Week |
Monday |
Tuesday (Lab) |
Wednesday |
Friday |
1. Introduction and beginning
review. Ch 0 |
8-31 Introduction Numbers |
9-2
Class Division Finish Intro. |
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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 |
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. |
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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] |
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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] |
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Lab #2 Submit by 9-16 |
Lab #2 9-13-05
on Blackboard |
Submit Problems from lab. |
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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] |
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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] |
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Lab #3 9-23 |
Lab #3 9-20-05 on Blackboard. |
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POW #1 Submit by 9-27 |
POW #1 on line. |
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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] |
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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. |
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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 |
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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 |
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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. |
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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] |
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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] |
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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 |
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Summary #2 Submit by 10-15 5 pm |
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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. |
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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. |
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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.] |
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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] |
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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 |
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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] |
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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] |
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HW #26 11-4 |
SM: 3.3 |
SM:p 268: 33-39,41 |
The
connection between Slope and Optimization [28] |
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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 |
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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. |
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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 |
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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] |
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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 |
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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. |
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HW 33 11-28 |
SM 3.1pp247-249 SM 3.6 Ex 6.6 |
SM: p 250 : 31- 36, 47,48 |
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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 |
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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 |
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HW
36 12-5 |
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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. |
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SC-Ch1.C1 (html Draft version) : 4,5,7,8 | *Graphing
Trig Functions[17] |
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SC IVA(On-line) | |||
On line
IVA:1(a,d,e,f),10 |
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SC
IVA(on-line) |
IVA: 4,
5(a,b),8,11 |
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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] |
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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] |
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SC IV.F READ |
Vertical asymptotes [9] | |||
SC
IVF(On
line) |
IV.F:
1,3,5,13,15,17(on-line) |
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SC VA (
On Line) |
V.A:
1,2
a (on line) |
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SC VA (
On Line) |
VA : 5(a,b) |
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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 |