Martin Flashman's Courses
Math 120 Calculus II Spring, '06
MWF 09:30am-10:25am Fowler 309
and Thursday May 4!
Optional review Session Friday TBA
Final Exams:
Checklist
5-8 Final Exam 1:00- 4:00 pm
in class room
5-9 Alternate Final Exam 1:00-4:00
in Lab room

Lab 1  01:30pm-02:55pm T FOWLER 307
Lab 2  03:00pm-04:25pm T  FOWLER 307






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Last updated: 1/22/06
Tentative Schedule for Math 120- Class and Labs - Subject to Revision.
Week
Monday
Tuesday (Lab)
Wednesday
Friday
1. Review
Indefinite Integrals
1-23 Introduction and initial review for derviatives.
1-24Review- DE's and estimation,
Direction Fields/ Euler's Method/Integral Curves
Anti-derivatives, IVP's
Linear Estimation
Winplot - and DE's
1-25
Indefinite Integrals
Core Functions and Linearity
1-27
Substitution
2. The Definite Integral
1-30 More substitution, DE's and Euler.
1-31 Estimating Areas
2-1Euler meets area-The Fundamental Theorem of Calculus I
2-3 The Definite Integral- Definition - Interpretations
The Fundamental Theorem of  Calculus I'
3.More about the Definite Integral
2-6 Average values
2-7 Areas and definite integrals.
2-8 Areas between curves.

2-10 Work

4. Misc. on Def. Int.
2-13 More work.
Start  Volume
2-14 More Volume
2-15 Volumes
2-17 Substitution w/ Def. Int.
Begin Numerical Integration
5. Numerical Integ.
2-20 Presidents Day- no class 2-2 Numerical Integration 2-22 Simpson's Rule 2-24 Arc Length SC:VIII.B
6. More Applications
2-27 Arc Length VIII.B
General planar curves.
2-28 Exam 1
3-1Using Functions to estimate Integrals. 
3-3 A preview of  Taylor theory.
Sensible Calculus IX.A (On-Line)
7. DE's and integration
3-6 Properties of the Definite Integral
3-7 Models and de's continued
Taylor's Theorem I (exp)
3-8  Taylor's Theorem I (exp) and estimating
int_0^1 exp(-x^2) dx
3-10Models and  DE's define functions.FTof C for DE's.
Learning and other rates that decrease over time: arctan.

3-13 Spring Break- No Classes
3-14 Spring Break- No Classes 3-15 Spring Break- No Classes 3-17 Spring Break- No Classes
9. DE's and Taylor
3-20 FTof Calc (DE's) Separable DE's  3-21 Integrals Definite and Indefinite- How they fit into solving DE's
3-22 Sensible Calculus IX.B (On-Line) Taylor's Theorem II
3-24 TT II
10.Series Testing 3-27   IX.B (On-Line)
Calculus for TT  IX.C (On-Line). 
3-28  Taylor's Theorem

3-29 The Logistic
Taylor III
Introduction to sequences, and convergence.
3-31 
11. Power series 4-3  Geometric  Series
4-4 Sequences and Series- spreadsheets and graphs  4-5 Harmonic and Power Series

4-7Integral and Comparison testing
 Alternating series.
12. Taylor Series Plus 4-10 Positive Series.
Integral test begun
4-11 Midterm Exam #2 4-12 Infinite integrals, Integral test again.
Integration by parts
4-14 Integration by PartsII,
Power Series.
Taylor Revisited and reviewed.
13..Integration Methods 4-17 Abs . converg. & Ratio test Power series II
Applications of Power series to DE's.
4-18 Power Series and De's 4-19 Finish Ratio Test and Applications to Taylor Series and DE's. Power Series Theorem -Differentiation/ Integration.
4-21 Last Breath on Series?Examples...Proofs?
14 4-24 Arc Tangent
4-25 Integration Gateway Test.
4-26 Improper Integrals II
4-28 More Arctan stuff
L'Hospital's Rule
15
5-1 Volume of a torus
Application of Improper Integrals
Area and The Normal Curve(review of integration!)


5-2 Overview of Course!
Open Problem Session.
5-3 Simple algebra for series.
Fourier Series?
Misc. Methods (partial fractions)?
ln(2)- Newton's computation/series?
Calculus and proabability- darts?

5-4 Thursday! Last class
Some last observations on the semester's work.
What about the final exam!
16 Final Exams
5-8 Final Exam 1:00- 4:00 pm in class room
5-9 Alternate Final Exam 1:00-4:00 in Lab room




Spring, 2006             MATH 120 : CALCULUS II         M.FLASHMAN  
Tentative Assignments-This will be revised further! [1-22-06]
(Text: SM = Smith and Minton, 2nd Ed. / SC = Sensible Calculus online materials) and recommended problems(tentative- subject to change!) 
Date Due Reading Problems
Optional Viewing: Ed Berger CD Tutorial  [# of minutes] 
* means optional #means on-line report on Blackboard
HW #1
1-27
SC IVD
SC IVE (on-line)
S&M:6.6
Math 110 Final Solutions
Ch Reviews
p238:1,2,23,31,37, 75
p319:1,49
553: 71, 75 a
A tutorial on slope fields with an interactive JAVA applet to explore slope fields. Calculus I in 20 minutes - watch only the first 15 minutes! Last five are a preview for the next 2 weeks! 9.1.1.
Antidifferentiation [14]
#9.1.2. Antiderivatives of Powers of x [18]
#9.1.3. Antiderivatives of Trigonometric and Exponential Functions [10]
HW #2
1-30
SC IVA(On-line)
SC IVB (On-line)
S&M: 4.1 pp322-328

On line IVA:1(a,d,e,f),10; 4, 5(a,b),8,11
S&M: 4.1 p322: 5-11; 15-21odd;55-57;67, 68
p334:79
A java graph showing 
f (x)=P'(x) related for f a cubic polynomial

A tutorial on antiderivatives and indefinite integrals.
9.2. Integration by Substitution
       9.2.1. Undoing the Chain Rule
       9.2.2. Integrating Polynomials by Substitution
9.3.1. Integrating Composite Trigonometric Functions by Substitution
HW #3
2-1
S&M: 4.6 pp374-378
SC IV.F READ
S&M: 4.6 p382:5-8,11,13,16,21,26,29,39
On-line tutorial for Substitution
Another Tutorial on substitution.


HW #4
2-3
SC IVF(On line) IV.F: 1,3,5,13,15,17(on-line)
9.4.1 Approximating Areas of plane regions.
HW #5
2-6
S&M: 4.2 p334- Example 2.5
SC VA ( On Line)
S&M: 4.2 p 340: 7-12
V.A: 1,2 a (on line)
S&M p 372: 5-7, 13,15,
A tutorial on summations and summation notation.
HW #6
2-8
S&M: 4.4 pp359-361
5.1 pp402-405
S&M p 373:77-82


18.1.1 Finding the Average Value of a Function [8]
HW #7
2-10
S&M: 5.1 pp402-405
S&M:5.6 pp453-454
S&M p 409: 5,7,9-13


9.4.4  Illustrating the fundamanetal  theorem of calculus[13]
9.4.5 Evaluating Definite Integrals [14]
10.2.1 The area between two curves [9]
HW
#8
2-13+15
S&M:
5.1 pp 405- 407
5.6 pp453-454
S&M p 409: 13,17, 27,29
S&M p462 :5, 11 (wait till 2-15)

10.2.2 Limits of integration and area[15]
10.2.3 Common Mistakes to Avoid

Summary #1
2-14

Partnership Summary #1 covering work through February 8th should be submitted by 5 pm
[2pages - 1 side or 1 page -2 sides.]


HW #9
2-(15) 17
S&M
5.6 pp453-454
5.2: 411-418
S&M p462 :5, 11
S&M p423: 5, 19, 20, 21a, 35

18.6 Work ( 3 segments)  [4 + 5+5]
18.2 Finding volumes using cross sections [9+12]
HW #10
2-17
S&M
5.2: 411-418
S&M p423:  211, 23a, 31 a,b


HW #11
2-22
S&M
4.6: pp380-381
4.3: p 347-348
4.7: pp 384-388
SC VA ( On Line)
S&M p382:47-51,54
S&M p349: 11-13,35,36,41,42
S&M p396 part a and b only for 9 and 10


HW #12
2-24
S&M
4.7 pp389-392 remk 7.3.
SC V.D (on- line)
S&M p396: 13, 31-33,37


16.9.1 Deriving the Trapezoidal Rule [12.5]
18.5.2  Finding Arc Lengths...[14]
HW#13
2-27
5.4  pp434-435
Probability
S&M p440: 5, 9 SC:Arc Length VIII.B
Exam I
2-28

 
Midterm Exam I covers material related to HW's 1-12.
Optional Review:
p398:1-11 odd; 21-25odd; 31,41,45,49 odd, 61
p 475 3,7, 11, ,15a, 33
p553: 71,75a.

HW #14
3-3&8
4.4 p351, 356-360
9.3 pp739-742
Sensible Calculus IXA (On-Line)
S&M: p745: 5, 9
p362:31-34
SC IXA: 1,2



HW #15
3-10
4.4 p351, 356-360
Sensible Calculus IXA (On-Line)
SC IXA: 3-5,10[a-e]


HW #16
3-22
4.5 p 367-269
6.4: p503-505
6.5: p  512-516
516-518?
S&M: p372: 41-43, 55, 57
S&M: p 509: 5,6;  p 519:13,17-19, 29
SC:VI.D models and inverse trig

HW #17
3-24
6.4ex 4.1
Sensible Calculus IX.B (On-Line)
S&M: p510: 13-15
S&M: p 519: 19,20 29,33
Sensible Calculus IX.B (On-Line) :1-5

20.3.1 Exponential Growth [12]
20.1.2 Solving Separable Differential Equations [9]
20.1.3 Finding a particular solution. [6]
HW #18
3-27
6.4 ex 4.2
IX.B (On-Line
)
In advance for class: IX.C (On-Line).
S&M p 510: 25-27, 29
Sensible Calculus IX.B (On-Line) :13-15

20.3.2 Radioactive decay [8]
19.12.2 Maclaurin Polynomials [9]
19.12.1 Taylor polynomials [14].
HW#19
3-29
IX.C (On-Line)
6.4 pp506-8
 IX.C (On-Line):1-5,7,8
S&M p 510: 31,33,35

16.6.1 Introduction to Partial Fractions [13]
Summary #2
3-29

Partnership Summary #2 covering work through March 24th should be submitted by 5 pm
[2pages - 1 side or 1 page -2 sides.]


HW #20
3-31
6.5: p516-518
IX.D
;
X.A

S&M p519:35, 37
IX.D: 1-4, 10,12
p520:55, 59

HW #21
4-3
X.A
X.B
8.1 pp622-623, 625-626
X.A : 1-9 odd
S&M: p634 5-8, 9-14 part a only, 15-21


19.1.1 The limit of a sequence.[10]
19.1.2 Deteremining the limit of  a sequence.[9]
HW #22
4-5
X.B
8.1 pp628-631
8.2 pp 636-641
S&M : p 634:51-53
S&M:  p644: 5-10, 19, 20, 25

19.3.1 Introduction to Infinte Series [11]
19.3.3 geometric series[13]
HW  #23
4-7
X.B
8.1 pp627-8;631-632.
8.2 pp641-644
S&M : p 634: 39-41;
p644: 13,15,16,25-28

19.4.1 properties of convergence [7]
19.4.2 test for divergence [8]
HW #24
4-10
8.3: pp 647-649
8.4 : pp 658-661
S&M:  p656: 5-11odd.;
p664: 5-11 odd, 31


Exam II
4-11

Midterm Exam II covers material related to HW's 13-24. Optional Review:
p362: 31,33;  p400: 59
p476:19;   p552: 17, 19, 49, 51, 55, 57, 61, 63, 75
p718: 1-5,9,10,19,21,25, 69

HW #25
4-14
7.2pp560-563
7.7pp610-613 omit example 7.8
8.3 pp647-649 omit example 3.1.
S&M 7.2 p566: 3-11
7.7 p617: 15-17, 25
8.3:  p 656: 4-9, 19
VII.C. Integration by Parts 16.6 .1- 3 Integration by parts.
19.5 .1&2 The integral test
HW #26
4-17
7.2 pp564-566
X.B5
S&M 7.2 567: 13,19,21, 25, 31, 32, 41,45


HW# 27
4-21
8.5: p666-670
8.6:675-678
X.B5
XI.A Power Series
S&M 8.5  p673: 5-9, 19, 20, 23, 24
S&M 8.6 p681: 23,24,33,37

19.9.1 Absolute and conditional Convergence [12]
19.10.1 The Ratio Test.
19.10.2 Examples of the Ratio Test
19.14.1- 19.14.3 Power Series
19.15.1 Diff'n and integ'n of power series.
HW #28
4-24
XI.A Power Series
8.7 Example 7.3, 7.6, 7.8
8.8 Example 8.4 and 8.5
S&M: 8.7: p694: 29-32, 39-42, 45-47, 49
S&M: 8.8  p702: 17,19.


HW #29
4-26
6.7  pp530-534
6.8 536-538; 540
p 648 Example 3.1
p679 Example 66.
S&M  6.7 p535: 5-10,13,20, 29
S&M  6.8 p 542: 7, 15; 17, 21, 22,27,28, 33
S&M  p 719:75
VI.DMore Models & Inverse Trigonometry
HW #30
4-28
7.7: pp 605-609 S&M:  7.7 p617: 3-9 odd, 11-13,37,38
17.1.Improper integrals
HW #31
5-1
7.6 S&M:  7.6 p603: 3-5, 17,18,23, 25, 26,29
14.1 and 14.2 L'Hopital's Rule
Summary #3
5-1

Partnership Summary #3 covering work through April 28th should be submitted by 5 pm
[2pages - 1 side or 1 page -2 sides.]


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OFFICE: Fowler 325                                    PHONE:  (323) 259- 2555
Hours (Tent.): M-F  11:30-12:30 AND BY APPOINTMENT or chance!
E-MAIL: flashman@oxy.edu              WWW:  http://www.humboldt.edu/~mef2/
***PREREQUISITES: Calculus I

Note that with the purchase of your textbook, you have access to the Calculus Online Learning Center, which helps students learn calculus with automatically graded practice quizzes, additional explanations of difficult topics and guides for TI calculators.  Live tutorial assistance is also available.

Many mathematical models in the natural and social sciences take the form of systems of differential equations. This introduction to the calculus is organized around the construction and analysis of these models, focusing on the mathematical questions they raise. Models are drawn from biology, economics, and physics. The important elementary functions of analysis arise as solutions of these models in special cases.

The mathematical theme of the course is local linearity. Topics include the definition of the derivative, rules for computing derivatives, Euler’s Method, Newton’s Method, Taylor polynomials, error analysis, optimization, and an introduction to the differential calculus of functions of two variables.

  CALCULUS 2: SCIENTIFIC MODELING AND INTEGRAL CALCULUS.

This course continues the study of the calculus through scientific modeling. While Calculus 1 is concerned with local changes in a function, Calculus 2 focuses on accumulated changes. Models solved by accumulation functions lead to the definition of the integral and the Fundamental Theorem of Calculus.

Additional topics include numerical and analytic techniques of integration, trigonometric functions and dynamical systems modeling periodic or quasiperiodic phenomena, local approximation of functions by Taylor polynomials and Taylor series, and approximation of periodic functions on an interval by trigonometric polynomials and Fourier series.



MORE THAN 4 ABSENCES MAY LOWER THE FINAL GRADE FOR POOR ATTENDANCE.
In my experience students who are actively engaged in learning and participating regularly in a variety of activities will learn and understand more and retain more of what they learn. Each component of the course allows you a different way to interact with the material.

Last Day to Drop Courses

CR/NC Forms Due

Withdrawal Period Begins

Last Day to Withdraw From Class

 
Math 120 Final Topic Check List Core Topics are italicized.
Differential Equations and Integral Calculus
A. Indefinite Integrals (Antiderivatives) 
Definitions and basic theorem
Core functions- including Arctangent.

Simple properties [ sums, constants, polynomials] 
Substitution 
B. Euler's Method, etc. 
Euler's Method 
Simple differential equations with applications 
Tangent (direction) fields/ Integral Curves 
C. The Definite Integral 
Euler Sums / Definition/ Estimates (endpoints/midpoints) /Simple Properties / Substitution 
Interpretations (area / change in position) 
THE FUNDAMENTAL THEOREM OF CALCULUS - evaluation form 
THE FUNDAMENTAL THEOREM OF CALCULUS - derivative form 
D. Applications 
Recognizing sums as the definite integral  
Areas (between curves).  
Volumes (cross sections- discs). Average value. Work.
Differential Equations and Integration  
   Tangent Fields and Integral Curves. 
   Numerical Approximations. 
            Euler's Method
            Midpoints. 
            Trapezoidal Rule. 
            Parabolic (Simpson's) Rule. 
  Integration by Parts.  
  Separation of Variables. 

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].

 
Bonus Essay question for final:
Suppose P(t) is a positive continuous function on [a,b] that gives the velocity at time t of an object moving on a straight line. Explain using the mean value theorem why there is some number c between a and b where P(c) = 1/(b-a) òx=a x=b  P(x) dx.
Interpret this equation with either
(i) a discussion of the  velocity and position of the object with the position function given by a definite integral from time x=a to time x=t or
(ii) a discussion of the area under the graph of Y=P(x) above the X-axis from X=a to X=b and the area of a rectangle with height P(c) and width (b-a).

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