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. 16:  
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 ur and utheta:) 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)  Absolute 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
 21.2: 4, 10, 12
 21.3: 4, 6, 8, 14, 20, 24, 30 Correct example
 20.8: 10, 18
21.4 1a
and 20.8: 20 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 (M, Th 10:20-11:15)

For the final exam you are allowed to use your own cheat sheet: one page (2-sided), with your own notes.
 
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, 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)