Martin Flashman's Courses
Math 106 Calculus for Business and Economics
Spring, '08
Current Assignment and Schedule
Checklist of topics for Final Exam


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] Comments
Optional Work

HW #1
1-24/1-28*
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
Introduction [in class] 
How to Do Math [in class]

HW #2
1-25/1-29*
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
1-31/2-1*
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 again! [19]
HW #4
2/1-4*
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 Moodle Practice Quiz on Functions
On-line Mapping Figure Activities
(this may be slow downloading)
HW #5
2/4-7*
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
2/7-11-12*
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
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]
Summary #1   2-8
Summaries: Every two weeks you will be asked to submit a summary of what we have covered in class. (No more than two sides of a paper.) These may be organized in any way you find useful but should not be a copy of your class notes. I will read and correct these before returning them. [Recommended:The summaries may be submitted in a partnership (2-3 members).]  Each individual partner will receive corrected photocopies.
HW #6.5
2/12-14*
3.2 Pages 154-158
The Derivative: A Numerical and Graphical  Viewpoint
3.2: 1, 2, 5, 9,12 3.1.1 Rates of Change, Secants, and Tangents (Disc 1, 18:53) try Moodle Practice quiz on writing responses.
HW #7
2/15-18*
3.2 derivative estimates 
3.3 The Derivative: An Algebraic Viewpoint
3.2: 13, 16, 17, 19, 20; 23, 24 
3.3:
Use  "4-step process" from class - 1, 2, 5 [Ignore the problem instruction!]
3.1.2 Finding Instantaneous Velocity (Disc 1, 19:57)
HW #8
2-18/19*
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) Practice Quiz on Slopes of Tangent Lines using 4 steps.
HW #9
2-19/21
3.3 The Derivative: An Algebraic Viewpoint
3.4 The Derivative:  Simple Rules
3.4:1-11 odd; 14-17; 19-21 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)
 
4.1.1 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)

Summary #2   2-22
Summaries: Every two weeks you will be asked to submit a summary of what we have covered in class. (No more than two sides of a paper.) These may be organized in any way you find useful but should not be a copy of your class notes. I will read and correct these before returning them. [Recommended:The summaries may be submitted in a partnership (2-3 members).]  Each individual partner will receive corrected photocopies.
HW #9.5
2-22/25*
3.2 Derivative function graphs, interpretation 3.2 :39, 41, 42, 59-64, 97,98, 109, 110 3.2.1 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
2-22/25*
3.4(Again)  The Derivative:  Simple Rules 3.4: 61, 65, 67, 71, 79;
29, 37, 41, 42, 53, 55, 63, 64


HW #11
2-25/26*
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
2-28
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
2-29
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
3-3/4*
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
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 Diffe More on Instantaneous Rate [19]
4.4: 53
6.2.1 Using Implicit Differentiation (Disc 2, 22:24)rentiation (Disc 2, 14:43)
HW#15
3-6/7*
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)
Midterm Exam #1 Self-Scheduled: 
Tuesday 3-11 evening 5:30-9:00 pm; Wednesday 3-12 morning 8:30-11:50 am.

Covers Material from HW # 1-15( part of 17) and related sections. see Sample Exam on Moodle.
HW #16
3-4/6*
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
3-4/6*
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
3-25/27*
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
5.2.2 Derivatives of Exponential Functions (Disc 1, 23:17)   
HW #19
3-25/27*
2.3: pp. 110-116 [Logarithmic functions]
Log's Properties (on line).
2.3: 1-4, 19 5.3.1 Evaluating Logarithmic Functions (Disc 2, 18:37) Sensible Calculus I.F.2
HW #19.5
3-28/4-1
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
5.3.2 The Derivative of the Natural Log Function (Disc 2, 13:24)
HW #20
4-1/3*
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
4-7/8*
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
4-7/8*
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
4-10/11*
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
4- 14/15*
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
7.4.3 The Box Problem (Disc 2, 20:38)
 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)
7.4.4 The Can Problem (Disc 2, 20:47)
HW #25
4-15/17*
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#26
4-18/21*
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 #27
4-21/22*
3.6,3.8  Again! On-Line: Linear Estimation 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, 3:2)
7.2.2 Using the Tangent Line Approximation Formula (Disc 2, 24:22)
On-line Problems on Linear Estimation  
L1-6; A1-5; App1-3
Midterm Exam #2 Self-Scheduled
Try to come 5 minutes before your starting time:
Tuesday 4-22 evening 5:30-9:00 pm BSS 302
Wednesday 4-23 morning 8:30-11:50 am come to BSS 356.
Covers Material from HW # 15-26 ( and related sections). see Sample Exam II on 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 #28
4-24/25*

6.1 The Indefinite Integral  p 353-358
On-line tutorial for 6.1.
Differential equations and integration SC IV.A
6.1: 1-13odd 9.1.2 Antiderivatives of Powers of x (Disc 2, 17:56)
9.1.1 Antidifferentiation (Disc 2, 13:59)
SC.III.AThe Differential
HW #29
4-24/28*
6.1 Applications p 359-361 6.1: 15,17, 27, 35, 41-44,51

HW #30
4-25/29*
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
9.4.1 Approximating Areas of Plane Regions (Disc 3, 9:39)
10.1.1 Antiderivatives and Motion (Disc 3, 19:51)

HW #31
4-29/5-2*
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
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 #32
4-29/5-2*
6.5 pp 395  - 396 6.5: 27-30, 61,63
9.3.2 Integrating Composite Exponential and Rational Functions by Substitution (Disc 3, 13:30)
HW # 33
5/11
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 ##34
5/11
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
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)
5.5 Elasticity and other economic
applications of the derivative
ASSIGNMENT INVENTORY
 From Fall, 2007

Reading
INVENTORY

Problems
INVENTORY

CD Viewing
INVENTORY

Optional
INVENTORY


7.5 p 442-445 +
8.2
8.4 p498-501 Critical points
7.5: 1-7 17.1.1 The First Type of Improper Integral (Disc 4, 9:42)
The second type of ... [8]
17.1.3 Infinite Limits of Integration, Convergence, and Divergence (Disc 4, 11:50)


7.4
Future and present value.







The 20 minute review. Common Mistakes [16]


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.

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




 





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) 1-11-08 
 
Monday  Tuesday Thursday
Friday
Week 1 1-21 No Class-
MLK Day
Course Introduction Numbers, Variables
Algebra Review
Begin Functions.
More functions review
The coordinate plane. 
Functions, graphs.
Week 2 1-28 Functions, graphs and models.
Points and Lines
 
Lines and models.
 

More Functions
Models: Linear Functions. Slopes and  rates

Week 3
Summary of Weeks 1&2
Due Friday 5 pm.

2-4 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) 2-11 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&4. Due Friday 3 pm. 2-18 Begin: The Derivative Calculus
Definition of the derivative.
Graphical Derivative as function graphs
Justification of the power rule for  n>0. Der. of  1/x
Justify the sum and constant multiple rules.
Constant Multiple Rule Interpretations
Notation.
Discuss Sum rule interpretations.

Marginal Applications.
Applications: Marginal vs. Average Cost
Start Product rule.
Week 6  2-25 Justify product rule. Start Quotient Rule More on the Quotient rule.
The Chain Rule
Implicit functions.
Week 7
Summary of Week 5&6  Due Friday 3 pm.

3-3 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
Midterm Exam #1 Self-Scheduled 3-11 and 3-12
3-10 Begin Exponential functions
Interest and value.
More exponentials. e and compunding interest continuously.
Last Review for Exam #1
More exponentials. e and compunding interest continuously. Derivatives of exponentials, esp'ly exp'(x)=exp(x)
Week 9 Spring Break - No classes
Week 10
Summary of Weeks 7 and 8 
Due 4pm  Friday
3-24 Finish derivatives of exp's, etc.
 Logarithmic functions. Start Logarithmic functions.
Derivatives of Logarithms and Exponentials
More on models with exp and log equations.
More on log properties.
Logarithmic differentiation
Logarithmic scales.
Slide Rules!?
More on log properties.
Logarithmic differentiation
Week 11  3-31 No Class
CC Day
Finish logs/exps.
limits and continuity,
Continuity
IVT
More on continuity and limits.
More on Continuity. IVT.
Week 12
Summary of Weeks 
9 & 10 Due Friday
4-7  IVT and bisection.
Begin Optimization 
and  First Derivative Analysis

First Derivative Analysis
More Optimization and Graphing.
Optimization  and IVT
Optimization: revenue example
More Optimization and Graphing.
The fence problem

Optimization: revenue example
Begin Second Derivatives- acceleration Concavity and Curves
Week 13
4-14 More on Concavity
Vertical Asymptotes
Horizontal Asymptotes.  4-18 Costs, marginal costs, and estimation.
Linear Estimation and "Differentials."
week 14 Self Scheduled  
Exam #2 Tues. and  Wed.
4-21Relative error.
Begin Differential equations and integration IV.A
More DE's. Acceleration and integration
Euler's Method.
Introduction to the Definite Integral.
IV.E
Riemann Sums  and Estimating Change
The definite integral and The FTofC
Week 15
Summary of Weeks 12-15
Due Friday
4-28
Substitution in an indefinite integral!
Intro to functions of  2 or more. 
Functions of many variables.
Tables for 2 variables.
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
Review Substitution then substitution in definite integrals
Week 16 5-5
Linear Estimations and Partial Derivatives.
Area between curves.
More on Area and integration.
Consumer& Producer Surplus; Social Gain.
  Elasticity
Extremes (Critical points)
Least Squares example
 
2nd order partial derivatives
Future and present value
Visualizing Functions of 2 variables: level curves,
graphs of z=f(x,y)
Improper Integrals I and II?
Week 17 Final Examination
Review Session  Sunday
Self Schedule for Final Examinations
Mon. May 12 15:00-16:50 TBA come to BSS 356
Wed. May 14 15:00-16:50 SH 128* (as per Exam Schedule)
Wed. May 14 12:40-14:30 NR 201
Thur. May 15 15:00-16:50 SH 128 OR
Special Appointment


  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 

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

      E. Several Variable Functions
                  Partial derivatives. first order
      

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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