Martin Flashman's Courses
Math 109 Calculus I Summer, '05
MTWR  13:00-14:20 SH 128
Final Examination
Part I- Wednesday - 8-3
Core Material- no Books or calculators.
Part II- Thursday - 8-4
Approved Summary Notes and calculators allowed!

Items marked \$\$ are important for students beginning the course.

Last updated: 7/31/05
 Date Due Reading Problems Optional Viewing: Ed Berger CD Tutorial  [# of minutes]  * means optional 6-1 SC 0.B2 [on-line] 1.1 rev. sheet (on-line): 1-3,6,13,15,16,18,19 1.1: 1,2,10,13,15,17,21,22,45, 47, 48, 51, 53 SC 0.B1 Numbers [on-line] Introduction;   How to Do Math 6-1and 2 Appendix B SC 0.B2 [on-line] pg. A-15: 7-10; 17-20; 21-35 odd; 62 On-line Mapping Figure Activities Functions [19] 6-6 1.2 1.3 1.4 1-5;8,10,11 3;5; 54, 55 1,3,37 SC 0.B2 On line # 19, 20, 21 Mechanical universe (Television program) VIDEO1364  Derivatives VIDEO1366 Integration Parabolas [22] Average Rates of Change [11] The Two Questions of Calculus [10] 6-7 2.1 Geom (i)1,2,4 0.C [on-line] Models and Mathematics- Probability Slope of a Tangent Line [12] 6-7 and 6-8 2.1 Motion  (ii) 5,8 Rates of Change, Secants and Tangents [19] 6-8 DO NOT Read 2.6 p119: 1(a),2(a),3, 5(a[ignore i and ii.Use 4steps as in class],b), 6(a[ignore i and ii.Use 4steps as in class],b), 9 Finding Instantaneous Velocity [20] Equation of a Tangent Line [18] 6-8 and 9 2.6 3.1 2.6: Use the 4 steps method with x or t = a when appropriate in 11,13,17-19; 15 3.1: 1,7 Use the 4 steps method to find f '(a) The Derivative [12]  The Derivative of the Reciprocal Function [18] 6-9 3.1 3.2 pp134-138 3.4 pp 157-159 3.1:  2,3, 8, 26,29; 19-21,23 3.2: 1,4-7; 19-23 odd 3.4: 1-3 3.1:11 3.4:11 Instantaneous Rate [15] Uses of The Power Rule [20] 6-13 and 14 3.3 pp 145-149 Read Appendix D  Especially formulae 6-8,10,12,13 3.3: 1-5, 7-15 odd, 34-36,45 3.3: 17-20; 23-26; 57a,58(a,b),61a, 65-67,70-72 Read 3.4 pp160-161, 164-165 3.4: 29,30 *The Derivative of  the Square Root [16] More on Instantaneous Rate [19] Short Cut for Finding Derivatives [14] The Product Rule [21] Review of Trig[12] 6-14 and 15 Summary #1 Due by 4:00 pm 3.3pp 150-155 3.5 (i) pp169-172 Read web materials on trigonometric derivatives. 3.5: 1,2,5,9,10,13,23, 25 3.3: 87, 22, 27-29, 51, 55, 56, 57(b,c), 60, 69 The Quotient Rule [13] The derivatives of trig functions [14] 6-16 3.5(ii)pp 172-173 3.5: 3,4,6, 15,21,27, 33 *Graphing Trig Functions[17] Differentiability [3] 6-20 3.2 pp 139-142 3.5 p173-4.READ Examples 4 and 5! 3.2:35,36,41,46 3.5: 35,36,38,39,43 Read on-line   Sens. Calc. 0.C on Probability Models 6-21 3.6 The Chain Rule  pp176 though 178 Ex.2 only! 3.6 pp180-181 3.6: 7-14 use Leibniz notation. 3.6: 16, 17,21,29,35,39 Introduction to The Chain Rule [18] Using the Chain Rule [13] 6-22 3.6 3.7 pp 184-187  Read web materials on implicit differentiation. 3.6: 45,51,53,55, 59, 63 3.7: 5-10, 15, 25, 26 3.7: 29, 41, 42, 51 3.7:*36 Intro to Implicit Differentiation [15] Finding the derivative implicitly [12] The Ladder Problem [14] Acceleration and the derivative.[5] 6-23 3.9 Related rates pp198-201 3.8 Higher Order Derivatives  pp190-194 3.8 2.5 (i) pp 102-104 ((ii) pp109-110 3.9: 3,5,11 3.8: 1-15 odd, 21 3.8:43,44,47,51; 35,36, 53 2.5: (i) 3,4,7,17-20 , 34,37,39 2.5: (ii) 41,43,45,48, 59 The Baseball Problem[19]or The Blimp Problem [12] Acceleration and the derivative.[5] One Sided Limits [6] Continuity and  discontinuity [4] 6-28 and 29 Summary 2. 4.9  Read web materials on Newton's Method. 3.10 pp 205-207 Read web materials on differentials 4.9: 1,3,5-7, 27 3.10: 5,7,9,10; for 4.9:*(11,15,16,25) Using tangent line approximations [25] 6-27 Examination #1 Covers all assignments through that assigned for 6-28. Sections covered: 1.1-1.4, 2.1,2.5,2.6, 3.1-3.9 0.B2 , 0.C 6-30 3.10 4.1 3.10:15-17, 21-25 odd, 31,33 SC IVA(On-line) The connection between Slope and Optimization [28] 7-5 4.1 plus  On-Line tutorial on Max/mins SC IVA(On-line) 4.1:3-6, 31-41 odd,:45,47 On line IVA:1(a,d,e,f),10 Intro to Curve Sketching [9]   Critical Points [18] 7-6 SC IVA(on-line)More 4.1 SC IVB (On-line) Read 4.1: 11, 34, 36,51; 554.7:1,2,7,9 4.7: 15,17,29 IVA: 4, 5(a,b),8,11 4.4:*69 Antidifferentiation[14] 7-7 4.2 4.10 4.2: 7,8,11,23, 254.7: 24, 34, 49, 53 4.10: 3-9 odd,  13-15, 23-25 [optional] The Box Problem [20] Three  Big Theorems [11] Acceleration & the Derivative [6] 7-11 4.2 4.3 pp 240-242 4.7 A java graph showing  f (x)=P'(x) related for f a cubic polynomial 4.2:15, 19,33 4.3: 5,6, 8(a,b), 11(a,b) 4.10: 29-35odd; 41,53, 55, 57 4.7: 52 Antiderivatives of powers of x [18] The First Derivative Test [3] Regions where a function is increasing...[20] Antiderivatives and Motion [20]   Graphs of Poly's [10] 7-12 4.3 pp243-246 4.4 pp 249-255 SC IVD (on-line) 4.10 4.3: 7,8, 11c, 17, 23,24, 27(c,d), 29(c,d), 47 4.7:54 4.10: 47,51,52 IV.D: 1-11 odd (online) The connection between Slope and Optimization [28] Using the second derivative [17] Concavity and Inflection Points[13]  The 2nd Deriv. test [4]  Domain restricted functions ...[11] 7-13 2.2 pp77-79 Vertical Asymptotes 4.4 pp 249-255 SC IVE (on-line) 2.2: 8,9, 23-27odd 4.4: 3,4, 9-13 , 35-38 IV.E: 1,2 Graphing ...asymptotes [10]   Functions with Asy.. and holes[ 4]   Functions with Asy..and criti' pts [17] Horizontal asymptotes  [18] 7-14 and 18 4.4 4.5 Read Examples 1-3! 10.2 pp628-634 SC IV.F READ 4.4: 43-45, 51-53, 59, 60 4.5:1-11 odd, 31, 36 10.2: 3-6, 7, 9, 19a,21, 10.2:24 Vertical asymptotes [9] 7-18 Summary # 3 due by 4pm. 4.5 SC IVF(On line) 4.5: 27, 31, 35, 37IV.F: 1,3,5,13,15,17(on-line) 7-19 SC VA ( On Line)4.6 Read Examples 1-3! V.A: 1,2 a (on line) 5.3:19-25 odd (Use F T of Calc) 4.6: 1,7 The Fundamental theorem[17]  Illustrating the FT[14]   Evaluating Definite Integrals [13] 7-20 SC VA ( On Line) 5.5 pp360-362 5.3: ex 5-ex 7 Appendix E p.A34  Sum Notation 5.4 pp350-354 VA : 5(a,b) 5.5: 1-4; 7-13 odd pA38:1-4,11-13,17,18 5.3: 27-39 odd 5.4: 1-9 odd Undoing the chain rule.[9]   Integrating polynomials by Substitution [15] 7-21 5.5 pp363-364 5.3 pp 340-344 5.5: 17-23; 37-41 5.3: 3, 5,7,12, 13,49 7-25 Examination #2 Sample Exam Posted on Blackboard. Covers all assignments though *** (Mainly material not covered in Examination #1)Tentative sections covered: 3.10, 4.1-4.7, 4.10, 10.2, IVA, IVB, IVD, IVE, VA, 5.3, 5.4, 5.5 and Appendix E. 7-26 5.2: pp 332-336 6.5 5.4: 45-49 5.2: 5, 17,19, 33,37, 48,49 6.5:1,3,5,13-15 Finding the Average Value of a Function [8] 7-27 6.1 pages 371-374 6.1: 1,2,7,11,15,16 Area between two curves [9]  Limits of integration-Area [15] 7-28 and 8-1 6.1 pages 374-376 6.2 pp 382-385 6.1: 3,4,17, 19, 45 6.2: 1,3,4,7 Finding volumes using cross sectional slices. Solids of revolution 8-1 and 8-2 6.2 pp 382-385, - 388 6.1: 29,33,39,41 6.2: 5,10,19,23, 31, 32 The disc method along the y-axis.  The washer methods... 8-2 6.3 6.4 p394-395 Probability and  DARTS 6.3: 1, 3, 7, 8, 28 6.4: 3,5,8 6.4:11, 13 Work....  Hooke's law Shells.... 8-3! The 20 minute review. Inventory of old assignments from the 4th Edition. 3.9 (ii) pp201-203 (i) (ii) 7,10,12  (iii)16,19,31,32 (ii) 4.6 (i) Read Examples 1-3!  (ii) Read Example 4 (i)1,7  (ii) 10, 21 (i)3-6,7,9  (ii) 19a, 21, 24 (i)*15, *17 Lab assignment from 4-7 Lab assignment 4-7 6.2 (i) pp 378-381   (ii) pp 381-384  (iii) p 385-386 (i)1,3,4,7  (ii) 5,10,19,23, 31, 32  (iii)  39, 40,51,52 *61,*59 6.3 6.3: 9, 13, 21, 29 , 41, 43 2.4? 5.1 3,11,13,14

 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   *Trignometric functions  Implicit differentiation  Higher order derivatives  C. Applications of derivatives  *Tangent lines  *Velocity, acceleration, rates (related rates)   *Max/min problems  *Graphing:          * increasing/ decreasing             concavity / inflection  *Extrema (local/ global)   Asymptotes  The differential and linear approximation   Newton's method D. Theory  *Continuity (definition and implications)  *Extreme Value Theorem /* Intermediate Value Theorem  *Mean Value Theorem  II. Differential Equations and Integral Calculus:  A. Indefinite Integrals (Antiderivatives)  *Definitions and basic theorem  *Simple properties [ sums, constants, polynomials, trig]  *Substitution  B. Euler's Method, etc.  Euler's Method  *Simple differential equations with applications  Tangent (direction) fields/ Integral Curves  C. The Definite Integral  Euler Sums / Definition/ Estimates (endpoints/midpoints) /Simple Properties *Substitution  *Interpretations (area / change in position)  *THE FUNDAMENTAL THEOREM OF CALCULUS - evaluation form  THE FUNDAMENTAL THEOREM OF CALCULUS - derivative form  D. Applications  *Recognizing sums as the definite integral   *Areas (between curves).   Volumes (cross sections- discs). Average value. [Work.?]

Bonus Essay question for final Part II:
Suppose P(t) is a positive continuous function on [a,b] that gives the velocity at time t of an object moving on a straight line. Using the mean value theorem, explain  why there is some number c between a and b where P(c) = 1/(b-a) Sx=a x=b  P(x) dx.
Interpret this equation with either
(i) a discussion of the  velocity and position of the object with the position function given by a definite integral from time x=a to time x=t or
(ii) a discussion of the area under the graph of Y=P(x) above the X-axis from X=a to X=b and the area of a rectangle with height P(c) and width (b-a).

OFFICE: Library 48    (and soon to be Library 1)                                 PHONE:826-4950
Hours (Tent.): MTWR 10:00-10:45 AND BY APPOINTMENT or chance!
I will try attend the Blackboard chatroom Tuesday and Wednesday evenings at about 9:00 pm.
E-MAIL: flashman@humboldt.edu               WWW:  http://www.humboldt.edu/~mef2/
***PREREQUISITE: Math 115 or Math code 50 or permission.

• TEXTS: Required: Calculus 5th Edition by James Stewart.(Brooks/Cole, 2003)
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:
Limits, continuity, derivatives, integrals, and their applications.
• SCOPE: This course will introduce the theory and application of what is often described as "differential and integral calculus." These are contained primarily in Chapters 2 through 6 of Stewart. Supplementary notes and text will be provided as appropriate on the web.
• Math 109 and General Education at HSU: This course satisfies part of the Area B General Education Requirement at HSU in the category of Inquiry into mathematical concepts and quantitative reasoning and their applications.

This requirement helps students cope with, and participate in, the changing world. Recognizing the importance of scientific methods as investigative tools, the courses present science as a unified discipline with a major impact on the human condition.
In particular this course attempts to enhance the general education goals to:

• provide an understanding of the nature, scope, and limits of science and its relation to other branches of human inquiry;
• teach the language of science to facilitate cognition, interpretation, and communication;
• develop scientific reasoning for use in the critical examination of information;
• identify sources of information for the pursuit of scientific inquiry;
• develop mathematical concepts and quantitative reasoning and demonstrate their widespread applications in problem solving;
• promote an understanding of the impact of scientific knowledge and technology on our civilization both past and present and recognize the contributions made by men and women; and
• consider the moral and ethical implications of science so as to nurture a respect for human values.
• \$\$ Algebra Review. I have listed several on-line sites (besides that of our text) for help with a review of algebra. You should use these in conjunction with the course when your background needs help.We will do some review of key topics (lines and functions) during the first week of the course.
• \$\$ Try some preliminary problems on-line or the Backgrounds Check Quiz on Blackboardor the calculus PRETEST (One attempt only  ....from SFSU).
If you don't do well on the on-line backgrounds assessment quiz or the calculus pretest , see me soon!

• TESTS AND ASSIGNMENTS: There will be several tests in this course. There will be many on-line reality check quizzes, two midterm exams and a comprehensive final examination (to be taken during the last two days of the course).
• We will use Blackboard for on-line reality quizzes. Click here for some information on how to use Blackboard.
• You can also go directly to the HSU Blackboard .
•  Homework assignments are made regularly. They should be done neatly.  Problems from the assignments will be discussed in class.
• 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 may be asked to respond to some relevant questions on  Blackboard  under the CD report title. These questions may be related to the solution of a specific problem, the development of a concept, or the organization of a technique as presented on the CD.  Each CD tutorial question will add 5 points to your CD Tutorial point total. CD Tutorial work will be used in determining the 50 course points.
• Exams will be announced at least one week in advance.
• THE FINAL EXAMINATION WILL BE GIVEN DURING THE LAST TWO CLASS MEETINGS.
• The final exam will be comprehensive, covering the entire course work.
• 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! ***

• 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, various individual and cooperative assignments.
• Midterm exams will be worth 100 points each and the final exam will be worth 200 or 300 points.
• On-line Reality quizzes will be used to determine 150 points.[I will not use the lowest 20% of these scores.]
• The CD tutorial responses 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 .
 Reality Quizzes 150 points CD Tutorials 50 points 2 Midterm Examinations 200 points Final Examination 200/300 points Total 600/700 points

Notice that only 400 or 500 of these points are from examinations, so regular participation with reality quizzes and the CD tutorals is essential to forming a good foundation for your grades as well as your learning.

In my experience students who are actively engaged in learning and participating regularly in a variety of activities will learn and understand more and retain more of what they learn. Each component of the course allows you a different way to interact with the material.

MORE THAN 4 ABSENCES MAY LOWER THE FINAL GRADE FOR POOR ATTENDANCE.

** See the university course schedule for the dates related to the following :

No drops will be allowed without "serious and compelling reasons" and a fee.
No drops will be allowed.
Students wishing to be graded with either CR or NC should make this request using the web registration procedures.
See the summer session course list for a full list of relevant days.
• Technology: The computer or a graphing calculator can be used for many problems.
• We will use Winplot. Winplot is freeware and may be downloaded from Rick Parris 's website or directly from one of these links for Winplot1 or Winplot2 . This software is small enough to fit on a 3.5" disc and can be used on any Windows PC on campus. You can find introductions to Winplot on the web.
• Students wishing help with any graphing calculator should plan to bring their calculator manual with them to class.
• Graphing Calculators: Though much of our work this semester will be using the computer, graphing calculators are welcome and highly recommended. The HP48G, HP 49 and the TI-89 and 92 are particularly useful though most graphing calculators will be able to do much of the work. HP48G's will be available for students to borrow for the term by arrangement with the Math department. Supplementary materials will be distributed if needed. If you would like to purchase one or have one already, let me know. Students wishing help with any graphing calculator should plan to bring their calculator manual with them. I will try to help you with your own technology when possible during office hours or by appointment (not in class).
• Use of Office Hours : Many students find beginning calculus difficult because of weakness in their pre-calculus background skills and concepts. A grade of C in Math 115 (Algebra and Elementary Functions) 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.
• I may 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.
• Later in the semester optional hours will be available to discuss routine problems from homework and reality check quizzes as well as using technology.
• 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.