Martin Flashman's Courses
Math 106 Calculus for Business and Economics
Spring, '10
Sign up for self scheduled final on Moodle
Review Session for final Sunday 1-3 pm BSS Room TBA
Checklist of topics for Final Exam
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   Recommended Problems
Related Graded problems are on WebAssign
Comments
Optional Work
HW #1
1/22-25
 A.1 Review of Real Numbers
A.3 Multiplying and Factoring 
1.1 pp 3-6
Moodle background assessment quiz.  
A.1: 1-21 odd 
A.3: 1-13 odd; 31-39 odd
HW #2
1/25-26
1.1 Functions and tables. 
A.5  pp A.22-24  
Solving equations  		 
A.5 1-7 odd, 13-19 odd
1.1: 1-5, 7,9, 12, 15, 16, 22, 23, 25, 33
HW #3
1/28-29

 1.2 Graphs  
Sensible Calculus 0.B.2 Functions		 Do the reading first!
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.]
HW #4
1/29-2/1

 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		 Try The Moodle Practice Quiz on Functions
On-line Mapping Figure Activities- 
(this may be slow downloading)
HW #5
2/2-4
 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
 1.4: 49
HW #6
2/2-8
 		1.4 Linear Models.
A.5 ppA23-A25
3.1 Average Rate of Change
 		1.4:  12, 19, 21,22,25
3.1: 1-10, 13-16, 21, 39, 40
On-line Mapping Figure Activities-  (Again... ;)
HW #6.5
2/9-11
 3.2 Pages 154-158
The Derivative: A Numerical and Graphical  Viewpoint
 3.2: 1, 2, 5, 9,12
HW #7
2/9-11
 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!]
HW #8
2/11		 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"]		 Try Moodle Practice quiz on writing responses.
HW #9
2/12-16
 3.3 The Derivative: An Algebraic Viewpoint
3.4 The Derivative:  Simple Rules		 3.4:1-11 odd; 14-17; 19-21 Practice Quiz on Slopes of Tangent Lines using 4 steps.
HW #10
2/16-19
 		3.2 Derivative function graphs, interpretation 3.2 :39, 41, 42, 59-64, 97,98, 109, 110
HW#11
2/19

 3.4(Again)  The Derivative:  Simple Rules 3.4: 61, 65, 67, 71, 79;
29, 37, 41, 42, 53, 55, 63, 64
HW #12
2/19-22


 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
HW #13 2/25-26
 4.1: Quotient Rule 4.1: 35, 37, 38, 43; 53, 59, 62
HW #14
2/22-24
 		4.2 The Chain Rule 4.1: 63, 64, 71, 73
4.2 : 13- 17, 55
HW #15
2/23-3/4

 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
HW#16
3/4-3/8

 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)
Midterm Exam #1 Self-Scheduled  : Covers Material from HW # 1-15 and related sections. see Sample Exam on Moodle.
HW #17
3/8-9

 A.2: Exponents A.2: 15,19, 23, 39, 41, 71  
HW #18
3/8-11
 		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
HW#19
3/8-11
 5.4 Related Rates
2.2: Exponential Functions		 5.4 17,  21, 25
2.2 : 3,4,9,11, 7, 13, 17
HW #20
3/9-11
3/22-25
 2 .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
HW #21
3/223-26
 2.3: pp. 110-116 [Logarithmic functions]
Log's Properties (on line).		 2.3: 1-4, 19 Sensible Calculus I.F.2
HW #22
3/23-26

 		4.3: Examples 1-5; pp 265-267.
Derivatives for Log's & Exponential Functions		 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
HW #23

 		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 #24
4/2-5
 		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 		continuity and differentiablity on-line materials( A and B)
HW #25
4/2-5
 		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
HW #26
4/5-6
 		5.2. Applications of Maxima and Minima5.1:  Maxima and Minima
5.3 2nd deriv.pp317-320		 5.2:15, 21 5.2: 25,  27, 29
5.3: 1-5,7,9,11,14
HW #27
4/12-13
 		5.2 and 5.3 again! 5.3 : 17-20, 23; 25, 29,31
5.2: 33, 35, 41, 45
HW#28
4/13-15

 		3.6: p212-216
3.8: p229
5.3: p321-324		 5.3: 35- 37,41, 63, 67
3.6: 1-11 odd
HW #29
4/16-20
 		3.6,3.8  Again! 3.8: 15,17,21,23,33,35,37
3.6: 25, 27,29
5.3: 39, 43, 45		 On-line Problems on Linear Estimation  

Exam #2

 EXAMINATION  # 2 will cover material from Assignments 15-28 and related sections of the text.
For Sample Exams II see Moodle.		 Review for Exam #2: (will not be collected):
p 136[138]: 2,3,4
p288[294]: 1(a,e,g,i),2(c,d),3a,8a
p350[361]: 1(a,d,f),2,4a,5(a-c)
HW #30
 		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
HW #31

 		6.1 Applications p 359-361 6.1: 15,17, 27, 35, 41-44,51
HW #32
 IV.E
6.3. The Definite Integral As a Sum.
p 373-376, 380
6.2 Substitution pp364-367 		6.3: 1-5 odd, 15, 19, 21
6.2: 1-6; 21,23		 SC.III.AThe Differential
HW #33
 		8.1 Functions of Several Variables. p467-471
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
8.1: 1-9 odd, 19, 20, 21, 29, 39, 43

 SC IV.E
HW #34
 		6.5 pp 395  - 396 6.5: 27-30, 61,63
HW # 35

 		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
HW #36
 		7.2 pp 416-420 (area between curves)
7.2 p420-426 (Surplus and social gain)
7.3  pp 430-431		 7.2:1,3,5,11, 15
7.2: 25, 37, 49
7.3: 1- 5odd, 29, 35a
ASSIGNMENT INVENTORY

Reading
INVENTORY
 Problems
INVENTORY
 Optional
INVENTORY

7.5 p 442-445 +
8.2
8.4 p498-501 Critical points 		7.5: 1-7 Graphing, Technology problems from lab





5.5 Elasticity and other economic
applications of the derivative 		5.5: 1, 3, 14

7.4
Future and present value.


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





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

7.5
8.4 pp 504-505

 7.5: 11, 13, 17
8.4 :13, 15,17,19

7.6 7.6: 1,3,13

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



8.2: 45

Tentative Schedule of Topics  (Subject to  some major changes) 1-31-10 
 
 Monday  Tuesday Thursday
 Friday
Week 1 No Class- MLK Day
   1- 19 Course Introduction Numbers, Variables Algebra Review
Begin Functions.
Week 2 1-25 More functions review
The coordinate plane. 
Functions, graphs.		  
1-16 Functions, graphs and models.

 

Lines and models. More Functions ,Points and Lines

Summary of Weeks 1&2
Due Friday 3 pm.  		2-1  Models: Linear Functions. Slopes and  rates More linear models.
Quadratic functions.
Estimation.		 More Quadratics.
Extremes and the tangent problem.
Average rates, and slopes of secant and tangent lines.
Week 4 (Graphing, Technology)
 2-8
Instantaneous Rates.
The Derivative

 More Motivation: Marginal cost, rates and slopes.

The Derivative and algebra. More on finding the derivative.Finding the derivative as function.

Week 5 Summary of Weeks 3-5. Due Monday 22-22 by 3 pm.
 2-15 Begin: The Derivative Calculus
Definition of the derivative.
Justify the sum and constant multiple rules.
Der. of  1/x



Notation.
Justification of the power rule for  n>0. 		Graphical Derivative as function graphs
Discuss Sum rule interpretations.
More on costs, revenues and profits
 Marginal Applications.
Applications: Marginal vs. Average Cost
Constant Multiple Rule Interpretations
Start Product rule.
Week 6 
2-22  Justify product rule.

 Start Quotient Rule. More on the Quotient rule.
The Chain Rule
Implicit functions.
Week 7
Summary of Week 6&7  Due Friday 3 pm.

Midterm Exam #1 Self-Scheduled  3-3

 3-1 More Chain Rule
 Implicit Differentiation
More Implicit Functions and related rates. 		More Implicit Functions and related rates.
  More Implicit Functions and related rates.
 Examples: f  does not have a derivative at a.

Week 8
3-8 Begin Exponential functions
Limits and continuity,


More limits and continuity 
Interest and value. No Class- Furlough Day
Week 9 Spring Break
Week 10
Summary of Weeks 7 and 8 
Due 4pm  Friday		 3-22 More exponentials. e and compunding interest continuously.Derivatives of exponentials, esp'ly exp'(x)=exp(x).


 Derivatives of  Exponentials.
Start Logarithmic functions.
Derivatives of Logarithms and Exponentials
More on models with exp and log equations.
 More on log properties.
Logarithmic scales.
Slide Rules!?
  Week 11 3-29  NO Class
Flashman Furlough Day

 More on log properties.
Finish logs/exps.



Log scales?
Continuity
 IVT
 More on Continuity. IVT.
.
 
Week 12
Summary of Weeks 
9 & 10 Due Friday
 4-5 Begin Optimization  and  First Derivative Analysis

First Derivative Analysis


 More Optimization and Graphing. Optimization: revenue example
Optimization  and IVT

. 		More Optimization and Graphing.
The fence problem
Optimization: revenue example
Begin Second Derivatives- acceleration
 		Concavity and Curves


  Week 13 4-12 More on Concavity
Horizontal Asymptotes.



Vertical Asymptotes
 Linear Estimation and "Differentials."

  
Estimating cost changes from marginal costs. Differential Notation(started)
Costs, marginal costs, and estimation.
11-10 Relative error. Elasticity
Begin Differential equations and integration IV.A

 Week 14Self Scheduled  
Exam #2 Wednesday 11-21

Lab ? 		4-19  Review for Exam #2? More DE's.
Acceleration and integration
Introduction to the definite Integral.
IV.E 		Euler's Method.
The Definite Integral
 Week 15
Summary of Weeks 12-15
Due Friday
 4-26
Intro to functions of  2 or more. 
Functions of many variables.
Tables for 2 variables.
Riemann Sums  and Estimating Change
The definite integral and The FTofC.
Area .
Finding area by estimates and using anti-derivatives.
Fundamental Theorem I  
 More Notation, Area and applications:  Interpreting definite integrals.
Average Value.

Partial derivatives. 1st order.
linear estimation.
 Substitution
 
Week 16

 5- 3
Linear Estimations and Partial Derivatives.
Visualizing Functions of 2 variables: level curves,

 More on Area and integration.
2nd order partial derivatives
Extremes (Critical points)

Substitution in an indefinite integral!
Area between curves.
Consumer& Producer Surplus; Social Gain.
graphs of z=f(x,y)		 Improper Integrals I and II
Future and present value.

Least Squares example 
Week 17 Final Examination
Review Session  Sunday 1-3 pm BSS Room TBA




  Checklist of topics for Final Exam
         I.  Differential Calculus:

           A. *Definition of the Derivative
                Limits / Notation
                Use to find the derivative
                Interpretation ( slope/ velocity/marginal *** )

           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
                Elasticity of  Demand 

           D. Theory
                *Continuity  (definition and implications)
                *Extreme Value Theorem 
                Intermediate Value Theorem 

       E. Several Variable Functions
                  Partial derivatives.
      

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            
         
          
 
 

 


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