Week |
|
|
|
Friday |
---|---|---|---|---|
1 | No Class MLK Day |
1-19 Introduction & Review
(Thinkwell) |
1-20 More review. Differential equations and IVA IVB IVC Direction Fields IV.D |
1-21 IVA IVB IVC Direction Fields IV.D |
2 |
1-24Direction Fields Continued. IV.D |
1-26 Euler's Method IV.E |
1-27 Begin Models for (Population) Growth
and Decay: y' = k y; y(0)=1. k = 1. The exponential function.VI.A estimate e from (1+1/n)n. Models for learning. y' = k / x; y(1)=0. k =1 VI.B |
1-28More on the relation between the DE y'=y with
y(0)=1 and
ex. |
3 POW #1 Due Thurday Feb 3. Summary #1 due Wed. Feb 2. |
1-31 Models for learning. y' = k / x; y(1)=0. k =1 VI.B |
2-2 y = ln (x) and ln(2) ln|x| and integration of 1/x. More on ln and exp! SC VI.C Review Substitution |
2-3 Begin Bounded learning. Improper Integrals I |
2-4 More on improper integrals Bounded learning and Arctan. VI.D |
4 POW #2: Due Thursday Feb 10 |
2-7More Review Substitution(ii) | 2-9 More DE models. Separation of variables.Growth/Decay Models. [Symbolic] . | 2-10 The Logistic Model | 2-11 More logistic. |
5 Summary #2 due Thursday Feb 17 |
2-14 Integration of rational functions I. VII.F |
2-16 Rational functions II | 2-17 Rational functions III VII.F |
2-18 End Rational Functions Begin Improper Integrals II Integration by parts I? |
6 POW #3: Due Thursday Feb 24 |
. 2-21Improper Integrals and comparison tests III | 2-23Integration by parts. II VII.C | 2-24 Numerical Integration. (linear), V.D |
2-25comparison
tests? Integration by parts (finale?) Numerical Integration. (quadratic), V.D |
7 Summary #3 due Thursday March 3 |
2-28 Comparison Tests for improper integrals. Reduction Fornula and integration by parts. |
3-2Start Taylor Theory for e^x. Application to estimation of integral. |
3-3
Taylor
Theory
I.
IXA Applications: Definite integrals and DE's. |
3-4Taylor theory: Finish IXA.. IXB MacLaurin Polynomials |
8
Exam I Self
scheduled: Wed. Mar. 9 |
3-7 Review for exam #1 (?) IXB MacLaurin Polynomials (cont'd) |
3-9 Taylor Theory for remainder proven. |
3-10
IX.C
More on finding MacLaurin Polynomials & Taylor theory. |
3-11More MacLaurin.
IX.D Taylor
Theory
derivatives,
integrals,
and
ln(x) Use of absolute values. |
9 | NO Classes : Spring Break! |
|||
10 POW #4: Due 3-24 Summary #4 due 3-25 |
3-21
IX.D Taylor
Theory
derivatives,
integrals,
and
ln(x) Use of absolute values. |
3-23Taylor Theory: End First Round How Newton used Geometric series to find ln(.9) Geometric sequences. |
3-24 Begin Sequences and series. |
3-25 Sequence properties: Unification. |
11 | 3-28 X.A |
3-30 Series Conv. I Geometric and Taylor Series. geometric series X.B1_4 Theorem on Rn Taylor polys and Series. |
3-31 NO Class
CC Day |
4-1 Series Conv. II Harmonic Series. The divergence test. Incr&bdd above implies convergent. Positive series & Integral test. |
12 POW #5: Due 4-7 | 4-4Series
Conv. III Positive comparison test Ratio test for Positive Series X.B5 |
4-6 Series Conv. IV Alternating
Series Absolute Convergence. |
4-7 Series
Conv.VI Absolute conv. & conditional: The
General
ratio test: |
4-8 Intro to
power series concepts of convergence and functions. Taylor Series convergence. Series to solve DE's - Motivations f''(x) = f(x) with f(0)=0 and f'(0)=1 |
13 Summary #5 due 4-15 | 4-11 Power
Series I XI.A
Start Trig Integrals I sin & cos |
4-13 Power
Series
II
(Interval
of
convergence)XI.A Taylor Series |
4-14 Power Series III (DE's) Trig Integrals II sec&tan |
4-15 Power Series IV (Functions and DE's) |
14 Exam
II self scheduled Wed. 4-20 |
4-18 Trig
substitution (begin- area of circle) I (sin) VII.E |
Area Revisited Favorite estimates. exp(pi*i) = -1 |
Area II Volume I Trig substitution II (tan and sec) VII.E |
More trig area More area ("dy") |
15 |
4-25 volume I Work Parametric curves I |
Parametric curves II :Arc Length VIII.B |
Average Value Volume II Polar Curves I |
Polar curves
II Parametric curves III tangents Conics I Intro to loci-analytic geometry issues.(parabolae, ellipses) Conics II More on Ellipse and Parabola. Conics III The hyperbolae |
16 POW #6: Due
Monday 5-2 Summary #6 :Thurs 5-5 |
5- 2 Surface
Area
--? The conics IV Hyperbolic functions: DE's, Taylor Series, Algebra and Hyperbolas. |
Darts
?? Probability density, mean |
L'Hospital's
rule? Proof Of L'Hospital's Rule? |
|
17 Final Examination Self scheduled Review Session: Sunday 5-8 12:00-2:15 BSS 302 |
Sign up for self -schedule- See
Moodle for time Wed., Thurs., Fri. |
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.
Assignment |
DateDue: | Read: | Web Assign |
Do:(Not collected) |
---|---|---|---|---|
#1 |
1/21-25 |
SC IVA;
SC
IVB;
SC IVC |
HW #1 Math 110 9.2 I Direction Fields | Background Reality
Check |
SC
IV.D |
1-11 odd [parts a and b only] 23,24 | |||
9.2:
pp 572-575 |
3-6 |
|||
#2 |
1/26-28 |
SC IV.E | HW #2 Math 110 9.2 II Euler's Method | 5-9 odd (a&b) |
9.2: pp 575-577 | 19, 21 |
|||
#3 |
1/27-31 |
SC IV.E | HW #3 DE's and exp. |
20,21,24 |
3.8 , 9.1 |
9.1:
3 |
|||
SC VI.A | 9, 10, 15, 16 |
|||
#4 | 1/28-2/3 |
SC VI.B 3.1 pp178-180; 3.6 pp 215-217;219 SC VI.C |
HW #4 110 DE's and ln. (3.6) | 13,14 p262: 20, 29, 33 |
#5 | 2/3-4 |
5.5 | HW #5 110 Subst'w/ ln& exp (5.5) | 5.5: 1-11 odd |
#6 | 2/3-7 |
7.8 pp 508-511( omit Ex. 2) | HW #6 110 Improper Integration I (7.8) | 7.8: 3-13 odd, 8 |
#7 | 2/4-11 |
SC VI.D 3.5:pg 212 |
HW #7 110 Arctan and more improper integrals (7.8) | 1-4;9-13;21,*(22&23) p214: 45, 54 On-line Mapping Figure Text and Activities |
#8 | 2/9-11 |
9.3 pp580-585 |
HW #8 110 Separable Diff'l Equations (9.3) | 9.3: 1-5, 11,19,* 21 |
#9 | 2/9-14 |
9.4 | HW #9 110 Cooling&Pop'n Models &DE's (9.4,3.8) | 9.4: 3, 7 |
#10 | 2/21 |
7.4 pp 473-476 VII.F through Example VII.F.5 (rational functions) |
HW #10 110 Partial Fractions I Quadratics (7.4) | 7.4: 1a,
2, 7-11, 15, 19, 21 *SC VII.F :5,6,7,17 |
#11 | 2/22 |
SC VII.F | HW #11 110 Partial Fractions II cubics+ | 7.4:
3,4,
17,25,
27,
29,
33 *SC VII.F :1,3,10,14,15 |
#12 | 2/23 |
7.8: pp511-515 |
HW # 12 110 Improper Integrals II ( 7.8 ) | 7.8: 27-33 odd, 32; 49; *55; 57 |
#13 |
2/24 |
7.1 VII.C. Integration by Parts |
HW #13 110 Integration by Parts ( 7.1 ) | 7.1:1-13
odd,26,28,
33,47,48 *[VII.C. 8,33,35] |
#14 |
2/28 |
HW #14 110 MORE Integration by Parts ( 7.1 ) | ||
#15 |
2/28 |
7.7:
pp
495-497;
500-502 Start reading V.D |
HW #15 110 Linear Numerical Integration ( 7.7 ) | 7.7:
1
(a-c),
31a [*VII.C: 12,16] |
#16 |
3/2 |
7.7:
500-502 More help on Simpson's rule,etc can be found in SC V.D |
HW #16 110 Quadratic Numerical Integration ( 7.7 ) | 7.7: 27, 29,30 |
#17 |
3/3 |
HW #17 110 More Improper integrals and Tests (7.8) | ||
#18 |
3/3-3/4 |
Read SC IXA | HW #18 - report on Moodle SC IXA 1,2, 3, 4, 6, 9, *10 | SC IXA 1,2, 3, 4, 6, 9, *10 |
#19 |
3/4-3/10 |
Read IX B | HW #19 - report on Moodle SC IX B 1,2,4,5,7 | SC IX B 1,2,4,5,7 |
Exam #1 self scheduled on 3-9-2011 covers Assigned Material through Assignment #18. | ||||
#20 |
3-22 |
IXB IX.C | HW #20 - report on Moodle IX B (ii)11,13,14 IX.C (i) 1-4 | IX
B (ii)11,13,14,*23 IX.C (i) 1-4 |
#21 |
3-23 |
IX.C IX.D |
HW #21 - report on Moodle IX.C(ii) 5-9; (iii) 12,14,16-18 | IX.C(ii) 5-9; (iii) 12,14,16-18 |
#22 |
3-24 |
IX.D X.A |
HW #22 - report on Moodle IX. D:1,3,5 X.A: 1-3,5,7-9 | IX. D:1,3,5 X.A: 1-3,5,7-9 |
#23 |
3-25 |
11.1
pp675-681 IX.D X.B1-4 |
HW #23 110 Sequences I (11.1) | 11.1:3-7;9-13
odd;17-21 IX.D: 8,10,14,15 |
#24 #25 |
3-29 3-30 |
X.B1-4 11.1 pp 682 - 684 11.2 |
HW #24 110 MORE
Sequences ( 11.1 ) HW #25 110 Series I (11.2) |
11.2: 9-17 odd;21-23,
41-43,47-49 |
#26 | 4-4 |
X.B1-4 11.3 pp 679-700; 703 11.5: pp 710-713 7.2 : pp 460-461 |
HW #26 110 MORE Series II ( 11.2 ) | 11.3: 3-6, 11-13, 17,18 11.5: 3-6, 9-11 (OOPS changed 11-9) |
#27 |
4-5 |
X.B5
Ratio Test For Positive Series 11.4: pp: 705-706 11.6: pp: 714-715 |
HW #27 110 MORE Series III (Pos<Integral) ( 11.3 ) | 11.4:3-7 11.6 : 7, 13, 27, 2,8 7.2: 1-9 odd |
#28 #29 |
4-11 |
XI.A 11.6 pp 716-718 middle, 719 |
HW #28 110 Positive
Series Comp&ratio (11.4/11.6) HW #29 110 Series IV (Ratio/altern gen'l) 11.5-6 |
11.6:3-5, 17-19, 31 |
#30 |
4-13 |
11.8 | HW #30 110 Power series I (11.8) | 11.8: 3-8, 15,16 |
#31 |
4-14 |
7.3 pp 467-469 example 2 5.2: p366-367 6.1:pp:415-417 |
HW #31 110 Power series II (11.8) | 7.3: 7, 13,14, 20, 21 5.2: 17, 19 6.1: 1,2 |
#32 |
4-15 |
7.2: pp462-465 | HW #32 110 integrals with sin and cos (7.2) | 7.2: 21-29 odd; 56,51 |
#33 |
4-18 |
7.2 |
HW #33 110 integrals with sec and tan (7.2) | |
Examination #2 | 4-20 |
Self Scheduled for 4-20 Covers material assigned through # 33 |
||
#34 |
VII.E Trigonometric Substitutions 7.3 pp 469-471 |
HW #34 110 trig subs [sin and tan] (7.3) | 7.3: 3, 9, 19; 1, 5 6.1: 7, 13 6.2:1,3 |
|
#35 |
6.1:pp 415-418 |
HW #35 110 Area
revisited (6.1) |
6.1:3,4,21, 22 |
|
#36 |
6.1 pp418-419 (area) | HW #36 110 Areas "dy", sec and trig subs (6.1,) | ||
#37 |
6.2 pp 422-425 example 2 6.2 pp 425-430 (volume) 6.4 (work) |
HW #37 110 Volume I ;Work I (6.2,6.4) | 6.2: 7,19,23,41 6.4: 3, 5,7 |
|
Below this line all assignments are not yet firm and due dates are to be determined. | ||||
Appendix C pp A16-A23 6.5 |
App C: 1,3,5, 11-23 odd 6.4:13, 17 6.5: 1- 4 |
|||
10.1 pp 621-623 8.1:p525-526 10.2 pp 633-634 10.2 pp630-633 10.3 pp639-643; 644-646 10.4 pp650, 652 |
10.1:1,3,5-7,11,12,19,24,28 10.2: 41, 42,45 *48 10.2:1,3,5, 11, 17, 31 10.3: 3,5(i), 15,17,56,57 10.4: 1,9 |
|||
Math 110 Reference
Topic
List for final Spring, 2011! 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. Parametric Equations- Arc length, tangents. |
Taylor's Theorem. Sequences and Series: Fundamental Properties. Power Series: Polynomials and Series. |
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