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);

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);

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

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

Group Work Target Practice adapted from Dr. Rhoads

with(Student[Calculus1]):

TaylorApproximationTutor();

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

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

9.4 Series Convergence slides and clicker for alternating series.

9.5 Power Series slides and clicker <94SeriesGroupWork.pdf>Group Work Target Practice

Continue 9.4 Series Convergence slides and clicker by limit comparison and ratio tests.

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.

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

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

Zeno's Paradox

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

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:

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));

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

8.1. Slice and Conquer slides and clicker

cone

sphere 1 sphere 2

cylinder

Area Practice, and Volume Practice

cone comic

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

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);

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).

7.4 slides and clicker questions #1

Group Work Target Practice.

adding the C

Intro to Maple in 303 computer lab. pdf. If time remains, work on hw in the lab.

Intro. Review of calc 1, including FTC, definite and indefinite integrals, derivatives and antiderivatives. Trig and Derivative Review. Calc I review contest.

7.1 slides and clicker (substitution).

Group Work Target Practice. with(Student[Calculus1]); ApproximateInt(exp(x^2),x = 0 .. 2, output = plot);

Go over the class webpages and Wiley.

Mention