Martin Flashman's Course Pages
Math 110 Calculus II  Spring, '15
Draft version- Work in Progress
MTRF 1400-1450 ART 027
Study Zone: 2 Hours Study for 1 Hour Class

NOTICE: All items on this syllabus are subject to change.
( last revision noted 2-25-15)
1  No Class
1-20 Introduction & Review

1-22 More review.
Differential equations and  IVA IVB
Direction Fields IV.D
1-23  IVA IVB
Direction Fields IV.D
1-26 Direction Fields Continued. IV.D

1-27 Euler's Method

 1-29 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

1-30 More on the relation between the DE y'=y with y(0)=1  and ex.

3 POW #1 Due 
Summary #1 due
2-2 Models for learning. 
y' = k / x; y(1)=0. k =1 
y = ln (x) and ln(2) 
ln|x| and integration of 1/x.
More on ln and exp!
Review Substitution

Begin Bounded learning.
Improper Integrals I
More on improper integrals
Bounded learning and Arctan. VI.D

2-6 More DE models.  Separation of variables.
4 POW #2: Due 2-16

2-9 More Review Substitution(ii) Growth/Decay Models. [Symbolic] . The Logistic Model 2-10 More logistic. 2-9 Integration of rational functions I. VII.F 2-10
  Problems from web Assign- Breath
5 Summary #2 due 2-23

2-16 Rational functions II VII.F
2-17End Rational Functions
Improper Integrals II Start
2-16  Improper Integrals II Continued
Start Integration by Parts. VII.C

Integration by parts I VII.C
6 POW #3: Due 3-2
2-23 Integration by parts. II VII.C 
Reduction Formula and integration by parts.
2-24Numerical Integration. (linear),  V.D  2-23Numerical Integration. (quadratic),  V.D
Improper Integrals and  comparison tests III

2-24Application to estimation of integral
 More Comparison Tests for improper integrals.

Summary #3 due 3-6
3-2 Breath
Start  Taylor Theory for e^x. Taylor .  IXA
 3-3Applications: Definite integrals and DE's. 3-5 Taylor theory: Finish  IXA.. 3-6 
IXB MacLaurin Polynomials

Exam I  Self scheduled:

3-9 IXB MacLaurin Polynomials (cont'd)
3-10 Review for exam #1 (?)Taylor Theory for remainder proven.
3-12 IX.C More on finding MacLaurin Polynomials & Taylor theory.
3-13 More MacLaurin.   IX.D Taylor Theory derivatives, integrals, and ln(x)
Use of absolute values.
How Newton used Geometric series to find ln(.9)
NO Classes : Spring Break!

10 POW #4: Due

3-23 IX.D Taylor Theory derivatives, integrals, and ln(x)
Use of absolute values.
3-24Taylor Theory: End First Round

3-26 Begin Sequences and series. Geometric sequences.

3-27 X.A  Sequence properties: Unification.
Bounded Monotonic convergence Theorem
11   3-30
Series Conv. I  
Geometric and Taylor Series.
geometric series
Theorem on Rn
Taylor  polys and Series.
3-31 NO Class CC Day
4-2   Series Conv. II
Harmonic Series.
The divergence test.
4-3 Incr&bdd above implies convergent.
12Summary #4 due 4-6 4-6 Series Conv. III
Positive series & Integral test.

4-7 Positive comparison test

4-9Ratio test  for Positive Series X.B5

4-10 Series Conv.  IV Alternating Series Series

13 Summary #5 due 4-17 4-13 Conv.VI Absolute conv. & conditional:  The General ratio test: 
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
Begin Power Series I  XI.A
Power Series II (Interval of convergence)XI.A
Taylor Series

4-16 Power Series III (DE's)
  Start Trig Integrals I sin & cos
4-17 exp(pi*i) = -1
Power Series IV (Functions and DE's)
Trig Integrals II sec&tan
14 Exam II  self scheduled 4-22
4-20 Trig substitution (begin- area of circle) I (sin) VII.E
Favorite estimates Arctan(1) = pi/4.

4- 21 Area Revisited

4-23 Area II
Volume I
Trig substitution II (tan and sec) VII.E
4-24 More trig
More area ("dy")

15    POW #5 Due: 4-27
4-27 volume I
Parametric curves I
4-28 Parametric curves II :Arc Length VIII.B

4-30 Average Value
Volume II
Polar Curves I

5-1 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 

Summary #6
5-4 Surface Area --?
The conics IV
 Hyperbolic functions: DE's, Taylor Series, Algebra  and Hyperbolas.
5-5 Darts  ??
Probability density, mean

5-7 L'Hospital's rule?
Proof Of L'Hospital's Rule?


17 Final Examination Self scheduled
Rooms TBA
Review Session:
Sunday 5-10

Monday May 11, 12:40-14:30 Wednesday May 13, 10:20-12:10Thursday May 14, 10:20-12:10
Thursday, May 14, 15:00-16:50.
Friday, May 15 10:20-12:10.

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Last updated: 1/19/2015

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Office Hours : Monday 3:00 - 4:00 BSS 346; AND BY APPOINTMENT or chance!
Shared Hours   Tuesday &Thursday 12:00-12:50; Wednesday 9:00-9:50 BSS 308. See schedule at bottom of page.
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***PREREQUISITE: Math 109 (One semester of college calculus or AP Calculus AB) or permission.

FINAL GRADES: Though final grades for the course are subject to my discretion, I will use the following overall percentages based on the total number of points for your work to determine the broader range of grades for the course.     A  85-100% ;   70- 84% ;  C  60- 60% ;  D  50- 59%  ;  F   0- 49%

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