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 casehint: 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 andcompare 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 sin3 θ 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)C_{v} |
|||

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) andannotate 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 d^{2}r/dt^{2} in termsof r & constants (including ang. mom. J) |
|||

7 | ||||

8 | ||||

9 | ||||

11 | ||||

12 | ||||

26 | 04/01 | 8.3 | 14 | replace r with cyl. radius r_{c} 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 (Z_{2})(Z_{1})^{-1} by hand |
|||

23 | ||||

38 | 04/29 | 10.5 | 4 | explicitly calculate S^{t}AS |

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) |

Link to my personal home page