Final
Exams: Checklist 
58
Final Exam 1:00 4:00 pm in class room 
59
Alternate Final Exam 1:004:00 in Lab room 
Week 
Monday 
Tuesday (Lab) 
Wednesday 
Friday 
1.
Review Indefinite Integrals 
123 Introduction and initial review for
derviatives. 
124Review
DE's and estimation, Direction Fields/ Euler's Method/Integral Curves Antiderivatives, IVP's Linear Estimation Winplot  and DE's 
125 Indefinite Integrals Core Functions and Linearity 
127 Substitution 
2.
The Definite Integral 
130
More substitution, DE's and Euler. 
131
Estimating Areas 
21Euler
meets areaThe Fundamental Theorem of Calculus I 
23
The Definite Integral Definition  Interpretations The Fundamental Theorem of Calculus I' 
3.More
about the Definite Integral 
26
Average values 
27
Areas and definite integrals. 
28
Areas between curves. 
210
Work 
4.
Misc. on Def. Int. 
213
More work. Start Volume 
214
More Volume 
215
Volumes 
217
Substitution w/ Def. Int. Begin Numerical Integration 
5.
Numerical Integ. 
220 Presidents Day no class  22 Numerical Integration  222 Simpson's Rule  224 Arc Length SC:VIII.B 
6.
More Applications 
227
Arc Length VIII.B
General planar curves. 
228
Exam 1 
31Using
Functions to estimate Integrals. 
33
A preview of Taylor
theory. Sensible Calculus IX.A (OnLine) 
7.
DE's and integration 
36
Properties of the Definite Integral 
37 Models
and de's continued Taylor's Theorem I (exp) 
38
Taylor's Theorem I (exp) and estimating int_0^1 exp(x^2) dx 
310Models
and DE's define functions.FTof C for DE's. Learning and other rates that decrease over time: arctan. 

313
Spring Break No Classes 
314 Spring Break No Classes  315 Spring Break No Classes  317 Spring Break No Classes 
9.
DE's and Taylor 
320 FTof Calc (DE's) Separable DE's  321
Integrals Definite and Indefinite How they fit into solving DE's 
322 Sensible
Calculus IX.B (OnLine)
Taylor's
Theorem II 
324
TT II 
10.Series Testing  327
IX.B (OnLine) Calculus for TT IX.C (OnLine). 
328
Taylor's
Theorem 
329
The Logistic Taylor III Introduction to sequences, and convergence. 
331 
11. Power series  43 Geometric
Series 
44 Sequences and Series spreadsheets and graphs  45
Harmonic
and
Power
Series 
47Integral
and Comparison testing Alternating series. 
12. Taylor Series Plus  410
Positive Series. Integral test begun 
411 Midterm Exam #2  412
Infinite integrals, Integral test again. Integration by parts 
414 Integration
by PartsII, Power Series. Taylor Revisited and reviewed. 
13..Integration Methods  417
Abs
. converg. & Ratio test
Power
series II Applications of Power series to DE's. 
418 Power Series and De's  419 Finish Ratio Test and Applications to Taylor
Series and DE's. Power Series Theorem Differentiation/ Integration. 
421 Last Breath on Series?Examples...Proofs? 
14  424
Arc Tangent 
425 Integration Gateway Test. 
426
Improper
Integrals II 
428
More Arctan stuff L'Hospital's Rule 
15 
51
Volume of a torus Application of Improper Integrals Area and The Normal Curve(review of integration!) 
52
Overview of Course! Open Problem Session. 
53
Simple algebra for series. Fourier Series? Misc. Methods (partial fractions)? ln(2) Newton's computation/series? Calculus and proabability darts? 
54 Thursday! Last class Some last observations on the semester's work. What about the final exam! 
16
Final Exams 
58
Final Exam 1:00 4:00 pm in class room 
59
Alternate Final Exam 1:004:00 in Lab room 
Date Due  Reading  Problems 
Optional  Viewing: Ed Berger CD Tutorial [# of
minutes] * means optional #means online report on Blackboard 
HW #1 127 
SC
IVD SC IVE (online) 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 #2 130 
SC IVA(Online) SC IVB (Online) S&M: 4.1 pp322328 
On line
IVA:1(a,d,e,f),10; 4,
5(a,b),8,11 S&M: 4.1 p322: 511; 1521odd;5557;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 21 
S&M: 4.6 pp374378 SC IV.F READ 
S&M: 4.6
p382:58,11,13,16,21,26,29,39 
Online
tutorial for Substitution Another Tutorial on substitution. 

HW #4 23 
SC IVF(On line)  IV.F: 1,3,5,13,15,17(online) 

9.4.1 Approximating Areas of
plane regions. 
HW #5 26 
S&M:
4.2 p334 Example 2.5 SC VA ( On Line) 
S&M:
4.2 p 340: 712 V.A: 1,2 a (on line) S&M p 372: 57, 13,15, 
A tutorial on summations and summation notation.  
HW #6 28 
S&M:
4.4 pp359361 5.1 pp402405 
S&M
p 373:7782 
18.1.1 Finding the Average
Value of a Function [8] 

HW
#7 210 
S&M: 5.1 pp402405 S&M:5.6 pp453454 
S&M p 409: 5,7,913 
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 #8 213+15 
S&M: 5.1 pp 405 407 5.6 pp453454 
S&M
p 409: 13,17, 27,29 S&M p462 :5, 11 (wait till 215) 
10.2.2
Limits of integration and area[15] 10.2.3 Common Mistakes to Avoid 

Summary
#1 214 
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 pp453454 5.2: 411418 
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
#10 217 
S&M 5.2: 411418 
S&M
p423: 211, 23a, 31
a,b 

HW
#11 222 
S&M 4.6: pp380381 4.3: p 347348 4.7: pp 384388 SC VA ( On Line) 
S&M
p382:4751,54 S&M p349: 1113,35,36,41,42 S&M p396 part a and b only for 9 and 10 

HW
#12 224 
S&M 4.7 pp389392 remk 7.3. SC V.D (on line) 
S&M
p396: 13, 3133,37 
16.9.1 Deriving the Trapezoidal
Rule [12.5] 18.5.2 Finding Arc Lengths...[14] 

HW#13 227 
5.4
pp434435 Probability 
S&M p440: 5, 9  SC:Arc Length VIII.B  
Exam I 228 

Midterm Exam I covers material
related to HW's 112. 
Optional Review: p398:111 odd; 2125odd; 31,41,45,49 odd, 61 p 475 3,7, 11, ,15a, 33 p553: 71,75a. 

HW #14 33&8 
4.4 p351, 356360 9.3 pp739742 Sensible Calculus IXA (OnLine) 
S&M: p745: 5, 9 p362:3134 SC IXA: 1,2 

HW #15 310 
4.4 p351, 356360 Sensible Calculus IXA (OnLine) 
SC IXA: 35,10[ae] 

HW #16 322 
4.5 p 367269 6.4: p503505 6.5: p 512516 516518? 
S&M: p372: 4143, 55, 57 S&M: p 509: 5,6; p 519:13,1719, 29 
SC:VI.D models
and inverse trig 

HW #17 324 
6.4ex 4.1 Sensible Calculus IX.B (OnLine) 
S&M: p510: 1315 S&M: p 519: 19,20 29,33 Sensible Calculus IX.B (OnLine) :15 
20.3.1 Exponential Growth [12] 20.1.2 Solving Separable Differential Equations [9] 20.1.3 Finding a particular solution. [6] 

HW #18 327 
6.4 ex 4.2 IX.B (OnLine) In advance for class: IX.C (OnLine). 
S&M p 510: 2527, 29 Sensible Calculus IX.B (OnLine) :1315 
20.3.2 Radioactive decay [8] 19.12.2 Maclaurin Polynomials [9] 19.12.1 Taylor polynomials [14]. 

HW#19 329 
IX.C (OnLine) 6.4 pp5068 
IX.C (OnLine):15,7,8 S&M p 510: 31,33,35 
16.6.1 Introduction to Partial
Fractions [13] 

Summary
#2 329 
Partnership
Summary #2 covering work through
March 24th should be submitted by 5 pm [2pages  1 side or 1 page 2 sides.] 

HW #20 331 
6.5: p516518 IX.D ;X.A 
S&M p519:35, 37 IX.D: 14, 10,12 
p520:55, 59 

HW #21 43 
X.A X.B 8.1 pp622623, 625626 
X.A :
19 odd S&M: p634 58, 914 part a only, 1521 
19.1.1 The limit of a
sequence.[10] 19.1.2 Deteremining the limit of a sequence.[9] 

HW #22 45 
X.B 8.1 pp628631 8.2 pp 636641 
S&M : p 634:5153 S&M: p644: 510, 19, 20, 25 
19.3.1 Introduction to Infinte
Series [11] 19.3.3 geometric series[13] 

HW #23 47 
X.B 8.1 pp6278;631632. 8.2 pp641644 
S&M : p 634: 3941; p644: 13,15,16,2528 
19.4.1 properties of convergence
[7] 19.4.2 test for divergence [8] 

HW #24 410 
8.3: pp 647649 8.4 : pp 658661 
S&M: p656: 511odd.; p664: 511 odd, 31 

Exam
II 411 
Midterm Exam II covers material related to HW's 1324.  Optional
Review: p362: 31,33; p400: 59 p476:19; p552: 17, 19, 49, 51, 55, 57, 61, 63, 75 p718: 15,9,10,19,21,25, 69 

HW #25 414 
7.2pp560563 7.7pp610613 omit example 7.8 8.3 pp647649 omit example 3.1. 
S&M 7.2 p566: 311 7.7 p617: 1517, 25 8.3: p 656: 49, 19 
VII.C. Integration by Parts  16.6 .1 3 Integration by parts. 19.5 .1&2 The integral test 
HW #26 417 
7.2 pp564566 X.B5 
S&M 7.2 567: 13,19,21, 25,
31, 32, 41,45 

HW# 27 421 
8.5: p666670 8.6:675678 X.B5 XI.A Power Series 
S&M 8.5 p673: 59, 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 #28 424 
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: 2932,
3942, 4547, 49 S&M: 8.8 p702: 17,19. 

HW #29 426 
6.7 pp530534 6.8 536538; 540 p 648 Example 3.1 p679 Example 66. 
S&M 6.7 p535:
510,13,20, 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 #30 428 
7.7: pp 605609  S&M: 7.7 p617: 39 odd, 1113,37,38  17.1.Improper integrals 

HW #31 51 
7.6  S&M: 7.6 p603: 35, 17,18,23, 25, 26,29  14.1 and 14.2 L'Hopital's Rule 

Summary
#3 51 
Partnership
Summary #3 covering work through
April 28th should be submitted by 5 pm [2pages  1 side or 1 page 2 sides.] 
Back to Martin Flashman's Home Page :)
(ISBN 0072398485) This browserbased electronic supplement provides access to the entire Calculus text in an interactive format. Features include over 200 textspecific JAVA applets and over 400 algorithmicallygenerated practice problems, designed to demonstrate key concepts and examples from the text. The electronic student solutions manual is integrated for full comprehension of exercises. 
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.
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, 4
for OK, 3 acceptable, or 2 or 1 unacceptable and
will be used in determining the 50 points allocated for cooperative
assignments.
Reality Quizzes  150 points 
2 Midterm Examinations  200 points 
Homework  150 points 
CD Tutorials 
discontinued 
0 points 
Cooperative work(Labs/POW's + Summaries)  100 points 
Final Examination  200/300 points 
Total  800/900 points 
** See the college course schedule for the dates related to the following :
Last Day to Drop Courses  
CR/NC Forms Due  
Withdrawal Period Begins  
Last Day to Withdraw From Class 
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.
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.
Power Series: Polynomials and Series.
