### 1120 Class Highlights

• Tues May 3 evaluations and then review
• Mon May 2 open office hours
• Tues Apr 26
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

• Mon Apr 25 Questions and quiz 12 on 11.3, 11.4 as well as setting up DEs (from Thursday).
• Thur Apr 21
Finish 11.4 slides and clickers
Animated Short Story-Differential Equations spot the error
Differential Equations 11.5 & 11.6 slides and clickers

• Tues Apr 19 Review 11.1 and 11.2.
11.3 and 11.4 slides and clickers

• Mon Apr 18 Review and take questions on 10.4, 11.1 and 11.2. Quiz 11.
• Thur Apr 14 Finish the last slide of
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

• Tues Apr 12
e^x Taylor series
Continue 10.3 and 10.4 Finding and Using Taylor Series and Error Bounds slides and clickers

• Mon Apr 11 Review 10.1, 10.2 and 10.3 using the 10.1 and 10.2 method for arctan x (from the practice problems) and then the 10.3 method for comparison. Write out in series notation. Look at the degree 10 taylor polynomial in Maple using:
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.
• Thur Apr 7
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

• Tues Apr 5
10.1 and 10.2 Taylor Series slides and clickers
Taylor Polynomials in Maple. Maple version

• Mon Apr 4 series review and series theorems, power series review.
Quiz 9.
• Thur Mar 31
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.
• Thur Mar 24
Review and clicker 4: Continue 9.4 Series Convergence slides and clicker Alternating Series.
9.5 Power Series slides and clickers.

• Tues Mar 22
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

• Mon Mar 21 Test 2. I am rooting for you! I'll try to have the test grades posted tonight, because today is the last day to drop (registrar told me you would have until late tonight)
• Thur Mar 17
Clicker
Begin 9.4 Series Convergence slides and clicker (Direct) Comparison Test
Discuss the study guide and review for test 2

• Tues Mar 15
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.

• Mon Mar 14
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.
• Thur Mar 3 Take questions. quiz on 9.1 and 9.2.
Begin working on worksheet.
9.2 Series, Geometric slides and clicker
slicing for volume, density and work practice
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
9.3 series partial sums, series divergence when terms not getting smaller, linearity arguments, and the integral test
9.1, 9.2, 9.3 summary sheet

• Tues Mar 1
Emily found this pizza comic
9.1 Sequences slides and clicker
9.2 Series, Geometric slides and clicker
Group Work Target Practice, solutions

• Mon Feb 29 Review 8.4 Density and 8.5 Work Group Work Target Practice solutions and Volume by Slicing Cone & Cylinder
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).
• Thur Feb 25 Review 8.4 Density slides and clickers
Continue 8.5 Work slides and clickers
Group work target practice and solutions

• Tues Feb 23
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
• Mon Feb 22 Review and quiz on 7.5, 8.1 and 8.2.
• Thur Feb 18 Continue
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);

• Tues Feb 16 Test 1. Allowed one handwritten side of the small card I gave you.
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
• Mon Feb 15 University cancelled our test.
• Thur Feb 11
7.5 Numerical Approximations and clicker
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

• Tues Feb 9 The difference between integrating exp(-x^2), xexp(-x^2) and x^2exp(-x^2).
Riemann sum
7.5 Numerical Approximations and clicker
partial solutions

• Mon Feb 8 Clicker question. Review improper integrals. Take questions on improper integrals. Quiz on improper integrals.
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!)
• Thur Feb 4
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);

• Tues Feb 2
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
• Mon Feb 1 Take questions on 7.4. Quiz on 7.4
• Thur Jan 28
• 7.4 Integration by Trig Substitution slides and clickers.
• Group Work Target Practice

• Tues Jan 26
• Finish 7.4 slides and clicker (Integration by Partial Fractions)
Visualization via the partial fractions representing local behavior of the function around the asymptotes.
• pdf of worksheet from lab
• Begin 7.4 Integration by Trig Substitution slides and clickers.

• Mon Jan 25
1. Review the first two slides from 7.4 slides and clicker (Integration by Partial Fractions)
2. Introduce your self to a neighbor or two and work in groups on Group Work Target Practice
4. 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.

• Thur Jan 21 Take questions on the hw. Quiz 2.
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).

• Tues Jan 19
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.
• Thur Jan 14
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.
7.2 slides and clicker (Integration by Parts).

• Tues Jan 12
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

• Mon Jan 11 Intro.
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.
pdf
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:
• Algebra, Geometry and Trig Practice Chap 0 & 1 (optional)
• Derivative Practice Chap 3 (optional)
• Integral Practice 5.2 and 6.2 (optional)
Calc I review contest.
Begin the philosophy of 7.1 (w-subs)