### 1120 Class Highlights

• Thur Jun 23 Test 3. Have a great rest of the summer!
• Wed Jun 22 Finish questions. Time for review.
• Tues Jun 21
Take questions on 11.5-11.6
Differential Equations Vermeer and last few slides
Population clock
Group work target practice
11.7: Logistic slides adapted from Holly Hirst
with(DEtools):
DEplot(diff(P(t), t) = 0.5e-1*P(t)*(1-(1/100)*P(t)), P(t), t = 0 .. 100, P = 0 .. 170, [P(0) = 20, P(0) = 170], arrows = medium, linecolor = black);

• Mon Jun 20
Take questions on 11.1-11.4. Quiz 12.
Differential Equations 11.5 & 11.6 slides and clickers
So you think you can fake a vermeer? Han van Meegeren

with(DEtools):
DEplot(diff(y(t),t) = y(t), y(t), t = -1 .. 1, y = -1 .. 1, [y(0) = .5, y(0) = -.5, y(0) = 0], arrows = medium, linecolor = black);
DEplot(diff(y(t),t) = -y(t), y(t), t = -1 .. 1, y = -1 .. 1, [y(0) = .5, y(0) = -.5, y(0) = 0], arrows = medium, linecolor = black);
DEplot(diff(y(t),t) = y(t)/t, y(t), t = -1 .. 1, y = -1 .. 1, [y(.1) = .5, y(-.5) = -.1, y(.1) = .1], arrows = medium, linecolor = black);
DEplot(diff(y(t),t) = y(t)*t, y(t), t = -1 .. 1, y = -1 .. 1, [y(0) = .5, y(0) = -.5, y(0) = 0], arrows = medium, linecolor = black);

• Fri Jun 19
Continue Differential Equations slides and clickers for 11.1-11.4 with 11.2, 11.3 and 11.4.
11.2 Group Work Target Practice

• Thur Jun 18
Review
10.2 Taylor Series slides and clickers
10.3 and 10.4 Finding and Using Taylor Series and Error Bounds slides and clickers
Take questions on 10.2, 10.3 and 10.4. Quiz 11 on those sections.
Finish up Lagrange Error being useful (sometimes) to show the series converges to the function
Fourier series and Fourier transform, Fourier Jean-Baptiste Joseph Fourier
Begin 11.1 Differential Equations slides and clickers

• Wed Jun 17 Take questions on 10.2. slides and clickers on 10.3 and 10.4. Finding and using Taylor Series. 10.4. Error in using a degree n Taylor polynomial to estimate a function.
Group Work Target Practice adapted from Dr. Rhoads
with(Student[Calculus1]):
TaylorApproximationTutor();

• Tues Jun 16
Review
9.2 Series, Geometric slides and clicker
9.3 Series, Partial Sums and Integral Test slides and clicker
9.4 Series Convergence slides and clickers
10.1 Taylor Polynomials slides and clickers
Take questions on 10.1 or 9.1, 9.2 and 9.4, and then quiz 10 on 10.1 and determining what series to use.
10.2 Taylor Series slides and clickers
Taylor series animation
Wolfram alpha

• Mon Jun 15
Review
9.4 Series Convergence slides and clickers
9.5 Power Series slides and clickers
Finish last slide of 9.5, and then take questions on them. Then quiz 9 on 9.4 and 9.5
10.1 Taylor Polynomials slides and clickers
Group Work Target Practice on Taylor Polynomials in Maple, pdf version

• Fri Jun 12 Take questions on 9.4.
9.4 Series Convergence slides and clicker for alternating series.
9.5 Power Series slides and clicker <94SeriesGroupWork.pdf>Group Work Target Practice

• Thur Jun 11 Test 2.
Continue 9.4 Series Convergence slides and clicker by limit comparison and ratio tests.

• Wed Jun 10 Holly Hirst's series sheet
Finish last slide of 9.3 Series, Partial Sums and Integral Test slides and clicker. quiz 8 on 9.3. Begin
9.4 Series Convergence slides and clicker Direct Comparison Test
review for test 2.

• Tues Jun 9 Review:
9.1 Sequences slides and clicker
9.2 Series, Geometric slides and clicker
quiz 7 on 9.1 and 9.2.
9.3 Series, Partial Sums and Integral Test slides and clicker
Dr. Rhoads' Group Work Target Practice on the Integral Test

• Mon Jun 8 Review
8.1. Slice and Conquer slides and clicker
8.2 Volumes (Revolutions) and Arc Length slides and clicker
8.4 Varying Density slides and clickers
8.5 Work slides and clicker
Quiz 6 on density and work.
George Berkeley The Analyst: A DISCOURSE Addressed to an Infidel MATHEMATICIAN. WHEREIN It is examined whether the Object, Principles, and Inferences of the modern Analysis are more distinctly conceived, or more evidently deduced, than Religious Mysteries and Points of Faith
9.1 Sequences slides and clicker
9.2 Series, Geometric slides and clicker
In Maple, when you first launch it, there are icons. After choosing the calculus icon, at the bottom of the list are sequence and series applets which check for convergence and plot the first n terms or the first n partial sums.
Group Work Target Practice
• Fri Jun 5
Review 7.5 Numerical Approximations and clicker,
8.1. Slice and Conquer slides and clicker
8.2 Volumes (Revolutions) and Arc Length slides and clicker
Quiz 5 on 7.5, 8.1 and 8.2. 8.4 and 8.5
Finish 8.4 Varying Density slides and clickers
Elizabeth's slides for work. 8.5 Work slides and clicker.
Group Work Target Practice. Choose some problems to work on:
8.1 11, 13, 15, 16, 18, 26
8.2 25, 26, 35, 53
with(plots);
a := plot(x^(1/3), x = 0 .. 9);
b := plot((1/4)*x, x = 0 .. 9);
display(a, b);

with(Student[Calculus1]): with(plots):
VolumeOfRevolution(sqrt(x^2-1),x=2..3,output=plot);
VolumeOfRevolution(sqrt(x^2-1),x=2..3,output=integral);

ArcLength(sqrt(x^2-1),x=2..3);
evalf(ArcLength(sqrt(x^2-1),x=2..3));

8.4 16 a and b and End of Chapter p. 487 Medical Case Study: Testing for Kidney Disease
8.5 22

• Thur Jun 4 8.2 Volumes (Revolutions) and Arc Length slides and clicker
with(Student[Calculus1]): with(plots):
plot(sqrt(x),x=0..4);
VolumeOfRevolution(sqrt(x),x=0..4,output=plot);
VolumeOfRevolution(sqrt(x),x=0..4,output=integral);
a:=VolumeOfRevolution(0,x=0..4,distancefromaxis=3,output=plot):
b:=VolumeOfRevolution(sqrt(x),x=0..4, distancefromaxis=3,output=plot):
display(a,b);
a:=VolumeOfRevolution(4,y=0..2,output=plot):
b:=VolumeOfRevolution(y^2,y=0..2,output=plot):
display(a,b);
VolumeOfRevolution(y^2,y=0..2,distancefromaxis=4, output=plot);

Int(sqrt(1+x^(-4))*1/x*2*\pi,x=1..infinity);
int(sqrt(1+x^(-4))*1/x*2*\pi,x=1..infinity);
8.4 Varying Density and clickers

• Wed Jun 3 Test 1 and Chapter 8.
8.1. Slice and Conquer slides and clicker
cone
sphere 1 sphere 2
cylinder
Area Practice, and Volume Practice
cone comic

• Tues Jun 2 Quiz 4 on improper integrals. Review and 7.5 Numerical Integration Methods. In Maple, review left and right sums with 3, 30, 300, 3000, 30000 partitions:
with(Student[Calculus1]);
ApproximateInt(exp(-x^2),x = 0 .. 2, method=left, partition=3, output = plot);
ApproximateInt(exp(-x^2),x = 0 .. 2, method=right, partition=3, output = plot);
ApproximateInt(exp(-x^2),x = 0 .. 2, method=midpoint, partition=3, output = plot);
ApproximateInt(exp(-x^2),x = 0 .. 2, method=trapezoid, partition=3, output = plot);
ApproximateInt(exp(-x^2),x = 0 .. 2, method=simpson, partition=3, output = plot);

Group Work Target Practice adapted from Greg Rhoads.
7.5 Numerical Approximations slides and clicker

• Mon Jun 1 Quiz 3 on partial fractions and trig substitution. 7.6 Improper Integrals slides and clickers.
plot(x^(-2),x=0..5);
plot(x^(-(1/2)),x=0..5);
plot(1/(1+x^2),x=-5..5);

google: plot ln(x), plot exp(x), plot 1/x^2, plot exp(-.4x), plot exp(-x^2), plot arcsin(x) drag the graph
Group Work Target Practice
7.6 marks the end of test 1 material. Discuss hw.
Begin Applications of Integrals, including 7.5 Numerical Integration Methods. In Maple, review left and right sums with 3, 30, 300, 3000, 30000 partitions:
with(Student[Calculus1]);
ApproximateInt(exp(-x^2),x = 0 .. 2, method=left, partition=3, output = plot);
ApproximateInt(exp(-x^2),x = 0 .. 2, method=right, partition=3, output = plot);

• Fri May 29 Continue partial fractions and trig substitution from 7.4. Visualization via the partial fractions representing local behavior of the function around the asymptotes. Take questions on the homework.
7.4 slides and clicker questions #2-3 7.4 Integration by Trig Substitution slides and clickers.
#1 on Group Work Target Practice
Didn't get to:
Group Work Target Practice
Assistants, Tasks and Tutors: Task, PartialFractionsStepwise. Stepwise Partial Fraction Decomposition in Maple on 3x+11/(x^2-x-6) and then compare to integrate as well as convert(f, parfrac, x).

• Thur May 28 Review parts and substitution. Take questions on the homework. Quiz 2 on parts and substitution. algebra. practice. 7.4 Integration by Partial Fractions presented by Elizabeth Tadvick.
7.4 slides and clicker questions #1

• Wed May 27 Take questions on the homework. Quiz 1 on w-substitution. Calculus II chance to turn weaknesses into strengths. 7.2 slides and clicker (Integration by Parts). visualization
Group Work Target Practice.