Week |
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Friday |
1 | 8/25 Introduction & Review (Thinkwell) |
8/26 More review. Differential equations and Direction Fields IVA IVB IVC 6.3; 6.5;11.1; 11.2 IV.D |
8/ Euler's Method 11.3; IV.E |
8/ More Euler's Method Discussed |
2 POW #1 Due 9/5 |
9/ 1
No Class. Labor Day. |
9/2 estimate e from (1+1/n)n.
Begin Models for (Population) Growth and Decay: y' = k y; y(0)=1. k = 1. The exponential function.VI.A |
9/4
More on the relation between the DE y'=y with y(0)=1 and
ex.
Models for learning. y' = k / x; y(1)=0. k =1 VI.B |
9/5 y = ln (x) and ln(2)
ln|x| and integration of 1/x. logarithmic differentiation.?? |
3 Summary #1 due 9/12 |
9/8 Review Substitution 7.1 (i) More on ln. Bounded learning and Arctan. VI.D |
9/9 More Review Substitution 7.1 (ii)Improper Integrals I 7.7 (i) |
9/11 More on improper integrals 7.7(ii) |
9/12 Separation of variables. 11.4, 11.5 |
4 POW #2 Due 9/19 |
9/15/Growth/Decay/Cooling Models. [Symbolic] The Logistic Model |
9/16 More logistic? All roads lead to Integration of rational functions 7.4 (i) I.VII.F |
9/18 More DE models. Rational functions II. | 9/19 More Rational functions? VII.F |
5 Summary #2 due 9/26 |
9/22 One more Meany!?
Rational functions III VII.F |
9/23 End Rational Functions | 9/25 Improper Integrals II 7.7; | 9/ 26 Begin (review) Numerical Integration.(Constant and Linear) 7.5 Improper Integrals and comparison tests III comparison tests 7.8? |
6 |
9/29 Integration by parts I and VII.C . |
10/1 Integration by parts. II | 10/3 Numerical Integration. (linear and quadratic)7.6, V.D | 10/4 Numerical Integration. (quadratic)7.6, V.D |
7 POW #3: Due 10/6 Exam I Self scheduled: 10/7 evening 10/8 day Summary #3 due 10/10 |
10/6 Last look at Numerical Integration Begin Taylor Theory I.IXA |
10/7 Review fro exam #1 | 10/9 Taylor theory II IXA..
IXB Applications: Definite integrals and DE's. |
10/10Taylor theory III. IXB
MacLaurin Polynomials |
8 POW #3: Due 10/20 | 10/13 IXB
MacLaurin Polynomials |
10/14 IXB
MacLaurin Polynomials |
10/16 IX.C Taylor Theory derivatives, integrals, and ln(x). |
10/17Taylor Theory for remainder proven? More on finding MacClaurin Polynomials & Taylor theory.IX.D . |
9Summary #4 due 10/24 |
10/20 Taylor theory.IX.D |
10/21
Begin Sequences and series. X.A Sequence properties |
10/ 23
Use of absolute values
geometric series
Geometric sequences. |
10/24
Unification. Geometric and Taylor Series. X.B1_4 9.2, 9.3 The divergence test. Harmonic Series. |
10POW #4: Due 11/3 | 10/27Series Conv. I
Incr&bdd above implies convergent. |
10/
12.3 Positive series & Integral test. Series Conv. II |
10/ Series Conv. III Alternating Series | 11/Taylor Series convergence. Theorem on RnSeries Conv. IV |
11 Summary #5 due 11/7 | 11/3
Series Conv. V Taylor polys and Series. |
11/4
Series to solve DE's - Motivations f''(x) = f(x) with f(0)=0 and f'(0)=1 Positive comparison test Ratio test for Positive Series X.B5 Trig Integrals I sin&cos |
11/6Trig IntegralsII sec&tan Series Conv.VI Absolute conv. & conditional: The General ratio test: Power Series I XI.A |
11/7Power Series II (Interval of convergence)XI.A How Newton used Geometric series to find ln(.9) Taylor Series |
12 Exam II self scheduled Wed. 11/12 |
11/10Power Series III (DE's) |
11/11 NO CLASS! Veteran's Day |
11/13
Power Series IV Functions and DE's) Area Revisited |
11/14 Trig substitution (begin- area of circle) I (sin) VII.E |
13 POW #5: Due 11/21 | 11/17 Trig sub I cont'd. (sin) VII.E |
11/ 18 Trig substitution II (tan and sec) VII.E Area II |
11/20More area Volume I |
11/21 Favorite estimates. Volume II |
14 No Classes
Thanksgiving |
11/24 | 11/ | 11/ Thanksgiving | 11/ |
15 Summary #6 due ?? | 12/1 Work
Arc Length VIII.B |
12/ Work? Darts Probability density, mean |
12/
Surface Area
--? Conics I Intro to loci-analytic geometry issues.(parabolae, ellipses) L'Hospital's rule I ? L'Hospital II. L'Hospital III |
12/ Conics II More on Ellipse and Parabola. Darts Probability density, mean |
16 |
12/
8 Conics III The hyperbolae Other Inverse Functions (Arcsin) |
12/ The conics IV
exp(pi*i) = -1 |
12/ Hyperbolic functions: DE's, Taylor Series, Algebra and Hyperbolas. |
12/ Proof Of L'Hospital's Rule? |
17 Final Examination Self scheduled | 12/15 | 12/ | 12/ | 12/ |
Reality Quizzes | 100 points |
Homework | 100 points |
POW's |
50 points |
Summary work | 50 points |
2 Midterm Examinations | 200 points |
Final Examination | 200 or 400 points |
Total | 700 or 900 points |
You may use my office hours for
some
additional work on these background areas either as individuals 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.
NEW! The grader for the course will be
available to give assistance to individuals of groups Monday,
10:00-10:50 and Wednesday, 11:00-11:50 in BSS 308.
Assignment |
DateDue: | Read: | Do: |
#1 |
8-29 |
IVA; IVB; IVC 6.3; 6.5;11.1 |
Background Reality
Check 11.1: 1, 3, 8, 10, 13,15,16 |
SC IV.D |
1-11 odd [parts a and b only] 23,24 | ||
11.2 | 4, 8,9 | ||
#2 |
8/29 9/2 |
SC IV.E | 5-9 odd (a&b) |
11.3 |
3,4,8,9 |
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#3 |
9-4 |
SC IV.E | 20,21,24 |
11.3 |
1,6 | ||
SC VI.A | 9, 10, 15, 16 |
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#4 |
9-5/8/9? |
SC VI.B | 13,14 |
7.1(i) (review: pp 312-316) |
3-6; 13,17; 29;50; 75 | ||
SC VI.C | |||
#5 |
9-9/11 | SC VI.D | 1-4;9-13;21,*(22&23) |
7.1(ii) | 54-56; 62; 78; 84 | ||
#6 |
9-11/12 |
7.7 pp348-351 |
2, 5-8, 11 |
#7 |
9-15 |
11.4 | 1-7odd;15,21,36,37,41,*(45-47) |
#8 |
9-16/18 |
11.5; 11.7 |
11.5:3,7,9,19,21,23 11.7:6,9 |
Begin reading VII.F through Example VII.F.5 (rational functions) | |||
#9 |
9-19/22 | SC VII.F 7.4: pp331-333 | SC VII.F :5,6,7,17 7.4:1-3;8-10; 15, 33-35 |
#10 |
9-23/25 | SC VII.F
check work on-line with Mathematica 7.4: pp331-333 | SC VII.F :1,3,10,14,15 7.4: 24,27, 39-41; 44 |
#11 |
9-26 |
7.7: pp352-354 |
7.7: 25 ,31 |
#12 |
9-29/30 |
7.8 (Improper Integrals); 5.2 pp248,249,252 (estimating Integrals); 7.5 (More Integral estimates) Start reading V.D More help on Simpson's rule,etc can be found in SC V.D |
7.8: 1-4, 16,17 5.2: 1,7,8 7.5:1, 8, 9 ,23 |
#13 |
9-30/10-2 |
7.2(i) Read SC VII.C |
7.2: 4, 5, 10, 11, 18, 22 VII.C: 2,3,8 |
#14 |
10-2/3 |
7.2(ii) |
7.2: 33, 35, 43, 51, 54 VII.C: 12,16 |
DueDate | Read: | Do: | |
#15 |
10-13/14 |
Read SC IXA |
SC IXA 1,2, 3, 4, 6, 9, *10 |
#16 |
10-16/17 |
10.1 pp 478-482 Read IX B |
SC IX
B 1,2,4,5,7 10.1: 1-7 ODD, 17, 18, 22, 24 |
#17 |
10-20/21 |
IXB IX.C 10.1 pp 478-484 |
IX
B (ii)11,13,14,*23 10.1: 13, 15, 16, 23, 33d IX.C (i) 1-4 |
#18 |
10-21 |
IX.C IX.D X.A |
IX.C(ii) 5-9; (iii) 12,14,16-18 |
#19 | 10-23/24 | IX.D X.A 9.1 pp 438-440 |
IX. D:1,3,5 X.A: 1-3,5,7-9 9.1: 1-5, 7-9,13, 14, 17, 18,41 |
#20 |
10-24/27 |
IX.D X.B1_4 |
IX.D: 8,10,14,15 9.2::1-7 odd; 11, 15, 18-21, |
#21 |
11-3/4 |
9.3, 9.4 p 460. X.B1_4 |
9.3: 1-4, 13-15, 17,18 9.4:: 46,47 |
#22 | 11- 6/7 | 9.4: pp455-456 10.2: 485-486 10.4 X.B5 Ratio Test For Positive Series |
9.4: 4-6, 8 10.2: 1-4, 31-33 |
#23 |
11-14/17 |
9.5 |
9.5: 5,7,9;11-14; 25-27, 34a. |
#24 |
11-18/20 |
7.4 pp. 334-337 |
7.4: 20, 22, 43, 53, 59 |
#25 |
11-20/21 |
VII.E 8.1 *On-line tutorials from Hippocampus Use Course view for Calculus II Lesson 48: Trigonometric Substitutions |
7.4: 23, 54, 55 8.1: 1,3,5 |
#26 |
11-21/12-1 |
8.1, 8.2 pp375-379 |
8.1:10, 11, 13 8.2: 1,3,5,10 |
#27 |
12-4/5 |
8.2 : pp 278, 379 8.5: pp 399-402 Darts |
8.2:11, 41 8.5: 1-3,7 |
VII.E | |||
XI.A |
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Math 110 Final Topic
Check List December 11, 2008 Core
Topics are italicized.
Differential Equations and Integration Tangent Fields and Integral Curves. Numerical Approximations. Euler's Method. Midpoints. Trapezoidal Rule. Parabolic (Simpson's) Rule. Integration of core functions (from Calc I) Integration by Substutition Integration by Parts. Integration of Trigonometric Functions and Elementary Formulas. Trigonometric Substitutions. Integration of Rational Functions. Simple examples. Simple Partial fractions. Separation of Variables. Improper Integrals: Extending the Concepts of Integration.
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Taylor's Theorem.
Sequences and Series: Fundamental Properties.
Power Series: Polynomials and Series.
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