Martin Flashman's courses- Math 110 Fall, '00

Martin Flashman's Courses
Math 110 Calculus II Fall, '00
MTWR 9:00-9:50 Art 27
Final Exam Check List (including Core Topic List)
Final Examination: self - scheduled rooms.

Course Description
Course Assignments: Text Problem lists

III

Course Problem of the Week (sometimes with hints, etc.)
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.
Visual Calculus (Univ. of Tenn.) calculus (first year) tutorials, etc.
Web-based study guides from Oregon State University
For an entertaining 20 minute review of the major concepts of Calculus I, you might try Thinkwell's Calculus [Contact me for more information.]
Live-Math interactive on Calculus and Differential Equations files using Live-Math plug-in.
Instructions for Winplot prepared by Gerald Hile (Hawaii).
Notes for Winplot authored by Al Lehnen (Madison Area Technical College in

Madison, Wisconsin)

Calculus web sites for surfing.

Back to Martin Flashman's Home Page :) Last updated: 8/25/00 Fall, 2000 Problem Assignments - Updated regularly. (Tentative as of 8-25-00) M.FLASHMAN
MATH 110 : CALCULUS II Stewart's Calculus 4th ed'n.

**Assignments and recommended problems I** (*= interesting but optional)
DateDue:	Read:	Do:
8-29	Background Reality Check
8-30	IV.D	1-11 odd	23	24
8-30	4.10	43	45	47	48	51	52
8-31	10.2	(i) 2-6	9	11	*15
9-5		(ii) 21	23
9-5	IV.E	5-9 odd (a&b)	20	21	24
9-6	*pp 416-422* *exponential functions*
9-6	*I.F.2* *pp 428-430* *(review of logs)*
9-7	*I.F.2*	3	4
9-7&11	VI.A
9-7	7.2	(i) 29	33	34	37	47-51	57	61	63	53
9-11		(ii) 62	70	71-77odd	79	80	85	86
9-11	7.3 Review of logs	3-17 odd	31	33	35	41	47	59-61	*78
9-12	VI.B.
9-13	7.4	(i) 3,7,9,13	25	28	8	22
9-14	*7.2
9-14	7.4	(ii) 15	13	35	52
9-18	(Log diff'n )	(iii) 45-47	53	58	*64
9-18	(Integration )	(iv) 65 - 71 odd
9-14	VI.B	13	14
9-14	VI.C
9-19	p468	19	23	33	37	51
9-19	inverse tangent p472-3
9-19	7.5	2a	3a	5b	16

**Assignments and recommended problems II** (*= interesting but optional)
DateDue	Read:	Do:
9-20	VI.D	1-4	9-13	21	*(22&23)
9-20	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
9-21	Read VII.C
9-21	8.1 (parts)	(i)1-11odd	33	51	54
9-25		(ii) 15, 21	23	25	29	30	41	42	45	46
9-25	10.3(sep'n of var's)	1	3	4	7	9	10	15
9-26	10.4 (growth/decay models)	(i) 1-7odd
9-27		(ii)9-11
9-28		(iii) 13	14	17
9-27	10.5 (logistic model)	1	5	*(11&12)
10-2	8.7(num'l integr'n)	(i) 1	4	7a	11(a&b)	27 (n=4&8)	33a
10-11	(simpson's method)	(ii) 7b	11c	31	32	35	36	*44
10-11	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
10-10		(ii) 27-30	33	34	37	38
10-11		(iii) 49	51	55	*60	61	57	71

**Assignments and recommended problems III** (*= interesting but optional)
DueDate	Read:	Do:
10/5	BeginVII.F (rational functions)
10/4	8.4	(i) 13	14	29
10/4		(ii) 15	16	17	20	21
10/5		(iii) 31	35	36	62	25
10/9	Handout on x ln(x).
10/10	VII.F	1	3	7	10	14	15
10/12	IXA
10/16	IXA	1-3
10/17	IXA	4	6	8	9	*10
10/17	Read IX B
10/18	IXB	(i)1	2	4	5	7
10/19		(ii)	11	13	14	*23
10/23	IX.C	(i) 1-5
10/23	IX.C	(ii) 6-9
10/24	IX.C	(iii) 12	14	16-18
10/25	IX.D	1	3	5	8	10	14	15
10/26	12.1 pp 727-729; examples 5-8 (sequences converge)
10/26	X.A
10/30	X.A	1-3	5	7-9
10/30	12.1	(i) 3-23 odd
10/31		(ii) 39-43 odd	51	53-57	61	*63	*64
10/.31	12.2 pp 738 -741 (series- geometric series)
11/1	12.2 (series- geometric series):	(i) 3	11-15	35-37	*51
11/1	X.B1_4
11/2	12.2 (geometric, etc)	(ii)41-45	49	50	51
11/7	12.2 pp 742-745	(iii) 21-31odd
11/14	12.3	(i) 1	3-7
11/14		(ii) 9-15 odd
11/9	X.B1_4
11/2	8.2 (trig integrals)	(i)1-5	7-15 odd
11/6		(ii) 21-25 odd	33	34	45	44	57	*59	*60	*61
11/13	9.5 pp 603-607 andDarts	1,3,4,5
11/28	8.3 (trig subs) pp 517-519 middle
11/29	(i) pp 517-519 middle	2	4	7	11
11/30	(ii) pp 519-520	3	6	19	9
12/4	(iii) pp 521-522	1	5	21	23	27	29
12/11?	Ch 8 review problems	1-11 odd	33	35

Assignments and recommended problemsIV (*= interesting but optional)
Date Due	Read:	Do:
11/27	7.7 p 487 note 3	(i) 5-11 odd
11/27	examples 1-5	(ii)21	27	29	15	23	18	33
11/28	examples 6-8	(iii) 39-43 odd	47-51 odd
12/5	examples 9-10	(iv) 55	57	63	*96	*97
12/5	11.6: pp709-11 (thru ex.3)
12/6	11.6 : pp 709-10	(i) 1-7 odd	27	29
12/6	pp 711-12	(ii) 11-14	31	33
12/7		(iii) 19-22	37	39	47	*50

	12.4 (comparison test)	(i) 3-7
		(ii) 9-17 odd
11/16	12.5	(i) 2-5; 23	25	31
11/27		(ii) 9-15 odd
11/15	12.6 Use the ratio test to test for convergence.	2	17	23	20	29	*34
11/29	12.6
11/30	12.6	3-9 odd	19	*(31&32)	33	35
	X.B5
	12.5	3-11 odd	21	23	27	*35
	12.7	1-11 odd
12/4	XI.A
12/4	12.8	3-11 odd
12/11	12.9	3-9 odd	25	29
12/13	12.10	31	35	56	41	45	57	58
12/11	9.1 though p 578
12/12	9.1	1	3	19	21
	9.2	5	7	9
	9.5	1	3	7*

CALENDAR SCHEDULE
(Subject to change)

Week	Mon.	Tues.	Wed.	Thurs.
1	8/28 Introduction & Review	8/29 Differential equations and Direction Fields IV.D [Demos from Bradley-Smith 1. 2 ]	8/30 More on Direction Fields	8/31 Euler's Method IV.E
2	9/4 No Class. Labor Day.	9/5 Exponential functions y=2^x. I.F.2; begin 7.2. e estimate from (1+1/n)ⁿ .	9/6 More on models for (Population) Growth and Decay: y' = k y; y(0)=1. k = 1.	9/7 The exponential function.VI.A
3	9/11Applications to graphing. More on the relation between the DE y'=y with y(0)=1 and e^x.	9/12 The natural logarithm function.I.F.2 y = ln (x) and ln(2) Models for learning. y' = k / x; y(1)=0. k =1	9/13 VI.B 7.3 & 7.4, 7.2*	9/14 Connections: 7.4* VI.C ln(exp(x)) = x exp(ln(y)) = y logarithmic differentiation. The Big Picture
4	9/18 Arctan.VI.D	9/19 Begin Integration by parts. 8.1 and VII.C	9/20 More integration by parts.	9/21 Parts with Definite Integrals. Separation of variables. 10.3
5	9/25 Growth/Decay Models.10.4	9/26 The Logistic Model 10.5	9/27 Improper Integrals I	9/28 More on improper integrals comparison test. Numerical Integration.(Linear)
6 Exam I Covers [8/28,9/28]	10/2 Integration of rational functions I.VII.F	10/3(probability density-Darts Examination #1 [8/28, 9/28]	10/4 Rational functions II	10/5 Rational functions III. VII.F
7	10/9.Improper Integrals II.	10/10 Improper Integrals III Numerical Integration. (quadratic) V.D	10/11 Taylor Theory I. IXA	10/12 Taylor Theory II. IXA
8	10/16 Applications: Definite integrals and DE's.IXA	10/17 Taylor theory III.IXB.	10/18 More on IXB.	10/19 Taylor theory IV. IX.C
9	10/23 Taylor Theory, derivatives, integrals, and ln(x).	10/24 Taylor theory.IX.D	10/25 Begin Sequences and series 12.1 & X.A	10/26 Geometric sequences Sequence properties.
10	10/30 Use of absolute values. Incr&bdd above implies convergent.	10/31 geometric series	11/1 Trig Integrals 8.2 I sin&cos	11/2 Trig Integrals 8.2 II sec&tan Geometric and Taylor Series. Series Conv. I
11 Exam II Covers [10/2,11/2]	11/6 How Newton used Geometric series to find ln(.9) Series Conv. II The divergence test.	11/7 Taylor Series convergence.X.B1_4 Harmonic Series. Series Conv. III	11/8 Breath Prove Theorem on R_n? More Darts, Probability density, mean. Examination #2 [10/2, 11/2]	11/9
12	11/13 12.3 Positive series & Integral test. Series Conv. IV	11/14 Positive comparison & ratio test [12.4 ++] Series Conv. V	11/15 alternating series Series [12.5] Conv. VI	11/16 Misc on series. Begin L'Hospital's rule I [7.7]
13 No Classes Thanksgiving	11/20	11/21	11/22	11/23 Thanksgiving
14	11/27 L'Hospital II Trig substitution (begin- area of circle) I (sin)	11/28 Continue Trig substitution II (sin) Other Inverse Functions (Arcsin) Series Conv. VII Absolute conv.	11/29 General ratio test: Series Conv.VIII Trig substitution III (tan)	11/30 Trig Substitution III (sec) Power Series I (Using the ratio test - convergence)XI.A
15	12/4 Conics I Intro to loci-analytic geometry issues L'Hospital III.	12/5Conics II(parabolae, ellipses) Proofs about absolute converg Power Series II (Interval of convergence)XI.A (Calculus)	12/6 Conics III hyperbolae	12/7 Power Series III (DE's)
16	12/11Arc Length VIII.B	12/12 Taylor Series 12.10	12/13 More on 12.10	12/14 int(exp(-x^2),x))
17 Final Examinations	12/18	12/19	12/20	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) = Integral from 1 to t of 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 and Difference Equations.
            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
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, 2000                 COURSE INFORMATION               M.FLASHMAN
MATH 110 : CALCULUS II                      MTWR 9:00-9:50 P.M. Art 27
OFFICE: Library 48                                        PHONE:826-4950
Hours (Tent.): M-R 10:15-11:20          AND BY APPOINTMENT or by 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.

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 the previous 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.

No late reports will be accepted! [Notice that missing one class will result in missing two report opportunities.]

The work on the daily writing will be worth 50 points (based on quality of work and coverage).

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.

2 Midterm exams	200 points
Daily Writing	50 points
Homework	80 points
Reality Quizzes	100 points
Cooperative work	80 points
Final exam	200 points
TOTAL	710 points

The total points available for the semester is 710. Notice that only 400 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

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 this link for Winplot . 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.

A version of X(PLORE) is available at the bookstore for MAC based PC's along with the PC version we may use.Windows and DOS versions of X(PLORE) are also available online...X(PLORE) for Windows.
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.

Optional "5th hour"s: 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. I will 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 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. These sessions should be especially useful for students having difficulty with the work and wishing to improve through a steady approach to mastering skills and concepts.

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