Martin Flashman's Courses
Math 106 Calculus for Business and Economics
Summer, '02
Final Exam
In class Thursday, 8-8
Take -home distributed 8-7, due 8-8 by 5 pm.
Checklist of topics for Final Exam
Check out BLACKBOARD for solutions  to on-line Reality Check Quizzes 10-17.

 MTWR 10:00-11:15 SH 128

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Summer 2002      AssignmentsLast updated: 7/10/02    M.FLASHMAN 
Due Date
Reading
Problems 
Optional
Watch CD Tutorial [# of minutes] 
* means optional
6-4 A.1 Review of Real Numbers 
A.3 Multiplying and Factoring 
1.1 pp 3-6 
On-line Interactive Algebra Review
A.1: 1-21 odd 
A.3: 1-13 odd; 31-39 odd 
Math 106 preliminary problems on-line
Introduction [in class] 
How to Do Math [in class]
6-5 1.1 Functions and tables. 
1.2 Graphs 
A.5 Solving equations ppA.21-23 
Sensible Calculus 0.B.2 Functions (added 6-2-02) 
On-line Tutorials
1.1: 1-5, 7,9, 12, 15, 16, 22, 23, 25, 33 
A.5 1-7 odd, 13-19 odd 
1.2: Draw a mapping-transformation figure for each function-1,2,4,5 [Read  0.B.2  to find out more about the mapping-transformation figure.]
The Two Questions of Calculus [10] 
Average Rates of Change [11] 
Functions [19]
6-6 1.3 Linear functions 
1.4 Linear Models. 
 Functions and Linear Models
On-line Tutorials
1.2: Draw a mapping figure for each function- 13, 15, 29 
1.3 : 1-9 odd, 11,12,15,21,23 
Graphing Lines [28]
6-10 1.4 Linear Models. 1.3: 27- 39 odd, 45, 47, 49 
1.4: 1-9 odd, 12, 19, 21,22,29
1.4: 47 Ok... catch up!  :)
6-11 2.1 Quadratic functions 
3.1  Average Rate of Change
2.1: 1-9 odd, 19, 21, 27 
3.1: 1-23 odd, 35, 36 
Parabolas [22] 
Rates of Change, Secants and Tangents [19] 
6-12 3.2 The Derivative: A Numerical Approach
3.3 The Derivative: A Geometric Approach
3.4 The Derivative:  An Analytic Approach
3.2: 1,5,7,9 
3.3: 1-11 odd 
3.4:1, 3, 5
Finding Instantaneous Velocity [20] 
The Derivative [12] 
Slope of a Tangent Line [12] 
Equation of a Tangent Line [18] 
*The Derivative of the Reciprocal Function [18]
6-13 3.4 (Again) 
Chapter 3 Summary as relevant.
3.2: 13, 17, 19; 33,35, 41 
3.3: 13,15,17, 23, 25, 39 
3.4: 11-33 odd
Instantaneous Rate [15] 
More on Instantaneous Rate [19] 
*The Derivative of  the Square Root [16] 
6-17 3.4 (Again) 
3.5 Marginal analysis
3.4: 11-33 odd [redo] 
3.4: 39,45,49,51,61,63 
3.5: 1,5,6,7,9, 11
Differentiability [3]
Short Cut for Finding Derivatives [14] 
Uses of The Power Rule [20]
6-18 3.5 (Again) 
4.1  Product Rule
3.4: 71, 75, 77, 81, 85, 87, 88 
3.5: 15, 17,19, 25, 27 
4.1: 13, 15, 17, 21
3.6: 29 The Product Rule [21] 
6-19 4.1: Quotient Rule
4.2 The Chain Rule
4.1: 43, 47, 55; 27,29, 31, 39  The Quotient Rule [13] 
Introduction to The Chain Rule [18] 
6-20 4.2 The Chain Rule 4.2 : 13- 21 odd, 55 Using the Chain Rule [13] 
Intro to Implicit Differentiation [15] 
6-24 4.5 Implicit Differentiation (Skip Examples 2 and 3!)
A.2: Exponents 
4.2: 47,51, 53, 63, 64 
4.5 :11, 15, 39, 41, 51 
A.2: 15,19, 23, 39, 41, 71
4.5: 57 Finding the derivative implicitly [12] 
Using Implicit Differentiation [23] 
The Ladder Problem [14]
6-25 5.4 Related Rates
2.2: Exponential Functions 
 and their Derivatives 
Sensible Calculus I.F.2
POW #1 is Due. 
5.4: 9, 11, 13, 17,  21, 25 
2.2: 3, 7, 9,11, 13, 17, 55, 61, 73 
4.3: 7,8, 45, 51, 53, 85
The Baseball Problem [19] 
Exponential Functions [10] 
Derivatives of Exp'l Functions [23]
6-26 2.3: Logarithmic functions REDO 2.2: 3, 7, 9,11, 13, 17, 55, 61, 73 Logarithmic Functions [19]
6-27 2.4: Derivatives for Log's 
Sensible Calculus I.F.2
2.3: 1-5, 7, 13 
4.3:1,2, 15-19 odd, 23
Derivative of log functions [14]
7-1 4.5 Example 3 4.5: 35 

Midterm Exam #1 covers assignments though 6-27.

Chapter 3 review: 2,3,4,5,9 
Chapter 4 review: 1(a-d,g,i), 2(a,b), 4(a,b)
 
7-2 3.6: limits and continuity Acceleration & the Derivative [6] 
Distance and Derivative [22] 
One Sided Limits [6] 
Continuity and discontinuity [4]
7-3  3.7: limts and continuity 
The Intermediate Value Theorem
Higher order derivatives and linear approximations.[21] 
Three  Big Theorems [Begin-3.5]
7-8 3.6 and 3.7 (Again?!) 
5.1:  Maxima and Minima
3.6: 21,22, 25 (a-e), 31 
3.7: 59-62 
5.1: 1-11 odd
Three  Big Theorems [11] 
The connection between Slope and Optimization [28] 
The Box Problem [20] 
Math Anxiety [6]
7-9 5.1:   Maxima and Minima (again)
5.2.  Applications of Maxima and Minima
5.1: 13,15,21,23,25, 35,  39, 41, 44 
POW #2 is Due. 
Intro to Curve Sketching [9] 
The Can Problem[21] 
Critical Points [18] 
The First Derivative Test [3]
7-10 5.2.  Applications of Maxima and Minima
5.3 2nd deriv.
5.2: 5, 11, 13 
5.3: 1,5,7,9,11,13
Regions where a function is increasing...[20] 
Concavity and Inflection Points[13] 
Using the second derivative [17] 
Morale Moment
7-11 3.6 and 3.7 again! 
More 5.3
5.2: 15, 21, 25,  27, 29, 33, 41, 43 
5.3 : 17-23 odd; 25, 29,31, 35, 37
5.2: 56 Graphs of Poly's [10] 
Cusp points &... [14] 
Domain restricted functions ...[11] 
The 2nd Deriv. test [4] 
Horizontal asymptotes  [18]
7-15 More 5.3 3.6: 1-11odd 
5.3: 39, 41, 43, 45, 47, 51, 67
Vertical asymptotes [9] 
Graphing ...asymptotes [10] 
Functions with Asy.. and holes[ 4] 
Functions with Asy..and criti' pts [17]
7-16 5.5 Elasticity and other economic applications of the derivative. 
On-Line: Linear Estimation
5.3: 73 
5.5: 1, 3 
On-line Problems on Linear Estimation 
L1-6; A1-5; App1-3
III.AThe Differential Using tangent line approximations [25] 
Antidifferentiation[14]
7-17 Differential equations and integration IV.A
6.1 The Indefinite Integral  p 315-321
6.1: 1-19 odd, 27, 37 Antiderivatives of powers of x [18]
7-18 6.1 Applications p321-323 
6.3. The definite Integral As a Sum. 
6.4. The definite Integral: Area p345-348
6.1: 43-46,49,53, 55-57, 59 
6.3: 1-5 odd, 19, 21
Approximating Areas of Plane regions [10] 
Areas, Riemann Sums, and Definite Integrals [14]
7-22 6.4 
6.5 {omit example 5) 
The Fundamental theorem
6.4: 1-5 odd, 21, 23, 27 
6.5 : 17-23 odd; 59,61
The Fundamental theorem[17] 
Illustrating the FT[14] 
Evaluating Definite Integrals [13]
7-23 Midterm Exam #2 covers assignments though 7-18 including 6.1 but not 6.3. Antiderivatives and Motion [20] 
Gravity and vertical motion [19] 
Solving vertival motion [12]
7-24 6.5 360-361 
6.2 Substitution pp326-329 (omit ex. 5)
6.5: 29-32;71; 51-55odd
6.2: 1-7 odd; 25,27
Undoing the chain rule.[9] 
Integrating polynomials by Substitution [15] 
Integrating composite exponential and rational functions by substitution [13]
7-25 6.2 pp 330-331 
6.5 example 5 
? 7.2 pp380-383?
6.5: 9,11,37-43 odd,67,81 
6.2: 35,37,39,63, 64 
6.4:22
Area between two curves [9] 
Limits of integration-Area [15] 
Common Mistakes [16]
7-29 7.2 
7.3  pp 393-394+
7.2:1,3,5,11;  15, 25, 37, 49 Finding the Average Value of a Function [8]
7-30 7.3 
8.1 Functions of Several Variables.
Summary is Due
7.3: 1-5 odd, 29, 39a
8.1: 1-9 odd, 19, 20, 21, 29, 39, 43
7-31 8.2 and 8.3
7.6
8.2: 1-9 odd; 11-18; 19-25 odd;41, 49
8.3:  1- 7 odd, 13, 41, 45
7.6: 1,3
8.2: 45
8-1 8.3 8.2:19-25 odd (again)
8.3: 19-25 odd; 29,33,38,49
The first type of improper integral[10] 
8-5 7.5 p 407-408
8.4
7.5: 1-7
8.4: 1-9 odd, 31, 35
The second type of ... [8] 
Infinite Limits of integration ... [12]?
8-6 2.3 Summary is Due
Check on-line quiz #17 !
2.3:1,3,4,5,7,11,13,31
The 20 minute review.
8-7 7.4
7.5
7.4:1, 9, 25, 31
7.5:11, 13, 17
8-8 Final Examination: Covers all work from summer.Till work assigned for 8-5.
Two parts. 
I. Distributed 8-7 at end of class. 
Due by  5pm
II In class on 8-8.
Reviewed summaries allowed for reference for  in-class work.
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. 
 
 

 


 
 
 
 
Tentative Schedule of Topics  (Subject to  some major changes) 7-22-02
 
Monday
Tuesday
 Wednesday Thursday
Week 1 6-3 Course Introduction 
Numbers, Variables, Algebra Review 
6-4 More Algebra review and The coordinate plane. 
Begin Functions
6-5 More Algebra review. 
Functions, graphs and models.
6-6 More Functions and Models: Linear Functions.
Week 2 6-10 Functions, graphs, technology. 
Slopes, rates and estimation. 
Quadratic functions.
6-11 The fence problem? 
The Derivative. 
Motivation: Marginal cost, rates and slopes.
6-12 More on the Derivative. Begin the Derivative Calculus 6-13 The Derivative Calculus I 
Week 3 
Summary of Weeks 1&2 
Due 6-17.
6-17 Justify Powers & Sums. 
Marginal Applications 
Product rule. 
Justify product rule?
6-18 The Quotient rule.  6-19 Justification of the power rule and the sum rule. 
The Chain Rule 
6-20 Implicit Differentiation 
More Chain Rule 
Week 4
POW #1 Due 6-25
6-24 Implicit Functions and Related rates. 
Start Exponential functions 
Interest and value. 
Derivatives of Exponentials.
6-25 More related rates. 
Logarithmic functions.
6-26  Derivatives of Logarithms 6-27  Logarithmic differentiation. Models using exponentials 
Week 5 
Summary of Weeks 3&4
Due 7-1.
7-1  Examination I 7-2 limits and continuity 
IVT 
Bisection Method
7-3 More IVT 
Begin First Derivative Analysis 
Optimization
7-4 No Class - Holiday
Week 6 
POW #2 Due 7-9
7-8 . More First Derivative analysis. 
More Optimization
7-9 More optimization and Second Derivative Analysis Higher order Derivatives 7-10 Curves III 
More on Concavity
7-11Horizontal Asymptotes. 
Vertical Asymptotes
Week 7 
Summary of Weeks 5&6
Due 7-15.
7-15 Differentials . 
Relative error.
7-16 More on differentials. 
Begin Differential equations and integration IV.A
7-17  Estimating costs from marginal costs. Introduction to the definite Integral. 
More DE's. 
7-18Finding area by estimates and using anti-derivatives 
The definite integral. 
FT of calculus I 
Week 8 
POW #3 Due 7-24
7-22More on the defintie integral and The FTofC. 
Area. 
Euler's Method  and Area  IV.E?
7-23 Examination II
Substitution 
7-24 
Substitution in definite integrals 
More area and applications.
7-25.More Area and applications: 
Consumer& Producer Surplus; Social Gain. 
Interpreting definite integrals.
Week 9 
Summary of Weeks 7&8
Due 7-30.
7-29 
Intro to functions of  2 or more. 
Average Value. 
7-30  Functions of 2 variables: level curves, graphs.Partial derivatives. 1st order. 
DE's -Separation of variables: Growth models and exponential functions.
7-31 More on graphs of z=f(x,y)
 2nd order partial derivatives 
8-1 
Extremes (Critical points) 
Improper integrals and value
Week 10 : Summary of Weeks 9&10
Due 8-6.
8-5 Least Squares. 8-6 Applications of linear regreession to other models using logarithms
Future and present value
8-7  Breath!
Probability
Final Examination 
Part I distributed. Due 8-8 by 5 pm.
8-8 Final Examination 
Part II
     Martin Flashman's Home Page :) Back to HSU Math. Department :}

Summer, 2002                 COURSE INFORMATION               M.FLASHMAN
MATH 106 : Calculus for Business and Economics                MTWR 10:00-11:15 SH 128
OFFICE: Library 48                                        PHONE:826-4950
Hours (Tent.):  MTWR 11:20-12:20 June 3 to July 3
                        MTWR 14:30-15:20 July 5 to August 8  AND BY APPOINTMENT or chance!
E-MAIL:flashman@humboldt.edu           WWW: http://www.humboldt.edu/~mef2/
***Prerequisite: HSU MATH 42 or 44 or 45 or math code 40.


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