Math 231 – Differential Equations

Fall Semester 2008

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Final exam: Monday, Dec. 15, 8:00-10:00, STJ 10

Class 43 Fri Dec 12   

         As far as solving differential equations with Laplace transforms, you are responsible for the equations of the type that I solved today in class.

         Also study Example 10.41 on p.308 & Example 10.42 on p.309. (Skip Example 10.43 and any of those involving the Dirac function).

         And work some of those assigned Wednesday.                                                                                                   

Class 42 Wed Dec 10   

         1.   More practice problems for Final Exam: 39, 43, 45, 56, 58, 61, 64 on p.312.

         2.   The following worksheets can be used to check answers that are not in the book:

                    Laplace Transforms of Functions

                    Inverse Laplace Transforms

                    Method of Laplace Transforms for Solving ODEs

         3.   Final exam: Monday, Dec. 15, 8:00-10:00, STJ 10 

               (About 20% to 25% of the Final Exam on Monday will cover Chapter 10. The rest will cover Chapters 1-9).       

Class 41 Mon Dec 7   

         1.   Homework 20 may be turned in Wed.

         2.   Final exam: Monday, Dec. 15, 8:00-10:00, STJ 10 

               (About 20% to 25% of the Final Exam on Monday will cover Chapter 10. The rest will cover Chapters 1-9).

         3.   Read pp. 302-310.

         4.   Practice problems for Final Exam: p.311: 15, 17, 19, 22, 23, 28, 29,48, 50, 51, 52, 53.                               

Class 40 Fri Dec 4    Exam 3

         Reminder:

         Homework 20 is due Mon: turn in 1, 5, 6, 8, 11 on p.311.                                                                       

Class 39 Wed Dec 3

         1.   Exam 3 on Friday will cover all of Chapter 9.

         2.   Please pick up the solutions to Hwk 18 & Hwk 19.  (No late papers will be accepted since these solutions are now available.)  

         3.   Read pp.279-302.

         4.   Practice problems on p. 311: 1, 2, 3, 5, 7, 9, 15, 17.  Also memorize Table 10.1 on p. 280.

         5.   Homework 20 is due Mon: turn in 1, 5, 6, 8, 11 on p.311.                                                                 

Class 38 Mon Dec 1

         1.   Read pp.269-279 (definition of a Laplace transform).

         2.   Practice problems on p. 311: 1, 2, 3, 5.                                                                                                  

         Reminder.

         Homework 19 is due Wed: turn in 68, 69, 73, & 75 on p.266.  Also, check 68 with Maple.                  

         Exam 3 will be Friday and will cover all of Chapter 9.                                                                                                             

Happy Thanksgiving!

Class 37 Wed Nov 26

         1.   Read about the “Variation of Parameters” Method on pp. 252-263.

         2.   Practice on p.266: 65, 70, & 76.

         3.   Homework 19: Wed (after Thanksgiving) turn in 68, 69, 73, & 75 on p.266.  Also, check 68 with Maple.

         Reminder.

               Exam 3 will be on Friday (after Thanksgiving) and will cover all of Chapter 9.                                                

Class 36 Mon Nov 24

         1.   Practice starting on p.265: 48, 50, 54, 57, 58, 60.

         2.   Homework 18: Wed turn in 46, 49, 52, & 53 starting on p.265.  

         3.   Course evaluations start today.

Announcement.

               Exam 3 will be on Friday, Dec 5 and will cover all of Chapter 9.                                                                               

Class 35 Fri Nov 21

         1.   In Chapter 9, read pp.241-252.

Reminder.

               Homework 17: Monday turn in 33, 37, 40, & 42 on p.265.  Also solve 37 & 42 with Maple & turn in the worksheet.

               See Linear Second-Order Homogeneous Equations to aid you.                                                                            

Class 34 Wed Nov 19

         1.   In Chapter 9, read pp.227-237.

         2.   Homework 17: Monday turn in 33, 37, 40, & 42 on p.265.  Also solve 37 & 42 with Maple & turn in the worksheet.

               See Linear Second-Order Homogeneous Equations to aid you.                                                                            

Class 33 Mon Nov 17  

         1.   In Chapter 9, read pp.224-227.

Reminder.

         Homework 16: Wednesday turn in 15, 18, 25, 29, & 31 starting on p.264.

         Suggestion: use Linear Second-Order Homogeneous Equations to check answers that are not in the back of the book.       

Class 32 Fri Nov 14  

         1.   Homework 16: Wednesday turn in 15, 18, 25, 29, & 31 starting on p.264.

         2.   Suggestion: use Linear Second-Order Homogeneous Equations to check answers that are not in the back of the book.

Class 31 Wed Nov 12  

         1.   In Chapter 9, read pp.217-224.

         2.   Practice 12 & 22 on p.264.

         3.   Suggestion: use Linear Second-Order Homogeneous Equations to check answers that are not in the back of the book.

Class 30 Mon Nov 10  

         1.   In Chapter 9, read pp.217-224.

         2.   Practice 28 & 30 on p.264.

         3.   Homework 15: Wednesday turn in 11, 13, 21, 23, & 27 on p.264.

         4.   Suggestion: use the worksheet Linear Second-Order Homogeneous Equations to check answers

Class 29 Fri Nov 7   Exam 2 covering Chapters 1-6 & Chapter 8.

Class 28 Wed Nov 5

         For next Monday:

         1.   In Chapter 9, read pp.215-219.

         2.   Practice 1, 3, 4, 6, 7, 8, 10, & 16 on p.264.

         3.   Homework 15: Monday turn in 11, 13, 21, 23, & 27 on p.264.

Class 27 Mon Nov 3

         1.   In Chapter 9, read pp.205-215.

         2.   Practice 1, 3, 4, 6, 7, & 10 on p.264.

         Reminder:

         Exam 2 is on Friday (Nov. 7).  It will cover Chapters 1-6 & Chapter 8.

Class 26 Fri Oct 31

         1.   I am changing the day of Exam 2 from next Monday to next Friday (Nov. 7).  It will still cover Chapters 1-6 & Chapter 8.

         2.   Homework 14: Monday, turn in 22, 24, 27, & 32 on p. 203 (give reasons for the answer in the back of the book).

               Halloween

Class 25 Wed Oct 29

         Some more practice problems in Chapter 8, starting on p. 202: 12, 14, 16, 17, 21, 23, 25, 27, 30, 31.

         Be sure to work these practice problems (and more if necessary) in Chapter 8 to prepare for Monday’s exam (don’t wait until the last minute).

         Exam 2 next Monday will cover Chapters 1-6 & Chapter 8. 

            The worksheet Classification of ODEs & Suggested Solution Methods can help you with problems such as 20-34 on p 203.

Class 24 Mon Oct 27

         1.   In Chapter 8, read pp. 183-199.

         2.   Practice 1, 3, 4, 6, 8 on p.202.

         3.   Reminder: Hwk 13 is due Wed.

         4.   Exam 2 will be on Monday, Nov. 3.  It will cover Chapters 1-6 & Chapter 8.                                      

Fall Break Oct. 20 – Oct. 24

Class 23 Fri Oct 17

         1.   Have a safe and happy Fall Break!

         2.   Don’t forget to work on the practice & turn-in problems in Chapter 6. 

         3.   Links for today’s class: Periodic table & E. coli bacteria.                                                                     

 

Class 22 Wed Oct 15

         Turn in Homework 12 on Friday!

         1.   Read pp.131-137.

         2.   Practice 1, 4, 7, 10, 16, 18, 20, 21 starting on p.149.

         3.   Hwk 13 is due Wed., Oct 29:  2, 5, 14, & 22 starting on p. 149.

         4.   Class example of a one-compartment system: Modeling with First-Order Equations.                          

Class 21 Mon Oct 13

         1.   Practice 1, 4, & 7 on p.149.

         2.   Hwk 12 is due Wed:  31 & 43 on p. 123 & 3 on p. 149.                                                                     

Class 20 Fri Oct 10

         1.   Read pp.125 – 131.

         2.   Practice 1 on p.149.

         3.   Hwk 12 is due Wed:  31 & 43 on p. 123 & 3 on p. 149.

         4.   Maple worksheet illustrating the error function: Error Function.

Class 19 Wed Oct 8

         1.   Hwk 11 is due Friday: 4, 13, 21, 25, 35 on p. 122.                                                                              

Class 18 Mon Oct 6

         1.   Read pp.99-113 in Chapter 5.

         2.   Practice on 1–9 (odd), 10, 12, 14, 16, 18, 23, 27, 28, & 32 on p.122.

         3.   Hwk 11 is due Friday: 4, 13, 21, 25, 35 on p. 122.                                                                                

 

Class 17 Fri Oct 3

         1.   Start reading Chapter 5.

         2.   Hwk 10 is due Monday: 2 & 8 on p. 96.  (In this course, CAS means Maple.)

         Today’s class:

1.   Another example of Euler’s Method: 9 p.97.                                                                                     

2.   Discuss Exam 1.

 

Class 16 Wed Oct 1

         1.   Read Chapter 4.

         2.   Go through the Maple worksheets Euler Polygonal Curves & Euler’s Method while reading Chapter 4.

         3.   Practice 1, 3, & 7 on p.96.

         4.   Hwk 10 is due next Monday: 2 & 8 on p. 96.  (For us, CAS means Maple.)

                    For 8(a) refer to Euler’s Method.  For 8(b) refer to Euler Polygonal Curves.  (For the numeric solver, use Maple’s DEplot command: see Sketching Solutions worksheet).

 

Class 15 Mon Sept 29

         Exam 1 on Chapters 1, 2, & 3.

Class 14 Fri Sept 26

         Exam 1 on Monday will cover Chapters 1, 2, & 3.  The following link is the first exam that I gave last fall:  Exam 1 Fall 2007.

         Sunday afternoon I will post a PDF link on this page with the solutions. 

         Click on Answers  for the solutions to the above exam.

         Hwk 9 is due next Wednesday:

On p. 62, turn in #55 (look up the formulas for volume & surface area of a sphere if you don’t already know them) and #56 (only for #50).

Class 13 Wed Sept 24

         1.   Read Chapter 4.

         2.   Practice 1, 3, & 7 on p.96.

            3.    Go through the Maple worksheets Euler Polygonal Curves  & Euler’s Method  as you read Chapter 4.

Reminder:

Exam 1 will be next Monday.  It will cover Chapters 1, 2, & 3.  Calculators will not be allowed on the exam.

Class 12 Mon Sept 22

1.      Begin reading Chapter 4 for Wednesday.

2.      More practice problems for Chapter 3: 14 & 16 on p.82.

3.       Maple worksheet for today’s class:  Sketching Solutions.

4.      Hwk 8 is due Wednesday: Problem 71 on p. 44 (Poiseuille’s law) and Problem 12 on p. 82 (sketching of solutions).

Reminder:

Exam 1 will be next Monday.  It will cover Chapter 1, Chapter 2, and Chapter 3.

Class 11 Fri Sept 19

5.      Read pp. 73–79. 

6.      Practice p.80: 2, 4, 5, 8, and 9. (Problems similar to the Practice Problems are on exams as well as the Turn-in Problems).

7.       For today’s & Friday’s classes:  Sketching Solutions.

8.      Hwk 8–Turn in on Wednesday: Problem 71 on p. 44 (Poiseuille’s law) and Problem 12 on p. 82 (sketching of solutions).

Reminder:

Exam 1 will be Monday, September 29.  It will cover Chapter 1, Chapter 2, and Chapter 3.

Class 10 Wed Sept 17

9.      Read pp. 63–73. 

10.  As you read Chapter 3, go through the worksheet: Direction Fields and Solution Curves.

11.  Practice p. 80: 2, 4, 5, 8.

12.    For today’s & Friday’s classes:  Sketching Solutions.

Hwk 7–Turn in on Friday: 10, 41, 42 on p.41 and check all three of your answers with Maple.

Class 9 Mon Sept 15

Keep working on the Practice Problems that were assigned on Friday.  Also, read about second-order partial derivatives and Euler’s Reciprocity Theorem in Section 8.4 (pp. 189-191) and to the Practice Problems add #8 on p.202.

Keep in mind that I hold you accountable for the Practice Problems as well as the Turn-in Problems.  Furthermore, I also hold you responsible for the reading assignments---for example, on exams I frequently ask questions to see if you know the statements of definitions and theorems.  I do EXPECT you to read the book and to TAKE notes in class and to STUDY them. 

Exam 1 is tentatively scheduled for Monday, September 29.  It will cover Chapter 1, Chapter 2, Section 8.4, and [more to be included later].

Class 8 Fri Sept 12

Read Sections 1.1.4, 1.1.5, & 1.2.3 (about partial derivatives).

Practice 9-12 & 39-42 on p.40.  Note. You can check your answers in Maple with commands such as “diff(f(x,y) y)” (where f(x.y) is the name of the function) and “pdsolve(PDE)” (PDE  is the name of a partial differential equation)”. 

Hwk 6–Turn in on Monday: 21, 33, 40, 44, 52 on p.61.  Also, solve 40 with Maple using the “dsolve” command.

Exam 1 is tentatively scheduled for Monday, September 29.  It will cover Chapters 1, 2, and ?.

Class 7 Wed Sept 10

Read pp. 57-59 (initial-value problems).

Practice 15, 16, 18, 20, 26, 29, 30, 34, 35, 40, 41, 42, 43, 45, 46, 47, 48, 50 starting on p. 60.

Hwk 6–Turn in on Monday: 21, 33, 40, 44, 52 on p.61.  Also, solve 40 with Maple using the “dsolve” command.

Class 6 Mon Sept 8

Read pp. 47-57.

Practice 1, 3, 5, 7, 10, 12, 14 on p. 60.

Hwk 5–Turn in on Wednesday the following assignment:

Submit a short Maple worksheet with a title, your name and the name of the course (namely, M231), the problem typed up, and Maple commands with the Maple solutions of 23, 32, and 74 starting on p. 41.  Add appropriate short paragraphs of explanation as I do in the Acquaint and Requisite Integration Skills worksheets.

Class 5 Fri Sept 5

Practice p. 41: 43, 45, 49, 51, 57, 60, 63.

Hwk 4–Turn in on Monday the following problems:  48, 54, 55, 59, 63 on p. 41. 

Start reading Chapter 2.

Class 4 Wed Sept 3

Hwk 3–turn in on Friday: 28, 29, 35, 38, 50 on p.41. 

Start reading Chapter 2.

Class 3 Fri Aug 29

Read Chapter 2.
pp. 40-45 # 2, 6, 8, 14, 16, 22, 27, 28, 29, 31, 33, 38 [x3-3x2+4x-12=(x-3)(x2+4)],

Hwk 2: 32 on p. 41.  (solutions for non-graded problems not answered in back of book).

Class 2 Wed Aug 27

Read pp. 1-11, 17(bottom of page)-24, 26-39
pp. 40-45 # 1, 3, 5, 7, 13, 15, 19, 21, 23, 25, 35, 43, 45, 49, 51, 57.

Homework 1: 24 and 26.

Class 1 Mon Aug 25

Read pp. 1-11, 17(bottom of page)-24, 26-39.
Work through Take a Tour of Maple under Maple Help Menu.
Work through Dr. Becker's Introduction to Maple: mw pdf.

Go to the Maplesoft Training Page and try some of the resources found on that page.

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