution in definite integrals Interpreting definite integrals. Geometric Area.

4-20 More on area and substitution.
Consumer& Producer Surplus; Social Gain.
4-22 Average Value. Intro to functions of  2 or more. Partial derivatives. 1st order.
4-23 Meet in SH 119
Visualizing Functions of 2 variables: level curves, graphs of z=f(x,y)
Week 14  4-26 More on partial derivatives and linear estimation. Visualizing functions of 2 variables.
4-27 2nd order partial derivatives 
Extremes (Critical points)
4-29 DE's -Separation of variables: Growth models and exponential functions.
4-30 Improper integrals I
Week 15
Summary of Weeks 13 & 14
Due 5-4
5-3 Improper integrals II
 
5- 4 Least Squares example
5-6 Future and present value. Applications of linear regression to other models using logarithms
Probability and 
DARTS?
5-7 ????
Week 16 Final Examination
Review Session  Sunday 4-6 pm Lib 56
5-10
5-11
Wed.5-12
Th. 5-13
    
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 )

           B. The Calculus of Derivatives
               * Sums, constants, x n, polynomials
                *Product, Quotient, and  Chain rules 
                *logarithmic and exponential functions
                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
                The differential and 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. 
 
 

 



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