HOMEWORK
for MATH 2182H: Honors
Calculus II
call number
19869, MTWThF 11:30
AM-12:25 PM, in 047 University Hall
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
Check out this
cool web page and this
one.
16.1:
1, 5, 9b
16.2: 1, 2ab, 4 aegh, 5 abcdef, 6abcd
16.3 1,2,7,13,15,17 (I
deleted 20)
Write up and turn in for grading on T Jan. 20:
15.2: 1a,f; plot the parabolas 3b,e; 9
15.3: 3
15.4: 18, 24a
16.1: 1j,l, 4, 6a
16.2: 5 def, 6 bcd
16.3: 2,7,17
(I deleted 20)
16.4: 2(did in class), 3ab (c did in class), 4, 5, 10, 15, 16
16.5: 2,4,5(did in class),6,7,8
..................................................Solve for practice:
Review integration Sec. 10.3, 10.4. Learn trig formulas
by heart.
17.1: from 1 to 11 (did 2 in class), 13
Partial
fraction decomposition
Write up and turn in for grading on T Jan. 27:
16.4: 4, 5, 12
16.5: 2,4,6
17.1: 4,6,8
.........................................Solve for practice:
17.2: 1, 2, 6, 7, 8, 11
Cycloid
Another cycloid
(with Maple code)
Here are some hypocycloids generated with this Maple code:
a=3,b=1
a=4,b=1
a=5,b=1
a=7,b=3
a=15,b=4
a=Pi,b=2
Hypocycloid
and another Hypocycloid
The
National Curve Bank (with Maple code)
17.3: you should be able to solve all problems there
Write up and turn in for grading on T Feb3:
17.2: 2, 6, 8
17.3: 4, 6, 8, 10
...........................................................Solve for practice:
17.4: you should be able to solve all problems there. The
first midterm includes this section.
17.5: 1, 2, 3, 4, 6,7,8,12, 13
How
Evolutes were discovered and how to plot them using Maple
17.5: you should be able to solve all problems there.
17.6: you should be able to solve all problems
there.
17:7: 1, 2
Write
up and turn in for grading on T Feb10:
17.4: 4, 6, 8, 1, 12
17.5: 2cd, 8, 13
17.6: 2, 4, 8, 12
17.7: 2
...................................................Solve for
practice:
18.1: you should be able to solve all
problems.
18.2:
you should be able to solve all
problems.
18.3:
you should be able to solve all
problems.
18.4:
you should be able to solve all
problems.
Write up and turn in for grading on T Feb17:
18.1: 4c, 6cd, 8, 10a, 12, 14a, 16a
18.2: 2, 4b, 6, 8a, 10
18.3: 2, 4, 6, 8, 10, 12
18.4: 4, 6, 8, 10a, 14a, 20, 22, 24
...................................................Solve
for practice:
18.5: you should be able to
solve all problems.
18.6: 1-16, 19-21, 24,25
18.7: 1, 2, 5-11, 13-18
19.1: you should be able to solve all
problems.
19.2: you should be able to solve all
problems. Example
where mixed derivatives are not equal.
Write up and turn in for grading on T Feb 24:
18.5: 2, 4, 6, 12, 16
18.6: 2, 4, 6, 12, 16, 24
18.7: 6, 8,10,16,18
19.1: 8, 10, 12, 24
19.2: 10, 16, 20, 22, 27, 30d
..................................................Solve
for practice:
19.3: 1...13
19.5: you should be able to solve all
problems.
Write up and turn in for grading on T March 3:
1. Show that the following functions do not have limits as
(x,y)->(0,0):
a) (x^2-y^2)/(x^2+y^2)
b) (x^4-y^2)/(x^4+y^2)
2. Show that the following function does have a limit as
(x,y)->(0,0):
x^2 (x^2-y^2)/(x^2+y^2)
19.3: 8, 12, 16, 18
19.5: 4, 6, 10
...................................................Solve
for practice:
19.6: 1...16, 19
19.10: you should be able to solve all
problems- except for 11 and 12
19.7: 1...8
Second midterm exam is from 17.5 to 19.7 (including) and
19.10.
You should be able to show that limits exist or not.
You should be able to use knowledge from previous sections as
needed!
Just because we are curious:
The cubic formula Quartic
equations. Abel proved (1823) that here are no formulas
in
terms of radicals for solving general higher order
polynomial equations.
Write up and turn in for grading on T March 10: (Second
midterm exam day!)
19.6: 8, 10, 14, 16
19.10: 8, 14
19.7: 8, 12
...................................................We
covered on 03/11/2015:
Absolute
extrema (see also here,
p. 84-90)
See
also this reference for Taylor
polynomial in several variables
...................................................Solve
for practice:
19.8: 3, 7, 20 (did in class 4b,12, 19)
Happy Spring Break!
Write
up and turn in for grading on T March 24:
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".
19.8: 2, 4a, 8,10 and 20!
..................................................Solve
for practice:
20.1: 1, 3-28 (we did 27 in class)
20.2: you should be able to solve all problems
20:4: 1-23, 39
On Fri March 27 we are going over on how to change variables in
double integrals, see e.g. these
notes. (You need to know!)
Write up and turn in for grading on T
March 31:
20.1: 10, 12, 18, 28
20.2: 6, 10, 12, 14, 16
20.4: 2, 6, 10, 14, 39a,e
Also: evaluate the double integral of exp[(x+y)/(x-y)] dA
over the trapezoidal region with vertices (1,0), (2,0),CORRECTION:
(0,-2) and (0,-1) by changing variables to x+y=u, x-y=v.
Also: 20.4: 28, 32
..................................................Solve
for practice:
20.5: by lecture on Apr 1 be sure you can solve: 1...20 (and/or ask
questions in class)
20.5: by lecture on Apr 2 be sure you can solve: 21...27 (and/or ask
questions)
20.5: by lecture on Apr 3 be sure you can solve: 28..30 (and/or ask
questions)
Write up and turn in for grading on T
April 7:
20.5: 8, 10, 12,16, 18, 20, 22, 24, 26, 28, 30
..................................................Solve
for practice:
20.6: 1, 3, 5, 13
20.7: 1, 3, 5, 9, 11, 13 See Bumpy
Spheres and calculation of the volume
21.1 you should be able to solve all problems
Write up and turn in for grading on T
April 14:
20.6: 6, 8, 10, 22
20.7: 4, 6, 8, 10
21.1: 6, 8, 10, 20, 22
..................................................Solve
for practice:
21.2: you should be able to solve all problems
21.3: 1, 3, 5, 7...11, 13...20, 23...28
21.4: 1
References for conservative vector fields in space (which we are
discussing in class and you will need to know): here,
or here
A spiral surface given parametrically
Write up and turn in for grading on T
April 21:
21.2: 4, 10, 12, 14
21.3: 2, 4, 6, 8, 12, 14, 16, 20, 24, 26, 30
21.4:
20.8: 10, 18
Also: Determine if the vector field is conservative. If so,
find a scalar function f so that F is the gradient of f:
F(x,y,z)=y^2z^3 i +2xyz^3 j + 3xy^2z^2 k
..................................................Solve
for practice:
21.4: 1, 3, 5, 7, 9, 11, 12, 14 ....you should be able to
solve all problems
21.5: 5, 7, 9, 11, 13, 15 see Klein bottle
and Mobius
strip
Write up and turn in for grading on Monday April 27:
21.4: 2, 4, 6, 8, 10, 18
21.5: 4, 6, 8, 12, 14, 16
Special office hours before the final exam:
Thursday Apr 30, 1-3 p.m.
Topics not to miss when reviewing for your final exam:
Conic sections (be able to recognize, plot and use)
Polar coordinates (be able to use when needed)
Parametric equations for lines, curves, surfaces (be able to
parametrize the objects you need and use in calculations)
Partial derivatives, the gradient vector, the tangent plane and linear
approximations, find normal vectors
Use the chain rule when needed, use implicit differentiation
Use dot product, find orthogonal projections of vectors and angles
between vectors
Use cross product, find area of parallelograms, find normal vectors
to surfaces
Cylindrical and spherical coordinates (be able to use them when
needed)
Extrema (local, absolute, Lagrange multipliers)
Multiple integrals (be able to set up, evaluate, use appropriate
coordinates, also calculate masses, centroids, volumes, area)
Line integrals: calculation, conservative fields (or not), find
potential of F (or argue it does not exist)
Green's Theorem (be able to state and use)
Gauss's Theorem (be able to state and use)
Stokes' Theorem (be able to state and use)
Final exam: Friday May 1st, 12:00-1:45 p.m.
as shown on the OSU Final Examination Schedule, please
check it here.
