# 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, 24a16.1: 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:

...................................................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.