Week 
Monday 
Tuesday (Lab) 
Wednesday 
Friday 
1. Introduction and beginning
review. Ch 0 
831 Introduction Numbers 
92
Class Division Finish Intro. 

2. Background and Motivation Ch
0 and 2.1 
95 No Class Labor Day 
96
Intro to Winplot Backboard 
97
Linearity Functions Visualization. Models and linearity: Physical, Geometric, Random, Economic. 
99More on functions and
models.Physical, Geometric, Random, Economic. 
3. The Derivative As a Number
Definition 2.1 , 2.2 
912 Change: The tangent problem. The Velocity Problem. 
913 Secant and tangents with winplot. 
914 More estimation of rates. Start the derivative. 
916 The derivative: Definition and four steps. 
4. The Derivative As a
Function. Core Algebraic Functions: Powers, roots, Linearity.
2.2, 2.3 
919 Begin Derivative as function. Number, graph, symbolic. Graphical connections between functions and their derivatives. 
920 Rates, Accumulation and. Estimation. [Euler?] 
921 Core functions and Rules.
Powers, sums, scalar multiples. Interpretations. 
923 More Core: Powers, sums,
scalar multiples. 
5. The Derivative, Other Models,
The Differential and Estimation. 3.1? The Calculus of Derivatives.
Trigonometry 2.5 
926 Roots. Interpretations of rules plus other interpretations of derivatives: Probability, economic interpretations. 
927 Estimations with population models:P'(t) depends on P and t 
928 The differential and linear
estimation. Intro to the Logistic Model. 
930 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 
103 Finish Sin'(x), Cos'(x). Intro to f '', f '''', etc. 
104 DE's,Winplot, Direction
Fields and Euler's Method. PredatorPrey Models 
105 The product rule. 
107 Begin Continuity. IVT Newton's Method? 
7.Direction Fields. Quotients 2.4 , Finish trig. 
1010 Finish Newton. Quotient Rule Apply to tan, sec 
1011Newton's method  with
excel and winplot 
1012 Misc. Details on limits,
continuity, Newton's Method. 
1014 "euler" and direction
fields. 
8. The Chain Rule! 2.7 Direction fields, Euler's method.  1017review euler and direction
fields 
1018 Midterm Exam #1 
1019 Begin the Chain Rule.The
Chain Rule! 
1021 Fall
Break No Class 
9. Exponential and log
functions. 2.6 Implicit Differentiation and related rates.2.8 
1024 More Chain Rule! Start Exponential Function derivatives. 
1025 Implicit functions
Implicit differentiation 
1026 More on implicit
functions. Derivative of Exponential functions. 
1028 Derivative of
ln(x).Related rates.More implicit differentiation. 
10.
Inferences based on the derivative: Extrema, 2.9, 3.3, 3.7, (4.1) 
1031Related rates.More implicit
differentiation. 
111Gateway 3 ln(2) estimation using euler with winplotand tables, and calculus! 
112 more related rates. Extrema "word problems". 
114 More on extrema and
word problems. 
11.
The MVT, and antiderivatives. First derivative analysis. Increasing/decreasing, 2.9,3.4, 6.4, 6.6 
117 More extreme problems.
Proof of CPT. Inferences based on derivatives.The MVT . 
118 Proof of MVT and its
immediate consequence for DE's. Arctangent estimation of pi, 
119 Solving initial value
problems. First derivative Analysis: Increasing/Decreasing. 
1111 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.  1114 Concavity 
1115 Exploring f where f '(x) = sin(x^{2}) 
1116 Concavity and differential
estimates. Asymptotes and infinite limits. 
1118 L'Hopital's
rule 0/0, etc. 
13 Misc. Applications.3.8 
1121 More on L'Hopital's Rule. Partial Derivatives.(on Line) 
1122 Midterm Exam #2 
1123 NO CLASS Thanksgiving Break 
1125 NO CLASS Thanksgiving Break 
14.
DE's and other Functions 6.7, 6.8 
1128 Partial Derivatives 
1129 Visualizing Partial
Derivatives when z = f (x,y) 
1130 More on L'Hospital. Darts revisited! "Euler Sums, Net Change, and Differential Equations." 
122 Estimations with Quadratic
polynomials. 
15. 
125 
126 
127 LAST CLASS Review & Final Remarks 
Friday 129 Final Exam Offering #11:004:00pm 
16. 
1212 
1213 
1214 
Thursday 12 15
Final Exam Offering #2 8:30 11:30 am 
Date Due  Reading  Problems 
Optional  Viewing: Ed Berger CD Tutorial [# of
minutes] * means optional 
HW#1 92 
SM 0.1 SC 0.B1 Numbers [online] 
rev.
sheet (online): 13,6,13,15,16,18,19 SM: p. 9: 5, 11, 21, 33, 43 
SM: p10 49, 51 
Introduction;
How to Do Math 
HW#2 97 
SM 0.2 SC 0.B2 [online] 
SM: p20:57,1317, 2125,4145; 5358; 75,76, 89, 90, 9698 
SM:9194 Online Mapping Figure Activities 
Functions [19] 
HW #3 99 
SM 0.2,
0.3, 0.4 SC 0.B2 [online] 
SM: p21: 3136, 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 
Online
Mapping Figure Activities SC 0.B2 On line # 19, 20, 21 
Parabolas
[22] Average Rates of Change [11] 
LAB #1 Submit by 99! 
Lab #1 9605 on Blackboard 
Problem #1 submit with partner. Problems #2 and 3 may be submitted solo or with partner. 

HW #4 912 
SM: 0.4, 0.8 (pp7273only) 0.C [online] 
Practice sheet for Gateway on
Functions. SM: p76: 3,4,8,9 Ch 0 rev: p78: 912,17,18, 63 
The Two
Questions of Calculus [10] 

HW #5 914 
SM: 2.1 pp 150152, 155156
middle. SC I.A (Draft version) 
SM: p161:914, 35, 36, 43, 44 SC: 0.C [online] 4,5 
Slope of
a Tangent Line [12] Rates of Change, Secants and Tangents [19] 

Lab #2 Submit by 916 
Lab #2 91305
on Blackboard 
Submit Problems from lab. 

HW #6 916 
SC I.A
(Draft version) 
SM: Use "4 step method "
to find the slope of the tangent line for these problems: p161: 2125,
39,40 
SM:
p163:57 
Finding
Instantaneous Velocity [20] Equation of a Tangent Line [18] 
HW #7 919 
SM: 2.2. pp164169. SC I.D (.pdf Draft version) 
SM: Use "4 step method " to find the derivative for these problems: p173: 9,10, 1315, 2126, 35, 37, 5356.  The
Derivative [12] 

HW #8 921 
SM: 2.2. pp164169. 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 #3 923 
Lab #3 92005 on Blackboard. 

POW #1 Submit by 927 
POW #1 on line. 

HW #9 923 
SM: 2.3.176178. SCI.F: pp 14 (Download pdf file) 
SM p184: 58, 13,14, 44, 45,
47, 48; 6367 
Uses of
The Power Rule [20] Short Cut for
Finding Derivatives [14] More on Instantaneous Rate [19] 

Summary #1 Submit by 927 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 #10 926 
SM: 2.3 pp179181. SCCh1.F (Download pdf file) 
SM: p184: 1517,21,23,24,49 SC CH1F.:2,3,5,9,13 
SC:
14,16 
Differentiability
[3] Review of Trig[12] 
HW #11 928 
SM:3.8 Example 8.5 
SM:p 184:19,
20,43; p317: 2730 

Lab #4 930 
Lab #3 92705 on Blackboard. 
Population models using
spreadsheets. 
Sample
for a logistic differential equation used
in class: 928 

HW
#12 930 
SCCh1.C1
(html Draft version) SCCh1.C2 (Download pdf file) SM 3.1pp242244middle example1.3 . 
SM:
p249: 58,19 
Read
web materials on differentials Read online Sens. Calc. 0.C on Probability Models 
Using tangent line approximations [25] 
HW #13 103 
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 #14 105 
SM 2.3 p1834 review SM 2.5 pp196 toThrm 5.2, Ex: 5.3, 5.4. SCCH3A1(pdf) 
SM p184:2530,
35, 37, 3941, 52, 53, 55 SM p204: 45, 46 
Read
web materials on trigonometric derivatives. 

HW #15 107 
SM:
2.4. pp 187189, Ex. 4.7 SM: 2.5 : Ex. 5.1 
SM p 194: 59, 33, 37, 39 SM p 203:9, 13, 17, 19, 34 
The Product Rule [21]  
HW #16 1010 
SM 1.3 pp102104; 108110 SM 2.2 p170 through Ex 2.9 SCCH1.I(pdf) 
SM:p 111: 510, 12, 15, 16,
37, 
One Sided
Limits [6] Continuity and discontinuity [4] 

HW #17 1012 
SM:
2.4. pp 189193 SM: 2.5.
pp200201, Ex. 5.5 SCCH1.IB(pdf) SM 1.3 pp102104; 108110 
SM p 194: 1113,19,20 SM p.203:7,10,18 
The
Quotient Rule [13] 

HW #18 1014 
SCCH1.IB(pdf) SM 1.3 pp102104; 108110 SM: 3.2 
SM: p 113:41, 43, 45 SM:: p256: 79, 11,17, 21,23,27, 29 

Summary #2 Submit by 1015 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 1017 
SCCH3A2(pdf)[newton's
Method] SC IVD [Tangent fields] SM 6.6 pp 524  527??{euler) 
SM: 528: 5,7 IV.D: 111 odd (online) 
Read
web materials on Newton's Method. 
20.1.4
Direction Fields
and Euler's Method [6] 
1018 
Examination #1 Self schedule: 6090 minutes 1:304:30 (lab time) 
Covers
all assignments and labs through that assigned for 1015 and related
reading. Sample exam available on Blackboard. 

HW#20 1019 
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 1024 
SM
2.7 pp213214. Examples 7.1,
7.4, 7.5,
7.6 SM 2.6 pp205207 [exponential functions] 
SM
p218: 5,911, 1317, 25,27,48 
Using the
Chain Rule [13] 

HW
#22 1026 
SC Chapter II.B SM 0.6 pp 5054 SM 2.6 pp205207 [exponential functions] 
SM
P61: 2124 SM: p 218: 6,12, 18, 25,27,29, 30, 42, 51,53 

HW #23 1028 
SM :
2.8 pp 220224 Read web materials on implicit differentiation. SC Chapter I.F.2 Derivatives of exponential and logarthmic functions (in part) 
SM: p 227: 57, 23, 26 SM : p 211: 58, 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 1031 
SM: p211 SM:2.8 pp225226 SC Chapter I.F.2 Derivatives of exponential and logarthmic functions 
SM:: p211: 1922,,26,27,35 SM: p219:23,24,35 
The Ladder
Problem [14] Acceleration
and the derivative.[5] 

HW#25 112 
SM:2.8
pp225226 
SM:
p227:31,33,34,4145,48,49,51,62 
The Baseball Problem[19] The Blimp Problem [12] 

HW #26 114 
SM: 3.3 
SM:p 268: 3339,41 
The
connection between Slope and Optimization [28] 

HW
#27 117 
SM: 3.3 SM: 3.7 pp298303 OnLine tutorial on Max/mins 
SM:p268;
p267: 511, 21, 23 SM: p306: 8, 13,15 
SC IVA(Online)  Critical
Points [18] Three Big Theorems [11] 
HW
#28 119 
SM:
2.9 SM: 3.7 pp303306 
SM
p237:11, 3537 SM: p268: 39, 41, 42 SM: p306: 15, 19 
The Box Problem [20]  Intro
to Curve Sketching [9] 
Summary #3 Submit by 1111 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 1111 
SM: 3.4 p269274 SC IVB (Online) Read 
SM:
p 276: 58, 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 1114 
SM:
3.5 pp278282 
SM:
p 276: 1517,27, 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 1115 
POW
#4 Available on Blackboard 

HW
31 1116 
SM:
3.5 pp278282 
SM::
p284: 7, 911,27,28, 4143, 47, 49 SM: p308: 36 
The
2nd Deriv. test [4] Acceleration & the Derivative [6] Graphs of Poly's [10] 

HW 32 1118 
SM 1.4 SM 3.5 examples 5.6 and 5.7 SM 3.6: pp287291 
SM: p122: 511 odd, 2127 odd SM p 296: 5,7,23,24 

1122 
Examination #2 Self schedule: 6090 minutes 1:304:30 (lab time) 
Covers
all assignments and labs through that assigned for 1118 and related
reading. Sample exam will be available on Blackboard. 

HW 33 1128 
SM 3.1pp247249 SM 3.6 Ex 6.6 
SM: p 250 : 31 36, 47,48 

HW 34 1130 
SM 3.6 EX. 6.2, 6.3 ONLINE: SM:12.3(optional) 
ONLINE
SM:chap12.3: 59,[27 and 29 just evaluate the partial
derivatives],47 
SM:
applets
tutorial at Harvey Mudd Partial Differentiation 

HW
35 122 
SM
7.6 DARTS 
SM
p. 37,1719, 2325, 2729. 
Basic Uses of L'Hospital's Rule 

HW
36 125 

Summary #4 Submit by 125 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. 


SCCh1.C1 (html Draft version) : 4,5,7,8  *Graphing
Trig Functions[17] 


SC IVA(Online)  
On line
IVA:1(a,d,e,f),10 


SC
IVA(online) 
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:
111 odd (online) 
The connection between Slope and Optimization [28]  Domain restricted functions ...[11] 

SC IVE (online) 
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(online) 

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 
Back to Martin Flashman's Home Page :)
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.
Every week (with some exceptions) partners will submit
a response to the "problem/ lab activity of the week."
All cooperative problem work will be graded +(5 well
done), ü(4
for OK), (3 acceptable), or unacceptable(1) and
will be used in determining the 50 points allocated for cooperative
assignments.
Reality Quizzes  150 points 
Oral Quiz  20 points 
2 Midterm Examinations  200 points 
Homework  130 points 
CD Tutorials 
50 points 
Cooperative work(Labs +)  100 points 
Final Examination  200/300 points 
Total  850/950 points 
** See the college course schedule for the dates related to the following :
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 