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Department of Mathematics College of Liberal Arts and Sciences

MAP2302 Homework — Fall 2015

Problems from  Differential Equations w/Boundary Value Problems by Zill & Wright, 8th edition.

When there are a range of problems given do all the odd ones in that range.

  • Section 1.1, page 10: 11-17, 21, 23
  • Section 1.2, page 17: 7-13
  • Section 2.2, page 51: 1-27
  • Section 2.3, page 61: 1-35
  • Section 2.4, page 69: 1-25, 31-37
  • Section 2.5, page 74: 1-21 (Problems 23-29 removed on 9/8/15)
  • Section 2.6, page 79: 1, 3 (You can use a calculator for these problems)
  • Section 3.1, page 91: 13, 15, 17, 19 (You can use a calculator for these problems)

The first in-class exam takes place on Friday, September 25, in the usual classroom. It covers all the homework above. The exam is closed book, no notes and no calculators.

This deexam1_prac (pdf file) (its solutions deexam1_prac_soln) will give you a good idea of the exam format and difficulty, but the actual exam will have different problems and could be a bit harder or easier, longer or shorter, etc. I suggest you sit by yourself with no notes and take the exam in a simulated testing situation to see where you stand and what you need to review.

In the attached rev_1 there are some problem circled in red which will provide additional review problems. The solutions to the odd problems are here rev_1_soln.

Answers to even numbered problems:

  • (4) $$y = x^3/6 -4x^2/5 + 3x/4 – C x^{-3}$$
  • (6) $$y^{-2} = 2 ln|1-x^2| + C$$
  • (32) $$ y^2 = x^2 ln(x^2) + 16 x^2$$

Here is another problem: A beer starting at 32 degrees (Centigrade) is put in a fridge which is 5 degrees. It cools to 13 degrees in 3 minutes. When was it 17 degrees?

Exam 1 solutions deexam1_soln

  • Section 4.3, page 137: 1-23, 29-33
  • Section 4.4, page 147: 1-19  27-31
  • Section 4.6, page 161: 1-5, 9-19
  • Section 4.7, page 168: 1-13, 19-23
  • Section 5.1, page 205: 1, 3, 5, 9(ab), 17, 19, 21, 23, 25, 29, 31, 33
  • Section 6.1, page 237: 1, 3, 5, 7
  • Section 6.2, page 246: 3, 5, 7, 9
  • Section 6.3, page 255: 15, 17, 19

 

The second in-class exam takes place on Friday, October 30, in the usual classroom. It covers all the homework above since the last exam. The exam is closed book, no notes and no calculators.

This sample exam deexam2samp (pdf file) (its solutions exam2_rev_soln_f )   will give you a good idea of the exam format and difficulty, but the actual exam will have different problems and could be a bit harder or easier, longer or shorter, etc. I suggest you sit by yourself with no notes and take the exam in a simulated testing situation to see where you stand and what you need to review.

In the attached  exam2_rev there are some problem circled in red which will provide additional review problems. The solutions to the odd problems are here exam2_rev_soln

Two additional problems.

  1.  The recursion relation for $$y” – y = 0$$ is $$a_{k+2} = frac{a_{k}}{(k+2)(k+1)}$$ Find the first three nonzero terms of the two series solutions expanded about zero
  2. Find the fundamental recursion relation for $$2y” + xy’ + y = 0$$

Answers to even numbered problems:

  • Chapter 4 review, number 38: The equation of motion is
    $$ y(t) = (-1/4) cos(5t) + (1/5) sin(5t)$$
    the amplitude is sqrt(41/400), the period is 2*pi/5, and the first time back through equilibrium is (1/5) arctan(5/4).
  • Section 4.9, number 8: It never returns to equilibrium as the solution is always positive.
  • Section 4.9, number 10: time of max displacement is 2 pi/sqrt(127) and the max displacement is exp(-pi/sqrt(127))

Answers to additional problems.

  1. $$y_1 = c_0(1 + x^2/2 + x^4/24+ dots)$$ $$y_2 = c_1(x + x^3/6 + x^5/120+dots)$$
  2. The recursion relation is $$ a_{k+2} = frac{-a_k}{2(k+2)}$$

Exam 2 solutions exam2_solnF15

  • Section 7.1, pg 280: 11-31
  • Section 7.2, pg 288: 1-19, 31-37
  • Section 7.3, pg 297: 1-17, 21-27, 37-45 (added on 11/8), 63-69
  • Section 7.4, pg 309: 1-13, Problem 57 eliminated on 11/16
  • Section 7.5, pg 315: 1-11

This Laplace transform table you can use on all quizzes and exams laplace (pdf). This is now the new version containing tsin(bt) and tcos(bt).

The third in-class exam takes place on Friday, December 4, in the usual classroom. It covers all the homework above since the last exam. The exam is closed book, no notes and no calculators.

This sample exam deexamsamp3a (pdf file) (its solutions deexamsamp3_soln)   will give you a good idea of the exam format and difficulty, but the actual exam will have different problems and could be a bit harder or easier, longer or shorter, etc. I suggest you sit by yourself with no notes and take the exam in a simulated testing situation to see where you stand and what you need to review.

In the attached  de_rev3 there are some problem circled in red which will provide additional review problems. The solutions  are here de_rev3_soln

Solutions to exam 3 deexam3_soln_F15

  • Section 5.1.4, pg 209: 45, 47
  • Section 1.2, pg 18: 15-21

The schedule for the rest of the semester.

  • QUIZ — Friday, November 13
  • QUIZ — Friday, November 20
  • QUIZ — *Monday*, November 30
  • REVIEW — Wednesday, December 2
  • EXAM3 — Friday, December 4
  • NO CLASS — Monday, December 7
  • QUIZ — Wednesday, December 9 covers HW from Section 5.1.4 and Section 1.2
  • FINAL — Wednesday, December 16, 3:00-5:00, in the regular classroom