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Carl E. Mungan, Professor
Carl E. Mungan, Professor

SP351 Spring 2015

HW# Due Sec# Prob# Notes
1 01/20 1.1 7 do it by hand
11
14
16(c)
22
1.2 2 hint: how long is curve ad?
4
7
11
20 print or write out CAS code
(how does one do the "0+"?)
2 01/22 1.3 12 graph f(x) on a computer
1.4 3 show all steps!
14 hint: use double-angle formula for tangent
17
19
28 print or write out CAS code
3 01/26 1.5 2 write answer in form V+/-ΔV
7 use radians!
9
10
11
1.6 2 show every step!
6
8
9
10
11
4 01/28 1.7 2(a)-(c) check by differentiating your answers
3(c)-(d)
8
12
21
22
24 & 25 use WolframAlpha and print out screen
5 01/30 1.8 2
5
25 & 27 print out from WolframAlpha (use more time)
and compare 2nd result to P1.9.14 result
1.9 5
7 hint: determine the constant
of integration from α = 0
6 02/02 2.1 7
10
11
12 find s in each case
hint: let x = 1/n in (c) & (d)
2.2 1
2
4
6
11
12
7 02/04 2.3 1
2
6
10
11
12
13
8 02/06 2.4 8 hint: use the full form of the limit test
9 substitute u = lnx to do the integral
10
12
15 also figure out what happens
if |x|=1 and if |x|>1
9 02/09 2.6 1 what function is the 2nd series?
2 separately test endpoints in ALL problems
4
5 write answer in sigma form
7
8 compare result to that of 2.6.5
10 INSTEAD sub x = 1 and comment w/o doing calculations
2.7 9
15(b)-(c) then compute limits as x -> 0 and
compare to l'Hopital results
10 02/11 2.7 2 what's the value in row n, column m?
19 print it out
2.8 1
2 print it out
3
12 write answer in sigma form
13
15 write answer in sigma form using double factorial
11 02/13 4.1 2
5 sketch curve by hand & compute all axis intercepts
6 sketch it by hand
8 sketch it by hand & correct typo in soln on pg. 1127
10 hint: use results of probs 1 to 4
11 INSTEAD use Euler identity
do all calculations w/o calculator!
16
12 02/18 4.2 1
2 correct typos in solns
3 cross off i in υ
4.3 1(a)-(c) express angles in rad using calculator
2 do NOT use a calculator
6
7 write answer for cos3θ as sum of powers of cosθ only,
and sin3θ as sum of powers of sinθ only
8
11 do NOT use a calculator
13 do NOT use a calculator
13 02/20 4.4 3
9
4.5 3 compute in rect. form w/ a calculator
4
8
9
4.6 1 plot them in complex plane
6 simplify the answer more
9 compute in rect. form w/ a calculator for n=0,1,-1
10 compute in rect. form w/ a calculator for n=0,1,-1
14 02/23 6.3 2 correct typo in soln
4(a)
5 ie. solns of Laplace equ.
7 ie. soln of diffusion equ.
9
10 ie. spherical harmonics
16
17 ie. partition fn.
20 ie. (γ-1)Cv
15 02/25 6.4 1
4 express answer in terms of t only
8 fully simplify the answer!
10
13 ie. wave equ.
14
16 02/27 6.5 4
6 hint: compute differentials of f and z
7
8(a)
10 write answer in form γ+/-Δγ
11
12
13
14
17 03/02 6.6 5
7
12 give dir. as a unit vector and magn. w/o calculator
16
6.7 1
3(b)
4
5(b)-(c)
6(a)
9
13
17 print out Mathematica (WolframAlpha doesn't work)
18 03/04 6.8 2 resolve indeterminacy by graphing f
3
4 resolve indeterminacy by calculating higher derivs.
7(a) show all work: back of text did NOT find all solns
11
12
19 03/06 6.10 1
2
3 calculate M first
6
13
15 hint: use cyl. coors. (see #10 for defn of I)
18
20 print it out
23 print it out
20 03/09 7.1 3
5
6
7
8
9 use chain rule to compute terms like ∂f/∂x
10 ie. compute div and curl
21 03/11 7.1 12
13
14
20 print it out
21 print it out
7.2 2
3 also calculate ∇ × A and comment
5 answer at back is wrong
22 03/23 7.2 7
8
11
12(a)
7.4 6 hint: split the surface integral into 6 faces
9 use cyl. coors. to do the vol. integral
23 03/25 7.5 4 answer at back is wrong
you have to do 4 line integrals and 5 surface integrals
5
9
11 use double-angle formula to do angular integral
18
19
24 03/27 8.1 2 print out WolframAlpha (use a=3 in part f) and
annotate the lobes on each plot that have r<0
10
11 what are the limits and why?
14
16
25 03/30 8.2 2 express components in terms of t (not r & θ)
4 find a formula for d2r/dt2 in terms
of r & constants (including ang. mom. J)
7
8
9
11
12
26 04/01 8.3 14 replace r with cyl. radius rc in all problems
15 ie. derive general formula for velocity in cyl. coors.
16
18 convert components AND unit vectors
19 use determinant to compute curl
27 04/03 8.4 7
11 use double-angle formulae for cos & sin
12
14
19 2nd integral should have 1 not 3 integral signs,
an angular prefactor is missing, and assume f(-r) = f(r)
28 04/06 8.5 4
5 convert components AND unit vectors
answer at back is wrong
7 prove it by expanding in rect. coors.
9 answer at back is wrong
12
29 04/08 9.1 1
2
3
4
6
7
10
21 print out WolframAlpha
30 04/10 9.1 16
9.2 2
5
6
8
10 cross out the word "unique" - how many solns are there?
31 04/13 9.3 2
4 what do they ALWAYS equal?
6(d) hint: use Eq. (12)
12 in (a) find a GENERAL form for B (not just one example)
and then find a nonzero B such that AB=0 and BA=0;
in (b) prove that the ONLY soln is B=0
14
15 hint: use Eq. (16)
32 04/15 9.3 9(a) show ALL steps by hand
19
9.5 7
8
9 prove it!
11 hint: use a cross-product
12 row reduce the augmented matrix to echelon form
33 04/17 9.6 16 use Gram-Schmidt
17 use Gram-Schmidt
9.7 2
3
4
6
7(a)
12 use Gram-Schmidt but report unnormalized vectors
(answer at back is NOT the one you'll get)
34 04/20 10.1 2 show that your matrix does what it should
4 hint: a nonsingular matrix is invertible
5
6 show ALL work
7
10
11
12
35 04/22 10.1 15
16 compute all 6 inner products
10.2 1 ALWAYS correctly number the eigenvalues and normalize the
eigenvectors; why are there that many lin. indep. eigenvectors?
2 why are there that many lin. indep. eigenvectors?
3
4
5 evaluate Eq. (4) at λ = 0
18 print out WolframAlpha (no need to normalize the vectors)
36 04/24 10.2 10
10.3 2
4
6
11
16 use the results of P10.3.15
hint: replace the identity matrix with the diagonal mass matrix
17
37 04/27 10.4 1
3
5
7
13
17 compute (Z2)(Z1)-1 by hand
23
38 04/29 10.5 4 explicitly calculate StAS
9 just compute the eigenvalues to answer the question
13 INSTEAD evaluate cosA using Maclaurin series & eigenvectors
15
10.6 1(a)
5 just compute the eigenvalues to answer the question
17
18(a)

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