Martin Flashman's Courses
Math 110 Calculus I Fall, '05
MWF 2:30pm-3:25pm FOWLER 302
Lab 1  03:00pm-04:25pm T  FOWLER 307
Lab 2  01:30pm-02:55pm T FOWLER 307
The final examination may be taken on
1) Friday, Dec. 9th  1:00 - 4:00 pm or
2) Thursday, Dec. 15th 8:30 - 11:30 am.
CHECKLIST FOR REVIEWING FOR THE FINAL






Back to Martin Flashman's Home Page :)
Last updated: 8/30/05
Tentative Schedule for Math 110- Class and Labs - Subject to Revision.
Week
Monday
Tuesday (Lab)
Wednesday
Friday
1. Introduction and beginning review. Ch 0


8-31 Introduction
Numbers
9-2 Class Division
Finish Intro.
2. Background and Motivation Ch 0 and  2.1
9-5 No Class
Labor Day
9-6 Intro to Winplot

Backboard

9-7 Linearity
Functions
Visualization.
Models and linearity: Physical, Geometric, Random, Economic.
9-9More on functions and models.Physical, Geometric, Random, Economic.

3. The Derivative- As a Number- Definition 2.1 , 2.2
9-12 Change:
The tangent problem. The Velocity Problem.
9-13
Secant and tangents with winplot.
9-14
More estimation of rates.
Start the derivative.
9-16
The derivative: Definition and four steps.


4. The Derivative- As a Function. Core Algebraic Functions: Powers, roots,  Linearity. 2.2, 2.3
9-19
Begin Derivative as function. Number, graph, symbolic. Graphical connections between functions and their derivatives.
9-20
Rates, Accumulation and.
Estimation. [Euler?]
9-21 Core functions and Rules. Powers, sums, scalar multiples. Interpretations.
9-23 More Core: Powers, sums, scalar multiples.
5. The Derivative, Other Models, The Differential and Estimation. 3.1? The Calculus of Derivatives. Trigonometry 2.5
9-26 Roots.
Interpretations of rules plus other interpretations of derivatives: Probability, economic interpretations.
9-27
Estimations with population models:P'(t) depends on P and t
9-28 The differential and linear estimation.
Intro to the Logistic Model. 
9-30 More applications of the differential.
Interpretations of rules. Other interpretations of derivatives: Probability, economic interpretations.
Begin Sin ' and cos'
6. The Calculus of Derivatives.Products. 2.4 Trigonometry 2.5 Continuity and the Intermediate Value Theorem.1.3 Newton's Method. , 3.2
10-3 Finish Sin'(x), Cos'(x).
Intro to f '', f '''', etc.
10-4 DE's,Winplot, Direction Fields and Euler's Method.
Predator-Prey Models
10-5
The product rule.

10-7
Begin Continuity. IVT Newton's Method?
7.Direction Fields.
Quotients 2.4 , Finish trig.

10-10 Finish Newton.
Quotient Rule
Apply to tan, sec
10-11Newton's method - with excel and winplot
10-12 Misc. Details on limits, continuity, Newton's Method.
10-14 "euler" and direction fields.
8. The Chain Rule! 2.7 Direction fields, Euler's method. 10-17review- euler and direction fields

10-18 Midterm Exam #1

10-19 Begin the Chain Rule.The Chain Rule!

10-21 Fall Break
 No Class

9. Exponential and log functions. 2.6
Implicit Differentiation and related rates.2.8
10-24 More Chain Rule!
Start Exponential Function derivatives.


10-25 Implicit functions- Implicit differentiation
10-26 More on implicit functions.
Derivative of Exponential functions.
10-28 Derivative  of ln(x).Related rates.More implicit differentiation.
10. Inferences based on the derivative: Extrema,  2.9, 3.3, 3.7, (4.1)
10-31Related rates.More implicit differentiation.
11-1Gateway 3
ln(2) estimation using euler- with winplotand tables, and calculus!
11-2  more related rates.
Extrema- "word problems".
11-4 More on extrema and  word problems.
11. The MVT, and antiderivatives.
First derivative analysis. Increasing/decreasing, 2.9,3.4, 6.4, 6.6
11-7 More extreme problems. Proof of CPT. Inferences based on derivatives.The MVT .
11-8 Proof  of MVT and its immediate consequence for DE's.
Arctangent estimation of pi,
11-9 Solving initial value problems.
First derivative Analysis: Increasing/Decreasing.
11-11
More increasing decreasing, extremes, begin Concavity.
12  Second derivative analysis: Concavity, qualitative estimation  3.5, 3.6 Graphing: the Big picture. 1.4, 3.6. 11-14
Concavity
11-15
Exploring f where
f
'(x) = sin(x2)
11-16 Concavity and differential estimates.
Asymptotes and infinite limits.
11-18 L'Hopital's rule 0/0, etc.
13 Misc. Applications.3.8
11-21
More on L'Hopital's Rule.
Partial Derivatives.(on Line)
11-22
Midterm Exam #2
11-23 NO CLASS Thanksgiving Break
11-25 NO CLASS
Thanksgiving Break
14. DE's and other Functions 6.7, 6.8
11-28 Partial Derivatives
11-29 Visualizing Partial Derivatives when z = f (x,y)
11-30 More on L'Hospital.
Darts revisited! "Euler Sums, Net Change, and Differential Equations."
12-2 Estimations with Quadratic polynomials.
15.
12-5
12-6
12-7 LAST CLASS
Review & Final  Remarks
Friday 12-9
Final Exam Offering #11:00-4:00pm

16.
12-12
12-13
12-14
Thursday 12- 15 Final Exam Offering #2
8:30- 11:30 am



Fall, 2005              MATH 110 : CALCULUS 1         M.FLASHMAN  
Tentative Assignments-This will be revised further! [8-30-05]
(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
HW#1
9-2
SM 0.1
SC 0.B1 Numbers [on-line]



rev. sheet (on-line): 1-3,6,13,15,16,18,19
SM: p. 9: 5, 11, 21, 33, 43
SM: p10 49, 51
Introduction;  
How to Do Math
HW#2
9-7
SM 0.2
SC 0.B2 [on-line]

SM: p20:5-7,13-17, 21-25,41-45;
53-58; 75,76, 89, 90, 96-98
SM:91-94
On-line Mapping Figure Activities
Functions [19]
HW #3
9-9
SM 0.2, 0.3, 0.4
SC 0.B2 [on-line]
SM: p21: 31-36, 59.
For the following problems ignore the instructions: Make a table with five entries. Sketch the corresponding graph and mapping figure for the data: 59, 60, 67,68,71.
SC 0.B2 On line # 2,3,11
On-line Mapping Figure Activities

SC 0.B2 On line # 19, 20, 21
Parabolas [22]

Average Rates of Change [11]
LAB #1
Submit by 9-9!
Lab #1 9-6-05
on Blackboard
Problem #1 submit with partner.
Problems #2 and 3 may be submitted solo or with partner.


HW #4
9-12
SM: 0.4,
0.8 (pp72-73only)
0.C [on-line]
 
Practice sheet for Gateway on Functions.
SM: p76: 3,4,8,9
Ch 0 rev: p78: 9-12,17,18, 63
  The Two Questions of Calculus [10]
 
HW #5
9-14
SM: 2.1 pp 150-152, 155-156 middle.
SC I.A (Draft version)
SM: p161:9-14, 35, 36, 43, 44
SC: 0.C [on-line] 4,5

Slope of a Tangent Line [12]
Rates of Change, Secants and Tangents [19] 
Lab #2
Submit by 9-16
Lab #2 9-13-05
on Blackboard
Submit Problems from lab.


HW #6
  9-16
SC I.A (Draft version)
SM: Use "4 step method " to find the slope of the tangent line for these problems: p161: 21-25, 39,40
SM: p163:57
Finding Instantaneous Velocity [20]
Equation of a Tangent Line [18]
HW #7
  9-19
SM: 2.2. pp164-169.
SC I.D (.pdf Draft version)
SM: Use "4 step method " to find the derivative for these problems: p173: 9,10, 13-15, 21-26, 35, 37, 53-56.
The Derivative [12] 
 
HW #8
  9-21
SM: 2.2. pp164-169.
SC I.E (.pdf Draft version)
SM :Use "4 step method " to find the derivative for these problems: p173: 7, 17, 36, 38, 47, 49, 50.
SC I.E (.pdf Draft version): 2, 3(a,b), 4, 5a, 6.

Instantaneous Rate [15]
The Derivative of the Reciprocal Function [18]
Lab #3
9-23
Lab #3 9-20-05
on Blackboard.



POW #1
Submit by 9-27
POW #1 on line.



HW #9
9-23
SM: 2.3.176-178.
SCI.F: pp 1-4 (Download pdf file)
SM p184: 5-8, 13,14, 44, 45, 47, 48; 63-67

Uses of The Power Rule [20]  Short Cut for Finding Derivatives [14]
More on Instantaneous Rate [19]
Summary  #1
Submit by 9-27 5 pm

This summary should cover work through HW #9.
Only partnership work will be accepted.
One submission per partnership.
2 sides of one page or one side for 2 pages.


HW #10
9-26
SM: 2.3 pp179-181.
SC-Ch1.F (Download pdf file)

SM: p184: 15-17,21,23,24,49
SC- CH1F.:2,3,5,9,13
SC: 14,16
Differentiability [3]
Review of Trig[12]

 
HW #11
9-28
SM:3.8 Example 8.5
SM:p 184:19, 20,43;  p317: 27-30


Lab #4
9-30
Lab #3 9-27-05
on Blackboard.
Population models using spreadsheets.
Sample for a logistic differential equation used in class: 9-28

HW #12
9-30
SC-Ch1.C1 (html Draft version)
SC-Ch1.C2 (Download pdf file)
SM 3.1pp242-244middle example1.3 .
SM: p249: 5-8,19
Read web materials on differentials

Read on-line Sens. Calc. 0.C on Probability Models
Using tangent line approximations [25]
HW #13
10-3
SM 2.5 pp196 toThrm 5.2, Ex: 5.3, 5.4.

SM p 203:5,6,11,29,31,33,36, 39,40,41
Read web materials on trigonometric derivatives.
The derivatives of trig functions [14]
HW #14
10-5
SM 2.3 p183-4
review
SM 2.5 pp196 toThrm 5.2, Ex: 5.3, 5.4.
SC-CH3A1(pdf)
SM p184:25-30, 35, 37, 39-41, 52, 53, 55
SM p204: 45, 46

Read web materials on trigonometric derivatives.

HW #15
10-7
SM: 2.4. pp 187-189, Ex. 4.7
SM: 2.5 : Ex. 5.1
SM p 194: 5-9, 33, 37, 39
SM p 203:9, 13, 17, 19, 34

 The Product Rule [21]
HW #16
10-10
SM 1.3 pp102-104; 108-110
SM 2.2 p170 through Ex 2.9
SC-CH1.I(pdf)
SM:p 111: 5-10, 12, 15, 16, 37,

One Sided Limits [6]
Continuity and  discontinuity [4]

HW #17
10-12
SM: 2.4. pp 189-193 SM: 2.5. pp200-201, Ex. 5.5
SC-CH1.IB(pdf)
SM 1.3 pp102-104; 108-110
SM p 194: 11-13,19,20
SM p.203:7,10,18


The Quotient Rule [13]
HW #18
10-14
SC-CH1.IB(pdf)
SM 1.3 pp102-104; 108-110
SM: 3.2

SM: p 113:41, 43, 45
SM:: p256: 7-9, 11,17, 21,23,27, 29




Summary  #2
Submit by 10-15 5 pm

This summary should cover work through HW #18.
Only partnership work will be accepted.
One submission per partnership.
2 sides of one page or one side for 2 pages.


HW #19
10-17
SC-CH3A2(pdf)[newton's Method]
SC IVD [Tangent fields]
SM 6.6 pp 524 - 527??{euler)
SM: 528: 5,7
IV.D: 1-11 odd (online)
 
Read web materials on Newton's Method.
20.1.4 Direction Fields and Euler's Method [6]

 

10-18
Examination #1
Self schedule:
60-90 minutes 1:30-4:30 (lab time)
Covers all assignments and labs through that assigned for 10-15 and related reading.
Sample exam available on Blackboard.


HW#20
10-19

SC IVE  [Euler's Method]
SM 6.6 pp 524 - 527??{euler)

SC IV.E: 1a,2a Estimate y(3) only.
SM: p 528: 17, 19 [use spreadsheets.]
 

Introduction to The Chain Rule [18]
HW #21
10-24
SM 2.7  pp213-214. Examples 7.1, 7.4, 7.5, 7.6
SM 2.6 pp205-207 [exponential functions]

SM  p218: 5,9-11, 13-17, 25,27,48

Using the Chain Rule [13]
HW #22
10-26
SC Chapter II.B
SM 0.6 pp 50-54
SM 2.6 pp205-207 [exponential functions]

SM  P61: 21-24
SM: p 218: 6,12, 18, 25,27,29, 30, 42, 51,53



HW #23
10-28
SM : 2.8 pp 220-224
Read web materials on implicit differentiation.
SC Chapter I.F.2 Derivatives of exponential and logarthmic functions (in part)
SM: p 227: 5-7, 23, 26
SM : p 211: 5-8, 17, 18, 29
SM : p 218: 7,19, 20, 49
SM: p229:63
Intro to Implicit Differentiation [15]
Finding the derivative implicitly [12]
Derivatives of exponential functions [23]

HW#24
10-31
SM: p211
SM:2.8 pp225-226
SC Chapter I.F.2 Derivatives of exponential and logarthmic functions
SM:: p211: 19-22,,26,27,35
SM: p219:23,24,35


The Ladder Problem [14] Acceleration and the derivative.[5]
HW#25
11-2
SM:2.8 pp225-226

SM: p227:31,33,34,4145,48,49,51,62


The Baseball Problem[19]
The Blimp Problem [12]

HW #26
11-4
SM: 3.3
SM:p 268: 33-39,41

The connection between Slope and Optimization [28]
HW #27
11-7
SM: 3.3
SM: 3.7 pp298-303
On-Line tutorial on Max/mins
SM:p268; p267: 5-11, 21, 23
SM: p306: 8, 13,15

SC IVA(On-line) Critical Points [18]
Three  Big Theorems [11]
HW #28
11-9
SM: 2.9
SM: 3.7 pp303-306
SM p237:11, 35-37
SM: p268: 39, 41, 42
SM: p306: 15, 19
The Box Problem [20] Intro to Curve Sketching [9]
Summary  #3
Submit by 11-11
5 pm

This summary should cover work through HW #28.
Only partnership work will be accepted.
One submission per partnership.
2 sides of one page or one side for 2 pages.


HW #29
11-11
SM: 3.4 p269-274
SC IVB (On-line) Read
SM: p 276: 5-8, 13,14, 43, 45.
SM: p 307:10,21
SM : p307: 27
The First Derivative Test [3]
Regions where a function is increasing...[20]

Antidifferentiation[14]
HW 30
11-14
SM: 3.5 pp278-282
SM: p 276: 15-17,27, 29,33, 35, 37
SM:  p308:37
Excerpts on line: Galileo: On Naturally  Accelerated Motion  and On the Motion of Projectiles
Using the second derivative [17] Concavity and Inflection Points[13] 
Antiderivatives and Motion [20]  
POW  #4
11-15
POW #4
Available on Blackboard



HW 31
11-16
SM: 3.5 pp278-282
SM:: p284: 7, 9-11,27,28, 41-43, 47, 49
SM: p308: 36

The 2nd Deriv. test [4]
Acceleration & the Derivative [6]

Graphs of Poly's [10]
HW 32
11-18
SM  1.4
SM 3.5 examples 5.6 and 5.7
SM 3.6: pp287-291
SM: p122: 5-11 odd, 21-27 odd
SM p 296: 5,7,23,24



11-22
Examination #2
Self schedule:
60-90 minutes 1:30-4:30 (lab time)
Covers all assignments and labs through that assigned for 11-18 and related reading.
Sample exam will be available on Blackboard.


HW 33
11-28
SM 3.1pp247-249
SM  3.6 Ex 6.6

SM: p 250 : 31- 36, 47,48


HW 34
11-30
SM 3.6 EX. 6.2, 6.3
ONLINE: SM:12.3(optional)


ONLINE SM:chap12.3: 5-9,[27 and 29 just evaluate the partial derivatives],47
SM: applets
tutorial at Harvey Mudd Partial Differentiation 

HW 35
12-2
SM 7.6
DARTS
SM p. 3-7,17-19, 23-25, 27-29.

Basic Uses of L'Hospital's Rule
HW 36
12-5




Summary #4
Submit by
12-5
5 pm

This summary should cover work through HW #36.
Only partnership work will be accepted.
One submission per partnership.
2 sides of one page or one side for 2 pages.




SC-Ch1.C1 (html Draft version) : 4,5,7,8 *Graphing Trig Functions[17]




SC IVA(On-line)



On line IVA:1(a,d,e,f),10 

 

SC IVA(on-line)

IVA: 4, 5(a,b),8,11



A java graph showing 
f (x)=P'(x) related for f a cubic polynomial


Antiderivatives of powers of x [18]
 



SC IVD 
IV.D: 1-11 odd (online)
The connection between Slope and Optimization [28]
 
Domain restricted functions ...[11]


SC IVE (on-line)
IV.E: 1,2
Graphing ...asymptotes [10]  
Functions with Asy.. and holes[ 4]  
Functions with Asy..and criti' pts [17]
Horizontal asymptotes  [18]


SC IV.F READ


Vertical asymptotes [9]

SC IVF(On line)
IV.F: 1,3,5,13,15,17(on-line)



SC VA ( On Line)
V.A: 1,2 a (on line)



SC VA ( On Line)

VA : 5(a,b)





Finding the Average Value of a Function [8]

Probability and 
 



CHECKLIST FOR REVIEWING FOR THE FINAL   * indicates a "core" topic.
I. Differential Calculus: 
A. *Definition of the Derivative 
Limits / Notation 
Use to find the derivative 
Interpretation ( slope/ velocity/marginal cost-profit-revenue ) 
B. The Calculus of Derivatives 
* Sums, constants, x n, polynomials 
*Product, Quotient, and Chain rules  
*Trignometric functions 
*Expononential and logarithmic functions
Implicit differentiation 
Higher order derivatives 
C. Applications of derivatives 
*Tangent lines 
*Velocity, acceleration, rates (related rates)  
*Max/min problems 
*Graphing:
         * increasing/ decreasing 
 
         
concavity / inflection 
*Extrema (local/ global)  
Asymptotes 
The differential and linear and quadratic approximation  
Newton's method
L'Hospital's Rule: "0/0"  "inf/inf"
D. Theory
 
*Continuity (definition and implications) 
*Extreme Value Theorem /* Intermediate Value Theorem 
*Mean Value Theorem 

II. Differential Equations:
 
A. Solving Differential Equations ( Initial Value problems)
*Definitions and basic theorem 
Simple properties [ sums, constants, polynomials, trig] 
B. Euler's Method, etc. 
*Euler's Method 
*Simple differential equations with applications 
Tangent (direction) fields/ Integral Curves 
*Interpretations ( Net change) 

Back to Martin Flashman's Home Page :)


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: The Calculus Readiness Exam and at least four years of high school mathematics.

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.



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.
October 26
(Wednesday)
Last Day to Drop Courses
October 26
(Wednesday)
CR/NC Forms Due
October 28
(Friday)
Withdrawal Period Begins
December 7
(Wednesday)   
Last Day to Withdraw From Class

 
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