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.


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=2x. 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 ex. 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 Rn?
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://www.humboldt.edu/~mef2/
***PREREQUISITE: Math 109 or permission.


Back to Martin Flashman's Home Page :)

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