Martin Flashman's courses- Math 110 Fall, '02

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

Course Description
Course Assignments: Text Problem lists

Most Recent

Course Problem of the Week (sometimes with hints, etc.)Next POW due Friday, 12-6
Calculus web sites for surfing.
Want to find out what your learning style is? Here are two interesting learning styles inventories on the web: (1) NC State (2) Diablo Valley College .
Calculus @UTK Courses at the Univ. of Tenn. that use the Stewart text book (Calculus: Concepts and Contexts) They provide some useful supplementary materials for Math 109,110,210.
NEW! Visual Calculus (Univ. of Tenn.) calculus (first year) tutorials, etc.
Online Mathematics Tutorials at Harvey Mudd College! ...many excellent tutorials...Calc I-III, DE's, Linear Algebra.
For an entertaining 20 minute review of the major concepts of Calculus I, you might try Ed Burger's Calculus [Contact me for more information.]
Live-Math interactive on Calculus and Differential Equations files using Live-Math plug-in.
Calculus@Internet Many references to resources.
Math 1002 calculus at University Of Aberdeen: Calculus Notes from Ian Craw.
Notes for Winplot authored by Al Lehnen (Madison Area Technical College in Madison, Wisconsin)
Professor Biles' (HSU) Introductions to WinPlot, X(PLORE), and MSExcel
Some advice on how to suceed in a calculus course (at the Univ. of Nebraska)

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CALENDAR SCHEDULE **(Subject to change-** last revision noted 9-9-02)
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=2^x. 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 e^x. Start work on logarithms. [ln(b)=a means e^a=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 R_nSeries 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

MTF 3:20-4:40

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

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.

**Assignments and recommended problems I** (*= interesting but optional)
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

**Assignments and recommended problems II** (*= interesting but optional)
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

Assignments and recommended problems III (*= interesting but optional)
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) = ò₁^t1/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)

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