Martin Flashman's Courses
Math 110 Calculus II Fall, '02
MRF 10:00-10:50 pm FOR 204A
Tuesday 10:00-10:50 pm WFB 258
Final Exam  Thursday Dec. 19: 10:20 12:20
Self Scheduled Final Exam Information
Final Topic Check List
Check out BLACKBOARD for final grades

 Week Monday Tuesday Thursday Friday 1 8/26 Introduction & Review 8/27  More review.  Differential equations and Direction Fields IV.D 8/29 Euler's Method  IV.E 8/30 More Euler's Method Discussed 2 9/ 2  No Class.  Labor Day. 9/3 More euler's method and Direction Fields.  Exponential functions y=2x. I.F.2. 9/5 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 9/6 Applications to graphing. Breath 3 9/9 More on the relation between the DE y'=y with y(0)=1  and ex.  Start work on logarithms. [ln(b)=a means ea=b.] 9/10 Quick summary I of exponential function.  The natural logarithm function:I.F.2 9/12 y = ln (x) and ln(2)  ln|x| and integration of 1/x.  logarithmic differentiation. 9/13Models for learning.  y' = k / x; y(1)=0. k =1  VI.B  7.3 & 7.4, 7.2* 4 9/16 Integration by parts I  8.1 (w/o ex. 5) 9/17  Connections: 7.4* VI.C  ln(exp(x)) = x  exp(ln(y)) = y 9/19 The Big Picture  Begin Arctan.VI.D 9/20 More on Arctan. 5 Summary #2 9/23 More on Arctan. 9/24  Integration by parts. II  8.1 and VII.C  Separation of variables. 9/26 10.3 Growth/Decay Models.10.4  Improper Integrals I 9/27 More on improper integrals Breath 6 Exam I  Self scheduled 10/2  Covers   [8/26,9/28] 9/30 Numerical Integration.(Linear) 10/1 Numerical Integration. (quadratic) V.D 10/3  Numerical Integration. (quadratic) V.D 10/4The Logistic Model 10.5 7 10/7 Integration of rational functions I.VII.F 10/8 Rational functions II. 10/10 More Rational functions VII.F 10/11-Darts  Probability density, mean Breath (9.5) 8 Summary #3 due 10/15 10/14 -More darts 10/15Darts  Probability density, mean 10/17 One more Meany!?  Rational functions III VII.F  .  . 10/18 End Rational Functions Begin Improper Integrals II comparison tests? 9 10/21 Improper Integrals II 10/22 comparison tests 10/24 Taylor Theory I.IXA 10/25 Taylor theory II IXA..  IXB  Applications: Definite integrals and DE's. 10Summary #4 due 10/29 10/28 Taylor theory III. IXB MacLaurin Polynomials 10/29 Taylor theory III. IXB  Taylor Theory for remainder proven! 10/31IX.C  Taylor Theory derivatives, integrals, and ln(x). 11/1 NO CLASS! 11 Exam II  self scheduled 11/6  Covers   [9/30,11/1] 11/4 More on finding MacClaurin Polynomials & Taylor theory.IX.D 11/5 Begin Sequences and series . 11/7 Geometric sequences  12.1 & X.A  Sequence properties. 11/8 Use of absolute values  Incr&bdd above implies convergent. 12 11/11geometric series  Series Conv. I 11/12  Geometric and Taylor Series.  The divergence test.  Harmonic Series.  Series Conv. II 11/14 12.3 Series Conv. III Positive series & Integral test. 11/15 Alternating Series [12.5]  Trig Integrals 8.2  I sin&cos 13 Summary #5 due 11/19 11/18  Taylor Series convergence.X.B1_4  Theorem on RnSeries Conv. IV  Trig Integrals 8.2 II sec&tan 11/19 Series Conv. V  Positive comparison test [12.4 ++]?  Ratio test  for Positive Series X.B5 11/21Series Conv.VI Absolute conv. & conditional:  The General ratio test:  Power Series I  XI.A 11/22 L'Hospital's rule I [7.7]  Power Series II (Interval of convergence)XI.A 14 No Classes  Thanksgiving 11/25 11/26 11/28 Thanksgiving 11/29 15 12/2  Power Series III (DE's)  L'Hospital II. 12/3 Conics I Intro to loci-analytic geometry issues.(parabolae, ellipses) 12/5  L'Hospital III  Conics II More on Ellipse and Parabola. 12/6 Trig substitution (begin- area of circle) I (sin) VII.E 16 12/9  Conics III  The hyperbolae  Other Inverse Functions (Arcsin)  Trig substitution II (tan) 12/10 The conics IV  Trig Substitution III (sec) 12/12 Arc Length VIII.B  Taylor Series 12.10 12/13 How Newton used Geometric series to find ln(.9)  Proof Of L'Hospital's Rule?  Hyperbolic functions: DE's, Taylor Series, Algebra  and Hyperbolas.  exp(pi*i) = -1 17 Final Examination Self scheduled 12/16 12/17 12/19 12/20
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Fall, 2002                 COURSE INFORMATION               M.FLASHMAN
MATH 110 : CALCULUS II                      MTRF 10:00-10:50 A.M. FH 235
OFFICE: Library 48                                        PHONE:826-4950
Hours (Tent.):  MTF 3:20-4:40 AND BY APPOINTMENT or chance!
E-MAIL:flashman@axe.humboldt.edu                WWW:      http://flashman.neocities.org/
***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.
• 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.
• We will use Blackboard for some on-line reality quizzes. Here is some information about how to use Blackboard.
• You can also go directly to the HSU Blackboard.
• 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 self-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. Groups wishing a review of particular topics from Calculus I  may schedule these during my office hours or on a Wednesday. Don't be shy about asking for an appointment outside of the scheduled office hours.

Fall, 2002     Problem Assignments - Updated regularly. (Tentative as of 8-15-02)       M.FLASHMAN
MATH 110 : CALCULUS II                   Stewart's Calculus 4th ed'n.
 DateDue: Read: Do: 8-27 IV.D Background   Reality Check 8-29 IV.D 1-11 odd [parts a and b only] 23 24 9-3 4.10 43 45 47 48 51 52 8-30 10.2 p 620-624 middle (i) 2-6 9 11 *15 9-3 10.2 p624-626 (ii) 21 23 8-30 3.10 7, 21, 33 8-30 IV.E 5-9 odd (a&b) 9-3 IV.E 20 21 24 9-5 10.2 (iii)13 14 19a 9-5 exponential functions  I.F.2  Stewart: pp 416-422 9-6 I.F.2 3 4 9-6&9 VI.A 9-6 7.2 (i) 29 33 34 37 47-51 9-9 7.2 (ii)57 61 63 53 9-9 7.2 (iii) 62 70 71-77odd 79 80 85 86 9-9 7.3 pp 428-430   (review of logs) 9-10 7.3 pp 428-430  (review of logs) 3-17 odd 31 33 35 41 47 59-61 *78 9-10 VI.A 9 10 15 16 9-10&12 VI.B. 9-12 7.4 pp 435-439 (i) 3,7,9,13 25 28 8 22 9-16 *7.2 9-13 7.4 (ii) 15 13 35 53 (changed 9-12) 9-13 (Log diff'n ) (iii) 45-47 52(changed 9-12) 58 *64 9-16 (Integration ) (iv) 65 - 71 odd 74-76 80 81 9-19 VI.B 13 14 9-19 VI.C 9-19 p468 19 23 33 37 51 9-20 inverse tangent   p472-3 9-20 7.5 2a 3a 5b 16 9-20 VI.D

 DateDue Read: Do: 9-23 VI.D 1-4 9-13 21 *(22&23) 9-23 7.5 Examples 9&10 (i) 25-27 34 38 58 59 9-24 (ii) 62 64 67 69 70 74* 75* TBA (iii) 22 23 24 29 20 47 48 63 68 9-23-24 Read VII.C 9-17 8.1 (parts) (i)1-11odd 29 30 51 (see page 390). 9-26 (ii) 15  [oops: 21 removed 9-26] 23 25 33 41 42 45 46 9-26 10.3 (sep'n of var's)(i) (i) 1 3 4 7 9-27 (ii) 9 10 15 29 9-27 10.4 pp637-641  (growth/decay models) (i) 1-7odd 9-30 10.4 pp641-642 (ii)9-11 9-30 10.4 pp642-643 (iii) 13 14 17 10-7 10.5 (logistic model) 10-7 Begin reading VII.F through Example VII.F.5  (rational functions) 10-11 (Again) 10.5 (oops- sorry if you thought this was VII.F) 1 5 *(11&12) 10-1 8.7(num'l integr'n) (i) 1 4 7a 11(a&b) 27 (n=4&8) 33a 10-4 (simpson's method) (ii) 7b 11c 31 32 35 36 *44 More help on   Simpson's rule,etc  can be found in V.D 9-27 8.8 (improper integrals) Type I only[omit ex. 2] 9-30 8.8 type I (i)3 5 7 8 9 9-30/ 10-1 (ii)13 21 41 10-22 8.8 type II (iii) 27-30 33 34 37 38 10-24 8.8 comparison (iv) 49 51 55 *60 61 57 71 10-24 IXA

 DueDate Read: Do: 10-8 Begin VII.F  (rational functions) 10-8 8.4 (i) 13 14 29 10-10 8.4 (ii) 15 16 17 20 21 10-11 (new) VII.F 5 6 7 17 10-11 10.5 (Again) 1 5 10-14 8.4 (iii) 62 63 65 10-18 8.4 (iv) 31 35 36 25 10-10/11 Darts 10-14&15 9.5 pp 603-607  andDarts 10-17 9.5 pp 603-607  andDarts 1,3,4,5 10-21 VII.F  on-line  check work on-line with Mathematica 1 3 7 10 14 15 10-21 read 8.8 type II and comparison 10-25 IXA 1 2 10-28 IXA 3,  4 6 8 9 *10 10-25&28 Read IX B 10-29 IXB (i)1 2 4 5 7 10-31 IXB (ii) 11 13 14 *23 10-31 IX.C 11-4 IX.C (i) 1-4 11-4 IX.C (ii) 5-9 11-4 IX.C (iii) 12 14 16-18 11-4 IX.D 11-5 IX.D 1 3 5 11-5 IX.D 8 10 14 15 11-7 X.A 11-8 X.A 1-3 5 7-9 11-8 12.1 pp 727-729;   examples 5-8   (sequences converge) (i) 3-23 odd 11-11 12.1 (ii)39-43 odd 51, 53-57 61 *63 *64 11-11 12.2 pp 738 -741   (series- geometric series) 11-12 12.2 pp 738 -741   (series- geometric series) 3 5 7 8 11-12And 14 X.B1_4 11-14 12.2  (series- geometric series): (i) 3 11-15 *51 11-15 12.2 (geometric, etc) (ii)41-45 49 50 51 11-15 12.2 READ!!pp 742-745 (iii) 21-31odd 11-15 12.3 (i) 1 3-6 11-18 12.3 (ii) 9-15 odd 11-18 X.B1_4 11-18 12.5 (i) 2-5; 23 25 31 11-19 12.5 (ii) 9-15 odd 11-18 8.2 (trig integrals) (i)1-5 7-15 odd 11-19 8.2 More Trig Integrals (ii) 21-25 odd 33 34 45 44 57 *59 *60 *61 11-21 12.4 (comparison test) (i) 3-7 11-22 (ii) 9-17 odd 11-21 X.B5 Ratio Test For Positive Series 11-21 12.6 Use the ratio test for positive series  to test for convergence. 2 17 23 20 29 *34 11-22 7.7 p487 Note 3 (L'H) 11-22 12.6 3-9 odd 19 *(31&32) 33 35 12-2 7.7 (i) 5-11 odd 12-2 7.7       examples 1-5 (ii) 21 27 29 15 23 18 33 12-3 7.7       examples 6-8 (iii) 39-43 odd 47-51 odd 12-6 7.7 examples 9-10 (iv) 55 57 63 *96 *97 12-2 XI.A and 12.8 3-11 odd 12-3 12.9 read Ex 1-3,5-8 12-5 12.9 (i)3-9 odd 25 29 34 *39 12-5 11.6 : pp 709-10 (thru ex.3) 12-6 11.6 : pp 709-10 (thru ex.3) (i) 1-7 odd 27 29 12-6 12.9 (ii) 13 14 21 27 12-6 8.3 (trig subs)  (i) pp 517-519 middle 12-9 8.3 (i)  VII.E 2 4 7 11 12-10 8.3 (ii) pp 519-520 3 6 19 9 12-12 8.3 (iii) pp 521-522 1 5 21 23 27 29 12-10 7.5 pp469-473 23 61 12-12 Ch 8 review problems p568 1-11 odd 33 35

 Date Due Read: Do: 12-3 11.6: pp709-11 12-9 11.6:    pp 711-12 (ii) 11-14 31 33 12-10 11.6 (iii) 19-22 37 39 47 *50 12-10 12.10 Read only pp785-792 12-10 12.7 Review of convergence tests 1-11 odd 12-12 Read 12.11 12-12 12.10 31 35 56 41 57 58 12-12 9.1 through p 578 12-13 9.1 1 3 19 21 9.2 5 7 9 9.5 1 3 7*

Math 110 Final Topic Check List     December 13, 2002 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 ln  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.  Differential Equations and 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  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) and at (a,b)