Differential Equations 11.5 & 11.6 slides and clickers

So you think you can fake a vermeer? Han van Meegeren

Population clock

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);

Group Work Target Practice

Logistic Growth

Finish 11.4 slides and clickers

Animated Short Story-Differential Equations spot the error

Differential Equations 11.5 & 11.6 slides and clickers

11.3 and 11.4 slides and clickers

10.3 and 10.4 Finding and Using Taylor Series and Error Bounds slides and clickers

Fourier series and Fourier transform, Fourier Jean-Baptiste Joseph Fourier

11.1 and 11.2 Testing Differential Equations and Slope Fields slides and clickers

11.2 Group Work Target Practice

e^x Taylor series

Continue 10.3 and 10.4 Finding and Using Taylor Series and Error Bounds slides and clickers

with(Student[Calculus1]):

TaylorApproximationTutor();

Review that the signs of the first three terms tell us whether the function is above or below the x axis, whether the function is increasing or decreasing, and whether the function is concave up or down, at the center.

Review that we can find the radius of convergence by using the geometric series or ratio test, or by inheriting it from a parent in 10.3.

Take questions. Quiz 10.

Finish Taylor Polynomials in Maple. Maple version

Clicker review for 10.2: 10.1 and 10.2 Taylor Series slides and clickers

Group Work Target Practice

Begin the first slide of 10.3 and 10.4 Finding and Using Taylor Series and Error Bounds slides and clickers

10.1 and 10.2 Taylor Series slides and clickers

Taylor Polynomials in Maple. Maple version

Quiz 9.

Take questions. Take out series theorems.

Review geometric power series from last class (Ex 2). clicker.

Finish last slides on 9.5 Power Series slides and clickers

1 + x + x^2 +... = 1/(1-x) for |x| < 1: animation of geometric power series

Begin 10.1 Taylor Polynomials slides and clickers

Taylor series animation

Review 9.2-9.4 series tests series review

Group Work Target Practice.

Review and clicker 4: Continue 9.4 Series Convergence slides and clicker Alternating Series.

9.5 Power Series slides and clickers.

Clicker

Continue 9.4 Series Convergence slides and clicker (Direct) Comparison Test, Limit Comparison and Ratio. Hand out Group Work Target Practice and series sheet

Clicker

Begin 9.4 Series Convergence slides and clicker (Direct) Comparison Test

Discuss the study guide and review for test 2

Review and finish 9.3 series partial sums, series divergence when terms not getting smaller, linearity arguments, and the integral test.

geometric series versus p-series slides

table of when series tests give convergence or divergence

Discuss the study guide.

Review the methods on the slides 9.3 series partial sums, series divergence when terms not getting smaller, linearity arguments, and the integral test, and introduce the integral test.

table of when series tests give convergence or divergence

pi-day activities!

Explore the worksheet.

Begin working on worksheet.

9.2 Series, Geometric slides and clicker

slicing for volume, density and work practice

George Berkeley

9.3 series partial sums, series divergence when terms not getting smaller, linearity arguments, and the integral test

9.1, 9.2, 9.3 summary sheet

Emily found this pizza comic

9.1 Sequences slides and clicker

9.2 Series, Geometric slides and clicker

Zeno's paradox comic

Group Work Target Practice, solutions

Emily found this pizza comic

Quiz on 8.4 density and 8.5 work

9.1 Intro in Maple Open Maple. When you first launch it, there are icons. After choosing the calculus icon, at the bottom of the list open the sequence applet. (If that doesn't work, you can open it from here).

Continue 8.5 Work slides and clickers

Group work target practice and solutions

Review slicing a cone and cylinder

Surface of revolution animation, animation 2, animation 3

8.4 Density slides and clickers

8.5 Work slides and clickers

math jokes

8.1. Slice and Conquer slides and clicker

8.1 volume practice

sphere 1, sphere 2

cone

cone comic

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);

a:=VolumeOfRevolution(0,x=0..4,distancefromaxis=3,output=plot):

b:=VolumeOfRevolution(sqrt(x),x=0..4, distancefromaxis=3,output=plot):

display(a,b);

VolumeOfRevolution(y^2,y=0..2,distancefromaxis=4, output=plot);

rocket science

int(sqrt(cos(x)),x);

8.1. Slice and Conquer slides and clicker with(plots);

a := plot(x^(1/3), x = 0 .. 9);

b := plot((1/4)*x, x = 0 .. 9);

display(a, b);

8.1 area practice

8.1 volume practice

7.5 Numerical Approximations and clicker

Finish Group Work Target Practice adapted from Greg Rhoads.

partial solutions

Scientific American article and cuneiform

Mention comparison methods. Bigger than a diverging integral or smaller than a converging integral.

with(plots):

a:=plot(1-x^2,x = -1.1 .. 1.1):

b:=plot(x^2-1,x=-1.2..1.2):

display(a,b);

Begin 8.1. Slice and Conquer slides and clicker

8.1 Area Practice

Write up exp(-x^2), xexp(-x^2), x^2exp(-x^2), x^2/sqrt(4-x^2), x/sqrt(4-x^2), 3/(4-x^2)

Review trig sub and the difference between w-sub and trig sub.

Review for Test 1

Riemann sum

7.5 Numerical Approximations and clicker

Group Work Target Practice adapted from Greg Rhoads

partial solutions

Download, open and work through the Maple Worksheet on 7.5 Numerical Integration pdf

Hand out the small card (one side allowed as a cheat sheet for next Monday's test), and 7.5 worksheet to bring to class tomorrow (or as part of what to work on if there is a snow cancellation!)

Review 7.6 Improper Integrals slides and clickers

Group Work Target Practice

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);

Practicing Correctly and ASULearn grades.

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

Visualization via the partial fractions representing local behavior of the function around the asymptotes.

- Review the first two slides from 7.4 slides and clicker (Integration by Partial Fractions)
- Introduce your self to a neighbor or two and work in groups on Group Work Target Practice
- Download and open this Maple worksheet and follow the directions there
- Make sure I've gotten around to see your work when you've finished, and if there is any time left, you may work on Wileyplus homework for tomorrow, ask me questions, or leave.

7.4 slides and clicker (Integration by Partial Fractions)

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).

Comic

7.2 slides and clicker (Integration by Parts).

visualization

Integration by Substitution and by Parts in Maple

Int(x^2*exp(x^3),x); int(x^2*exp(x^3),x);

Int(x*sin(x),x);int(x*sin(x),x);

Changing a) so that it is an integration by parts (double):

Int(x^2*exp(x),x);int(x^2*exp(x),x);

Int(x^10*ln(x),x); int(x^10*ln(x),x);

Int(sin(x^2),x); int(sin(x^2),x);

?FresnelS and google search for The Fresnel Sine Integral

Group Work Target Practice.

adding the C

practicing correctly

7.1 substitution review

Group Work Target Practice

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

Take questions on the homework. Quiz 1 on w-substitution.

Advice from previous students

7.2 slides and clicker (Integration by Parts).

7.1 substitution slides and clicker

Algebra, Trig and Derivative Review

Calculus II chance to turn weaknesses into strengths

Grading Policies and Where to Get Help

Class webpages review.

If time remains, begin 7.2 integration by parts slides and clicker

Review of calc 1, including FTC, definite and indefinite integrals, derivatives and antiderivatives.

Download and open the Intro to Maple file and execute the commands.

Grading and Policies and Where to Get Help

Algebra, Trig and Derivative Review.

Go over the class webpages and Wiley Course ID: 488252 flyer

Hints are always visible. Solutions after first try (give the first try a reasonable effort!). Attempts after Due Date will be Marked Late & Score will be Reduced (50%).

Optional, but for homework, choose at least one problem from one of these to complete by tomorrow:

Calc I review contest.

Begin the philosophy of 7.1 (w-subs)