Week 



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)
lnx 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  10/11Darts
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_{n}Series 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 locianalytic 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 
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.
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.
DateDue:  Read:  Do:  
827  IV.D  Background
Reality Check 

829  IV.D  111 odd [parts a and b only]  23  24  
93  4.10  43  45  47  48  51  52  
830  10.2 p 620624 middle  (i) 26  9  11  *15  
93  10.2 p624626  (ii) 21  23  
830  3.10  7, 21, 33  
830  IV.E  59 odd (a&b)  
93  IV.E  20  21  24  
95  10.2  (iii)13  14  19a  
95  exponential functions
I.F.2 Stewart: pp 416422 

96  I.F.2  3  4  
96&9  VI.A  
96  7.2  (i) 29  33  34  37  4751  
99  7.2  (ii)57  61  63  53  
99  7.2  (iii) 62  70  7177odd  79  80  85  86  
99  7.3 pp 428430
(review of logs) 

910  7.3 pp 428430
(review of logs) 
317 odd  31  33  35  41  47  5961  *78 
910  VI.A  9  10  15  16  
910&12  VI.B.  
912  7.4 pp 435439  (i) 3,7,9,13  25  28  8  22  
916  *7.2  
913  7.4  (ii) 15  13  35  53 (changed 912)  
913  (Log diff'n )  (iii) 4547  52(changed 912)  58  *64  
916  (Integration )  (iv) 65  71 odd  7476  80  81  
919  VI.B  13  14  
919  VI.C  
919  p468  19  23  33  37  51  
920  inverse tangent
p4723 

920  7.5  2a  3a  5b  16  
920  VI.D 
DateDue  Read:  Do:  
923  VI.D  14  913  21  *(22&23)  
923  7.5 Examples 9&10  (i) 2527  34  38  58  59  
924  (ii) 62  64  67  69  70  74*  75*  
TBA  (iii) 22  23  24  29  20  47  48  63  68  
92324  Read VII.C  
917  8.1 (parts)  (i)111odd  29  30  51 (see page 390).  
926  (ii) 15
[oops: 21 removed 926] 
23  25  33  41  42  45  46  
926  10.3 (sep'n of var's)(i)  (i) 1  3  4  7  
927  (ii) 9  10  15  29  
927  10.4 pp637641
(growth/decay models) 
(i) 17odd  
930  10.4 pp641642  (ii)911  
930  10.4 pp642643  (iii) 13  14  17  
107  10.5 (logistic model)  
107  Begin reading VII.F
through Example VII.F.5
(rational functions) 

1011 (Again)  10.5 (oops sorry if you thought this was VII.F)  1  5  *(11&12)  
101  8.7(num'l integr'n)  (i) 1  4  7a  11(a&b)  27 (n=4&8)  33a  
104  (simpson's method)  (ii) 7b  11c  31  32  35  36  *44  
More help on
Simpson's rule,etc can be found in V.D 

927  8.8 (improper integrals) Type I only[omit ex. 2]  
930  8.8 type I  (i)3  5  7  8  9  
930/ 101  (ii)13  21  41  
1022  8.8 type II  (iii) 2730  33  34  37  38  
1024  8.8 comparison  (iv) 49  51  55  *60  61  57  71  
1024  IXA 
DueDate  Read:  Do:  
108  Begin VII.F
(rational functions) 

108  8.4  (i) 13  14  29  
1010  8.4  (ii) 15  16  17  20  21  
1011 (new)  VII.F  5  6  7  17  
1011  10.5 (Again)  1  5  
1014  8.4  (iii) 62  63  65  
1018  8.4  (iv) 31  35  36  25  
1010/11  Darts  
1014&15  9.5 pp 603607
andDarts 

1017  9.5 pp 603607
andDarts 
1,3,4,5  
1021  VII.F
online
check work online with Mathematica 
1  3  7  10  14  15  
1021  read 8.8 type II and comparison  
1025  IXA  1  2  
1028  IXA  3, 4  6  8  9  *10  
1025&28  Read IX B  
1029  IXB  (i)1  2  4  5  7  
1031  IXB  (ii)  11  13  14  *23  
1031  IX.C  
114  IX.C  (i) 14  
114  IX.C  (ii) 59  
114  IX.C  (iii) 12  14  1618  
114  IX.D  
115  IX.D  1  3  5  
115  IX.D  8  10  14  15  
117  X.A  
118  X.A  13  5  79  
118  12.1 pp 727729;
examples 58 (sequences converge) 
(i) 323 odd  
1111  12.1  (ii)3943 odd  51, 5357  61  *63  *64  
1111  12.2 pp 738 741
(series geometric series) 

1112  12.2 pp 738 741
(series geometric series) 
3  5  7  8  
1112And 14  X.B1_4  
1114  12.2
(series geometric series): 
(i) 3  1115  *51  
1115  12.2 (geometric, etc)  (ii)4145  49  50  51  
1115  12.2 READ!!pp 742745  (iii) 2131odd  
1115  12.3  (i) 1  36  
1118  12.3  (ii) 915 odd  
1118  X.B1_4  
1118  12.5  (i) 25; 23  25  31  
1119  12.5  (ii) 915 odd  
1118  8.2 (trig integrals)  (i)15  715 odd  
1119  8.2 More Trig Integrals  (ii) 2125 odd  33  34  45  44  57  *59  *60  *61 
1121  12.4 (comparison test)  (i) 37  
1122  (ii) 917 odd  
1121  X.B5 Ratio Test For Positive Series  
1121  12.6 Use the ratio test for positive
series
to test for convergence. 
2  17  23  20  29  *34  
1122  7.7 p487 Note 3 (L'H)  
1122  12.6  39 odd  19  *(31&32)  33  35  
122  7.7  (i) 511 odd  
122  7.7 examples 15  (ii) 21  27  29  15  23  18  33  
123  7.7 examples 68  (iii) 3943 odd  4751 odd  
126  7.7 examples 910  (iv)  55  57  63  *96  *97  
122  XI.A and 12.8  311 odd  
123  12.9 read Ex 13,58  
125  12.9  (i)39 odd  25  29  34  *39  
125  11.6 : pp 70910 (thru ex.3)  
126  11.6 : pp 70910 (thru ex.3)  (i) 17 odd  27  29  
126  12.9  (ii) 13  14  21  27  
126  8.3 (trig subs)
(i) pp 517519 middle 

129  8.3 (i)
VII.E 
2  4  7  11  
1210  8.3 (ii) pp 519520  3  6  19  9  
1212  8.3 (iii) pp 521522  1  5  21  23  27  29  
1210  7.5 pp469473  23  61  
1212  Ch 8 review problems p568  111 odd  33  35 
Date Due  Read:  Do:  
123  11.6: pp70911  
129  11.6: pp 71112  (ii) 1114  31  33  
1210  11.6  (iii) 1922  37  39  47  *50  
1210  12.10 Read only pp785792  
1210  12.7 Review of convergence tests  111 odd  
1212  Read 12.11  
1212  12.10  31  35  56  41  57  58 
1212  9.1 through p 578  
1213  9.1  1  3  19  21  
9.2  5  7  9  
9.5  1  3  7* 
The Transcendental Functions.
The Natural Exponential Function. Basic Properties The Natural Logarithm Function. L(t) = ò_{1}^{t }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
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.
Power Series: Polynomials and Series.
Analytic Geometry, the Conic Sections

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