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

 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.
 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.

 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

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://flashman.neocities.org/
***Prerequisite: HSU MATH 42 or 44 or 45 or math code 40.

• TEXT: Required: Applied Calculus, 2nd Edition, by Stefan Waner and Steven R. Costenoble. Brooks/Cole Pub. Co. ISBN/ISSN 0-534-36631-7

• Calculus I, CD, by Ed Burger- Great Lecture Series, Thinkwell Publishing.
Excerpts from Sensible Calculus by M. Flashman as available on the web from Professor Flashman.
• Catalog Description: Logarithmic and exponential functions. Derivatives, integrals; velocity, curve sketching, area; marginal cost, revenue, and profit, consumer savings; present value.
• SCOPE: This course will deal with the theory and application to Business and Economics of what is often described as "differential and integral calculus."  Supplementary notes and text will be provided as appropriate.
• TESTS AND ASSIGNMENTS: There will be several tests in this course. There will be several reality check quizzes, two midterm exams and a comprehensive final examination.
• New: We will be trying to use Blackboard for some on-line reality quizzes. Here is some information about how to use Blackboard. I will discuss this further in class- Wednesday, 6-5.

• You can also go directly to the HSU Blackboard.
• Homework assignments are made regularly. They should be done neatly. I will collect assignments at random for grading. Homework is graded Acceptable/Unacceptable with problems to be redone. Redone work should be returned for grading promptly. Each missing or unacceptable (not redone)  homework will result in a deduction of 2 points from your point total for the course.
• Using the CD Tutorials: Whenever a CD tutorial is assigned, that should be viewed by the due date of the assignment. As part of that assignment, you should include a brief statement reporting on the tutorial's content. This content may be the solution of a specific problem, the development of a concept, or the organization of a technique. This CD tutorial report should be clearly presented in the assignment so that it can be read easily without searching through the problem work of the assignment. When homework is collected, the report on the CD tutorial will result in the addition of 2 points to your point total for the course.
• LATE HOMEWORK WILL NOT BE ACCEPTED AFTER THE DUE DATE.
• You must submit a written request at the start of class for me to discuss in class a problem or a question you have about the previously assigned reading. I will be available after class and during my office hours for other questions.
• Exams will be announced at least one week in advance.
• THE FINAL EXAMINATION WILL BE GIVEN AT THE LAST CLASS.
• The final exam will be comprehensive, covering the entire semester.
• MAKE-UP TESTS WILL NOT BE GIVEN EXCEPT FOR VERY SPECIAL CIRCUMSTANCES!

• It is the student's responsibility to request a makeup promptly.
*** DAILY ATTENDANCE SHOULD BE A HABIT! ***
• Cooperative Activities: Every two weeks your partnership 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. Each individual partner will receive corrected photocopies.

• Your summaries will be allowed as references at the final examination only.

Every two weeks partnerships will submit a response to the "problem/activity of the week." All  cooperative problem  work will be graded as follows: 5 well done, 4 for OK, 3 acceptable, or 1 unacceptable.
Summary work will be used along with the problem of the week grades will be used in determining the 50 points allocated for cooperative assignments.

• GRADES: Final grades will be determined taking into consideration the quality of work done in the course as evidenced primarily from the accumulation of points from tests and various  assignments.
•  Reality Quizzes 100 points 2 Midterm Examinations 200 points Cooperative work 50 points Final Examination 200 or 300 points Total 550 or 650  points
• Cooperative problem assignments and summaries will be used to determine 50 points.
• The final examination will be be worth either 200 or 300 points determined by the following rule:

• The final grade will use the score that maximizes the average for the term based on all possible points .
• Notice that only 400 or 500 of these points are from examinations, so regular participation is essential to forming a good foundation for your grades as well as your learning.
• MORE THAN 4 ABSENCES MAY LOWER THE FINAL GRADE FOR POOR ATTENDANCE.

• ** See the course schedule for the dates related to the following:
• No drops will be allowed without "serious and compelling reasons" and a fee.
• Students wishing to be graded with either CR or NC should make this request to the Adm & Rec office in writing or by using the web registration procedures.
• No drops will be allowed.
• Technology: The computer or a graphing calculator can be used for many problems. We will use Winplot and Microsoft Xcel.
• \$\$ Winplot is freeware and may be downloaded from Rick Parris's website or directly from this link for Winplot .
• Graphing Calculators: Graphing calculators are welcome and highly recommended.
• HP48G's will be available for students to borrow for the term through me by arrangement with the Math department. Supplementary materials will be distributed if needed.
• If you would like to purchase a graphing calculator, let me know.
• Students wishing help with any graphing calculator should plan to bring their calculator manual with them to class.
• \$\$ Use of  Office Hours and Optional "5th hour"s: Many students find  beginning calculus difficult because of weakness in their pre-calculus background skills and concepts. You might also check Teresa (Tami) Matsumoto's  CALCULUS PREPARATION Information Page . A grade of C in Math 44 might indicate this kind of weakness.

• Difficulties that might have been ignored or passed over in previous courses can be a major reason for why things don't make sense now.

You may use my office hours for some additional work on these background areas either as individuals or in small groups. My office time is  also available to discuss routine problems from homework after they have been discussed in class and reality check quizzes as well as using  technology. Representatives from groups with questions about the Problem of the Week are also welcome.

I will try to organize and support additional time with small (or larger) groups of students for whom some additional work on these background areas may  improve their understanding of current coursework.
Regular use of my time outside of class should be especially useful for students having difficulty with the work and wishing to improve through a steady approach to mastering skills and concepts.
Don't be shy about asking for an appointment outside of the scheduled office hours.