**Homework ****MATH
2182H Sp 2018: Honors Calculus II **

**Instructor:** Rodica D. Costin

*
***Solve for practice:**

**15.2**: 1, 2, 3 and plot
the parabolas in 3, 9

**15.3:** 1,
3, 4

**15.4:** 1,3,5,7, 17, 18, 19, 24a

*15.6: complete the squares and
identify the curves in problems 1,3,5. Here are their graphs, plotted
with Maple.*

*A
picture showing the plane of the ecliptic.*

*Visitor
from outside the solar system, identified by its
hyperbolic trajectory.*

**16.1: **1, 5, 9b

**16.2: **1, 2ab, 4 aegh, 5
abcdef, 6abcd

*
***Write up and turn in
for grading on T Jan.**** 1***6*:

15.2: 1a,f; plot the parabolas 3b,e; 9

15.3: 3d,e,f,
9, 11

15.4: 18, 24a

15.6: complete the squares and identify the curves (that is,
name them) in problems 2,4,6

16.1: 1j,l, 4, 6a 16.2: 5 def, 6 bcd

16.2: 2b, 4e, 6g, 10a

**Solve for practice:**

16.3 1,2,7,13,15,17

16.4: 5, 11, 14, 17 and also

16.5: you should be able to solve all the problems there

17.1:1, 3

**Write up and turn in for grading
on T Jan.**** 23:**

16.3: 2,7,11

16.4: 6, 10, 12, 15 and also 3ab, 4,
18, 19

16.5: 2,4,6,7

17.1: 11, 13

**Solve for practice:**

17.1: from 1 to 13

17.2: 1,7,11

Cycloid

Hypocycloids: a=3,b=1 a=4,b=1 a=5,b=1
a=7,b=3 a=15,b=4
a=Pi,b=2

17.3: 3, 10, 11

17.4: 1,3

**Write up and turn in for grading
on T Jan.**** 30 (midterm day! You can bring a cheat sheet:
one regular size paper with your own notes. No books, textbooks or
electronic devises are allowed.**

17.1: 4, 6, 8

17.2: 2, 6, 8

17.3: 4, 6, 8

17.4: 2, 4

**Write
up and turn in for grading on T Feb 7**** **

**17.4**: 6, 10, 12

**17.5**:
2cd, 6, 7 and 13

**17.6**:** **2, 4, 8, 12

How
to find the weight of Earth

Who
figured out the shape of the Earth

Why
leap years?

Cavendish
experiment

Maple code for
graphing evolutes, and their history

**and** **Solve more problems, for practice, **here are problems not to
miss:

**17.4:** you should be
able to solve all problems here

**17.5:** you should be
able to solve all problems here

**Write
up and turn in for grading on T Feb 13:**** **

**17.7**:
(To build intuition for
**u**r and **u**theta:) A point is in uniform circular
motion: **R**(t)=a cos(omega t)**i**+a sin(omega t)**j**. Find the
radial and angular components of the velocity and of acceleration.
Find a physical intuition for your results.

**17.7**: 2

18.1:
4c,
6cd, 8, 10a, 12, 14a, 16a **AND **17 and 13 done in class
needs correction

18.2: 2, 4b, 6, 8a, 10 **AND **21, 22

18.3: 2, 6, 10, 12

**Write
up and turn in for grading on T Feb 20:**

18.4: 4, 6, 8, **AND**** **10a,
14a, 15, 16, 20, 22, 24 **AND **19,
25, 26, 27, 30

**18.5: **1, 2, 6, 10, 15(do not just use the formula in 14,
but deduce it), 16

AND 12, 13c

**and** **Solve more problems, for practice**

**18.4:
****you
should be able to solve all the problems there**** **

**Sign
up for the math competition! **

**Write
up and turn in for grading on T Feb 27:**

18.6: 2, 4, 6, 12, 16, 20, 24 (And solve for
practice 1-16, 19-21, 24,
25**) Here
is the intersection of #19.**

18.7: **
6, 8,10,16,18**

**19.1:** 2, 8, 10, 12, 13 **AND **24
Here is the plot of problem 20 (using
Maple).

19.2: 16, 17, 19, 21b, 29a, 30c

MATLAB and Mathematica can be
downloaded at the website of the Office of the CIO (Maple too). Computer
labs are found here.

**Learn Mathematica!** Here
are some old files, to get you started. A first plot in polar
coordinates

Here is the
rose with 8 leaves: the
file used (same, but printed
as a pdf
file). Learn
to solve equations and to integrate: the
file (its pdf
print).

Midterm information:

You are allowed to bring one
cheat sheet.

Material required: everything we do in
class, up to Monday March 5 (planned to be Sec. 19.4)

Special office hour: Sunday March 4, 2-3PM.

No office hour the next day.

**Write up and turn
in for grading on T March 6:**

19.2: 32c (verify formula
of differentiation under the integral sign written
above 32) 3Dplots with Mathematica (pdf file here)

**19.3**: 2, 4, 8, 16 Plotting
curves/surfaces given by equations with
Mathematica (here
is the pdf print)

AND
18, 19

**Solve** the problems on p.2 of this hand-out: Linear
Approximations

Review problems are here.
Many will be discussed on Tuesday. Since there are
more problems that time permits discussing try to
solve them and select which ones you would like
solved in class.

**Write
up and turn in for grading on
Thursday March 22:**

19.10: **6,
10 ****(use
the formula, ***then
also***
use implicit
differentiation
and ***check*
that they
agree),
12, 14b Plot
of the polynomial we studied
today** **

19.5: 2b,d,
3a, 4, 5, 6, 8, 9, 10

19.6:
5, 6, 7, 8

**Have a great Spring Break!**

**19.6: **10,
13b, 14, 19c

**19.7: **8, 12
We discussed Taylor polynomials in two variables

We will cover today (Wed)
**A**bsolute
extrema (see
also here,
p. 84-90)

also turn in for grading
on Th March *22nd**:*

**19.7**: 29 and

**A**. Find the absolute max and min of f(x,y)=1+4x-5y on
the closed triangular region with vertices (0,0), (2,0) and (0,3).

**B.** Find
the absolute max and min of f(x,y)=x^4+y^4-4xy+2 on the domain
D={(x,y)|0<x<3,0<y<2} where here < means "less or
equal".

**Write up and
turn in for grading on
Tuesday March 27:**

19.8:
**2, 4a, 8,10 AND 12, 19, **20(yes, both a and b)

also **19.7**: 28

**20.1: **10, 12, 18, 28

**Write up and
turn in for grading on
Tuesday April 3rd:**

20.1: **23, 25, 27**

**20.2: ****6, 10, 12, 14, 16 AND 8**

20.3:
(after we talk more
about symmetries on Thursday, solve:) 4, 6, 8, 14

**20.4: **4, 6, 10, 14, 39h, 40

Write up and
turn in for
grading on
Tuesday April
10th:

**20.5:
****
10, 12, 18, 20 ****
and
22,24,26,28,30 However,
you need to be able to solve all the
problems here. **

20.6: 24 AND find the volume
of the solid cone a^2y^2=x^2+z^2,
0<y<h. Plot this cone.

**20.7: **3,
11, 12, 13 See
bumpy spheres (here is the
pdf file)

AND 19, 21** **

**Write
up and turn in
for grading on
Tuesday April
17:**

**
****21.1:** 6, 8,
10, 20, 22

**
****2****1.2**: 4, 10, 12

**
****21.3:** 4,
6, 8, 14, 20, 24, 30 Correct e**xample**

**
****20.8: **10, 18

**21.4 **1a

and** 20.8:
****2**0
and:

** Show that **the
vector field** F**=2xyz** i**+(x^2z+1)** j
**+x^2** k
**is **not
**conservative
in two ways:

1)
find curl**(F)
**and
conclude from your
result;

2)
assume, to arrive at
a contradiction,
that there is an f
so that **F**=**grad
**f**, **attempt
to calculate f and
see what happens.

**Write
up and turn in
for grading on
MONDAY April
23:**

**21.4**: 2,
4, 6, 10
and
12c, 14, 18

For simply
connected
domains in 3d: see here
and the informal
discussion
here.

**21.5**:
1, 5, 7, 9,
11, 13,
15 see
Klein bottle
(a closed
surface with
no interior or
exterior)
and Mobius
strip**
**

Review problems and more problems

Office hours week of Apr 23-27 are as always