Martin Flashman's Courses
Math 110 Calculus II Fall, '01
MWF 2:00-3:10 pm SH  128
Check List of Topics for Final Examination

Fall, 2001     Problem Assignments - Updated regularly. (Tentative as of 8-15-01)       M.FLASHMAN
MATH 110 : CALCULUS II                   Stewart's Calculus 4th ed'n.
 DateDue: Read: Do: 8-29 IV.D Background  Reality Check 8-31 IV.D 1-11 odd [parts a and b only] 23 24 8-31 4.10 43 45 47 48 51 52 9-5 10.2 (i) 2-6 9 11 *15 9-7 (ii) 21 23 9-5 IV.E 5-9 odd (a&b) 20 21 24 9-7 exponential functions I.F.2 Stewart: pp 416-422 9-10/12? I.F.2 pp 428-430  (review of logs) 9-10 I.F.2 3 4 9-10 VI.A 9-10 7.2 (i) 29 33 34 37 47-51 57 61 63 53 9-12 (ii) 62 70 71-77odd 79 80 85 86 9-12 7.3 Review of logs 3-17 odd 31 33 35 41 47 59-61 *78 9-14 VI.B. 9-14 7.4 (i) 3,7,9,13 25 28 8 22 *7.2 9-17 7.4 (ii) 15 13 35 52 9-17 (Log diff'n ) (iii) 45-47 53 58 *64 9-17 (Integration ) (iv) 65 - 71 odd 9-19 VI.B 13 14 9-19 VI.C 9-19 p468 19 23 33 37 51 9-21 inverse tangent  p472-3 9-21 7.5 2a 3a 5b 16

 DateDue Read: Do: 9-21 VI.D 1-4 9-13 21 *(22&23) 9-21 7.5 (i) 25-27 34 38 58 (ii) 59 62 64 67 69 70 74* 75* (iii) 22 23 24 29 20 47 48 63 68 9-24 Read VII.C 9-24 8.1 (parts) (i)1-11odd 33 51 54 9-26 (ii) 15, 21 23 25 29 30 41 42 45 46 9-26 10.3(sep'n of var's)(i) (i) 1 3 4 7 9-28 (ii) 9 10 15 10-1 10.4 (growth/decay models) (i) 1-7odd 10-1 (ii)9-11 10-3 (iii) 13 14 17 10-8 10.5 (logistic model) 1 5 *(11&12) 10-3 8.7(num'l integr'n) (i) 1 4 7a 11(a&b) 27 (n=4&8) 33a 10-8 (simpson's method) (ii) 7b 11c 31 32 35 36 *44 10-8 More help on  Simpson's rule,etc can be found in V.D 9-28 8.8 (improper integrals) (i)3 5 7 8 9 13 21 41 10-15 finish reading 8.8 10-17 (ii) 27-30 33 34 37 38 10-19 (iii) 49 51 55 *60 61 57 71
 DueDate Read: Do: 10/10 BeginVII.F (rational functions) 10/10 8.4 (i) 13 14 29 10/10 (ii) 15 16 17 20 21 10/12 (iii) 31 35 36 62 25 10/10&12 Darts 10/17 9.5 pp 603-607 andDarts 1,3,4,5 TBA VII.F 1 3 7 10 14 15 10/15&17&19 IXA 10/22 IXA 1-3 10/22 IXA 4 6 8 9 *10 10/22 Read IX B 10/24 IXB (i)1 2 4 5 7 10/26 (ii) 11 13 14 *23 10/26 IX.C (i) 1-5 10/29 IX.C (ii) 6-9 10/29 IX.C (iii) 12 14 16-18 10/31 IX.D 1 3 5 8 10 14 15 11/2 12.1 pp 727-729;  examples 5-8  (sequences converge) 10/31 X.A 11/2 X.A 1-3 5 7-9 11/5 12.1 (i) 3-23 odd 39-43 odd 11/5 (ii)51 53-57 61 *63 *64 11/5 12.2 pp 738 -741  (series- geometric series) 11/7 12.2 (series- geometric series): (i) 3 11-15 35-37 *51 11/9 X.B1_4 11/9 12.2 (geometric, etc) (ii)41-45 49 50 51 11/12 12.2 pp 742-745 (iii) 21-31odd 11/14 12.3 (i) 1 3-7 (ii) 9-15 odd X.B1_4 11/12 8.2 (trig integrals) (i)1-5 7-15 odd 11/14 (ii) 21-25 odd 33 34 45 44 57 *59 *60 *61 11/28 8.3 (trig subs) pp 517-519 middle 11/28 (i) pp 517-519 middle 2 4 7 11 11/30 (ii) pp 519-520 3 6 19 9 12/3 (iii) pp 521-522 1 5 21 23 27 29 Ch 8 review problems 1-11 odd 33 35

 Date Due Read: Do: 11/16 7.7 p 487 note 3 (i) 5-11 odd 11/16 examples 1-5 (ii)21 27 29 15 23 18 33 11/16 examples 6-8 (iii) 39-43 odd 47-51 odd 11/28 examples 9-10 (iv) 55 57 63 *96 *97 12/5 11.6: pp709-11 (thru ex.3) 12/7 11.6 : pp 709-10 (i) 1-7 odd 27 29 12/7 pp 711-12 (ii) 11-14 31 33 12/10 (iii) 19-22 37 39 47 *50 11/28 12.4 (comparison test) (i) 3-7 11/30 (ii) 9-17 odd 11/28 12.5 11/30 (i) 2-5; 23 25 31 12/3 (ii) 9-15 odd 11/30 12.6 Use the ratio test  to test for convergence. 2 17 23 20 29 *34 12/3 12.6 3-9 odd 19 *(31&32) 33 35 11/30 X.B5 12/5 12.5 3-11 odd 21 23 27 *35 12/5 12.7 1-11 odd 12/5 XI.A 12/10 12.8 3-11 odd 12/12 12.9 3-9 odd 25 29 12/12 Read Only 12.10 31 35 56 41 45 57 58 9.1 though p 578 12/12 9.1 1 3 19 21 9.2 5 7 9 9.5 1 3 7*

 Week Monday Wednesday Friday 1 8/27 Introduction & Review 8/29  More review. Differential equations and Direction Fields IV.D 8/31 Euler's Method  IV.E 2 9/3 No Class.  Labor Day. 9/5 More euler's method Exponential functions y=2x. I.F.2. 9/7e estimate from (1+1/n)n.  Begin 7.2 and Models for (Population) Growth  and Decay: y' = k y; y(0)=1. k = 1. The exponential function.VI.A Applications to graphing. 3 9/10More on the relation between the DE y'=y with y(0)=1  and ex. The natural logarithm function.I.F.2  y = ln (x) and ln(2) Models for learning. y' = k / x; y(1)=0. k =1 9/12 VI.B 7.3 & 7.4, 7.2* 9/14 Connections: 7.4* VI.C logarithmic differentiation. 4 9/17 ln(exp(x)) = x exp(ln(y)) = y 9/19 The Big Picture Arctan.VI.D 9/21 More on Arctan. Integration by parts. 8.1 and VII.C 5 9/24 Parts with Definite Integrals. Separation of variables. 10.3 9/26 Growth/Decay Models.10.4  Improper Integrals I 9/28 More on improper integrals 6 Exam I  Covers  [8/28,9/28] 10/1 Numerical Integration.(Linear) 10/3Numerical Integration. (quadratic) V.D The Logistic Model 10.5 10/5 Examination #1 [8/27, 9/28] 7 10/8Integration of rational functions I.VII.F 10/10 probability density-Darts Rational functions II. VII.F 10/12  More Darts Probability density, mean 8 10/15 Rational functions III VII.F Improper Integrals II 10/17 Improper Integrals III comparison tests. 10/19 Taylor Theory I. IXA Applications: Definite integrals and DE's.IXA . 9 10/22Taylor theory II.IXB 10/24  Taylor theory III. IXB & IX.C 10/26  Taylor Theory derivatives, integrals, and ln(x). 10 10/29 Taylor theory.IX.D 10/31Begin Sequences and series  12.1 & X.A 11/2 Geometric sequences  Sequence properties. Use of absolute values. Incr&bdd above implies convergent. 11 Exam II Covers  [10/2,11/2] 11/5 How Newton used Geometric series to find ln(.9) geometric series Series Conv. I 11/7 Examination #2 [10/2, 11/2]. 11/9  Trig Integrals 8.2 I sin&cos Geometric and Taylor Series.  Series Conv. II The divergence test. Harmonic Series. 12 11/12 Trig Integrals 8.2 II sec&tan Series Conv. III 12.3 Positive series & Integral test. Taylor Series convergence.X.B1_4 Prove Theorem on Rn? 11/14 L'Hospital's rule I [7.7] 11/16 L'Hospital II. 13 No Classes Thanksgiving 11/19 11/21 11/23 Thanksgiving 14 11/26  Series Conv. IV Positive comparison test [12.4 ++] Begin Alternating Series [12.5]  Trig substitution (begin- area of circle) I (sin) 11/28 Series Conv. V Misc & ratio test intro. Trig substitution II (tan) 11/30 Trig Substitution III (sec) Other Inverse Functions (Arcsin)   Series Conv.VI Absolute conv. & conditional Convergence 15 12/3 Power Series I General ratio test: (Using the ratio test - convergence) XI.A Conics I Intro to loci-analytic geometry issues. Conics II(parabolae, ellipses) 12/5 Power Series II (Interval of convergence)XI.A (Calculus) Conics III hyperbolae 12/7 Breath  Power Series III (DE's) 16 12/10 Arc Length VIII.B Taylor Series 12.10 12/12 More on 12.10 Proof Of L'Hospital's Rule? 12/14 int(exp(-x^2),x)) 17 Final Examinations 12/17 12/19 12/21
Math 110 Final Topic Check List     December 14, 2000 Core Topics are italicized.
 The Transcendental Functions.   The Natural Exponential Function.    Basic Properties    The Natural Logarithm Function.     L(t) = ò1t 1/x dx:          Basic properties of L(t) = ln(t) = LOG(t) .         "inverse" relation between L  and exp.          Applications of  LN .                  --Logarithmic Differentiation.                  --Functions with exponents:  a summary.   The Trigonometric Functions.     The Inverse Trigonometric Functions and Their Derivatives.     The Trigonometric Functions and Their Derivatives.     Integration of Trigonometric Functions and Elementary Formulas.  Integration , Tangent Fields, and Integral Curves.    Numerical Approximations.             Euler's Method.             Midpoints.             Trapezoidal Rule.             Parabolic (Simpson's) Rule.    Integration by Parts.     Integration of Trigonometric Functions.    Trigonometric Substitutions.    Integration of Rational Functions.             Simple examples. Simple Partial fractions.    Separation of Variables. Applications: Probability: distributions, density, mean     Arc Length Formula Improper Integrals: Extending the Concepts of Integration.                Integrals with noncontinuous functions.                Integrals with unbounded intervals. L'Hopital's Rule: 0/0    inf/inf    inf - inf   0*inf    0^ 0   1^inf Taylor's Theorem.   Taylor Polynomials. Calculus.   Using Taylor Polynomials to Approximate:  Error  Estimation.       Derivative form of the remainder.       Approximating known functions, integrals       Approximating solutions to diff'l equations using Taylor's theorem. Sequences and Series: Fundamental Properties.   Sequences.   Simple examples and definitions: visualizing sequences.          How to find limits.          Key theory of convergence.              The algebra of convergence.              Convergence for monotonic sequences.   Geometric series. Harmonic series. Taylor approximations.   Theory of convergence (series).      The divergence test.      Positive series.       Bounded convergence tests.       Integral tests.       Ratio test (Part I).       Absolute convergence.          Absolute convergence implies convergence.          Alternating Series Test. Ratio test (Part II). Power Series: Polynomials and Series.  The radius and interval of convergence.  Functions and power series [derivatives and integrals]. Analytic Geometry, the Conic Sections           The Conic Sections as Loci.  Equations for conics centered at (0,0)

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Fall, 2001                 COURSE INFORMATION               M.FLASHMAN
MATH 110 : CALCULUS II                      MWF29:00-3:10 P.M. SH128
OFFICE: Library 48                                        PHONE:826-4950
Hours (Tent.):  MWF 9:30-10:30  AND BY APPOINTMENT or chance!
E-MAIL:flashman@axe.humboldt.edu                WWW:      http://www.humboldt.edu/~mef2/
***PREREQUISITE: Math 109 or permission.

• TEXTS: Required: Calculus 4th Edition by James Stewart.(Brooks/Cole, 1999)

• Excerpts from Sensible Calculus by M. Flashman as available from this webpage.
• Catalog Description: Logarithmic and exponential functions, inverse trigonometric functions, techniques of integration, infinite sequences and series, conic sections, polar coordinates..
• SCOPE:This course will deal with a continuation of the theory and application of what is often described as "integral calculus" as well as the calculus of infinite series. These are contained primarily in Chapters 7 through 11 of Stewart. Supplementary notes and text will be provided as appropriate through this webpage.

•
• TESTS AND ASSIGNMENTS There will be several tests in this course. There will be several reality check quizzes and cooperative problem assignments, and two self-scheduled midterm exams.
• Homework assignments are made regularly and should be passed in on the due date.

• Homework should be neat, legible and clearly organized. Sloppy and poorly organized homework will not be graded.
Homework is graded Acceptable/Unacceptable with problems to be redone. Redone work should be returned for grading promptly.
• Writing Assignments: At the beginning of each class you will submit a brief statement (at most four sentences) describing the content from previous class, a question related specifically to the reading assignment for that class, and any topics you would like to discuss further either in class or individually. I will read these and return them the next class. These will be used in determining 30 of the 100 points assigned for homework.

• No late reports will be accepted! [Notice that missing one class will result in missing two report opportunities.]
• Mid-Term Exams will be scheduled and announced at least one week in advance.
• THE FINAL EXAMINATION WILL BE SELF SCHEDULED .
• 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! ***
• Partnership 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. Partners will receive corrected photocopies.

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

Each week partnerships will submit a response to the "problem/activity of the week." These problems will be special problems distributed in class (and on this web page) or selected starred problems from the assignment lists.

All  cooperative problem  work will be graded 5 for well done; 4 for OK; 3 for acceptable; or 1 for unacceptable; and will be used together with participation in writing summaries in determining the 80 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, various individual and cooperative assignments.
• 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.
•  2 Midterm exams 200 points Daily Writing 30 points Homework 70 points Reality Quizzes 100 points Cooperative work 80 points Final exam 200/300 points TOTAL 680/780 points
The total points available for the semester is either 680 or 780. 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 3 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.
No drops will be allowed.
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.
See the fall 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 Winplot1or 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.
• Graphing Calculators: Graphing calculators are welcome and highly recommended. Most graphing calculators will be able to do much of this course's work. I may use the HP48G for some in-class work but will generally use Winplot. 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 one or have one already, let me know.
• I will try to help you with your own technology during the optional "5th hour"s, or by appointment (not in class).Students wishing help with any graphing calculator should plan to bring their calculator manual with them to class..

•
• Use of  Office Hours: Many students find the second semester of calculus difficult because of weakness in their Calculus I and pre-calculus background skills and concept. A grade of C in Math 109 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 indicividuals 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. 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.