Spring 2015

**Instructor:** Elizabeth Meckes

**Office:** Yost 208

**Phone:** 368-5015

**Email:** ese3 [at] cwru.edu

**Office Hours:** MW, 1 -- 2, or by appointment

**TA sessions:** weekdays from 1 -- 3, in Yost 335 every day
except Thursday; in Yost 343 on Thursdays.

**Textbook:** *Differential Equations, 4e* by
Blanchard, Devaney, and Hall

**Course description:**
From the course catalog:

A first course in ordinary differential equations. First order equations and applications, linear equations with constant coefficients, linear systems, Laplace transforms, numerical methods of solution. Prereq: MATH 223.

We will cover most of the material in chapters 1–3 of the textbook, and selected topics from chapters 4–7. In addition to attending the lectures, you should be reading the text book since there won't be time to discuss all the material in class.

**Definition of a credit hour (approved by the Faculty Senate):**

For courses in lecture format, one credit-hour represents the subject content that can be delivered in one academic hour of contact time each week for the full duration of one academic semester, typically fourteen weeks along with a final examination period.For undergraduate courses, one credit-hour also includes associated work that can be completed by a typical student in 2-3 hours of effort outside the classroom.(Emphasis mine)

If you are spending more than three hours outside of class
*per lecture* on a regular basis, please let me know.

**Homework:**
How much you work on
the homework problems is probably the
single biggest factor in determining how much you get out of the course.
If you are having trouble with the problems, please come ask for help; you will
learn much more (and probably get a rather better grade) if you figure out
all of the homework problems, possibly with help in office hours, than if you
do them alone when you can and skip the ones you can't.

Homework is due daily and is posted below. You will be assigned to a homework group; at the beginning of each class, you will have 10 minutes to discuss your solutions and revise them as you like before turning them in. Remember that your goal should be to write solutions that your classmates (and the grader!) can easily understand. This means you should generally be rewriting your solutions after you figure out how to do the problems, rather than turning in the paper on which you figured them out.

You may discuss the homework with other students, however, you must write up solutions on your own.

**Exams:**
There will be five
midterm exams and one final exam. The tentative dates for the midterm exams are: Friday, January 30; Wednesdayy, February 18; Friday, March 6; Monday, March 30; and Friday, April 17. The final exam is scheduled for Friday, May 1 at 4 pm.

**Last semester's exams and solutions:** I
strongly suggest that you study until you feel prepared for the
exam, then give yourself 50 minutes and try taking the exams as
practice, then look at the solutions, compare with your own, and
then study some more.

Exam 1 Solutions (Please note that this exam did not
cover section 1.8, but our first exam will!)

Exam 2 Solutions (Please note that this exam did not
cover section 2.7, but our exam 2 will!)

Exam 3 Solutions (Please note that this exam did not
cover section 3.4, but our exam 3 will!)

Exam 4 Solutions (Please note that this exam included
material from sections 3.4, while ours won't, but ours will
include sections 4.1 and 4.2.)

Exam 5 Solutions (Note that our exam will include sections 5.3,
6.1 and 6.2, 6.3, which this one didn't.)

Exam 6 Solutions (We won't have a sixth midterm, but this old exam includes material from sections 5.3, 6.1, 6.2, and 6.3.)

**This semester's exams and solutions:**

**Grading:**
Homework is worth 20% of the grade. Each of your four highest midterm scores is worth 13% of the grade (the lowest midterm score will be dropped). The final is worth 28%.

**A couple articles worth reading:**

Forget What You Know About Good Study Habits appeared in the *Times*
in Fall 2010. It offers some advice about studying based on current
pedagogical research.

Teaching and Human Memory, Part 2 from *The Chronicle of Higher
Education* this past December. Its intended audience is professors, but
I think it's worth it for students to take a look as well.

**Computing:** The goal of this course is to help you develop and understanding of the underlying ideas behind the use of differential equations in modeling and analyzing real-world problems; there are other courses that focus more specifically on the use of computers in solving differential equations. We will occassionally make use of technology throughout the term; the web applets below should suffice. You are free to use any of them, or other technology, when appropriate.

- Slope Field Calculator
- Euler's method applet
- Vector Field Plotter
- Euler's method for systems applet
- Improved Euler's method applet
- Runge-Kutta method applet

Lecture | Section | Problems | Due date |
---|---|---|---|

Monday 1/12 | 1.1 | 4, 14, 18, 22 | 1/14 |

Wednesday 1/14 | 1.2 | 2, 21, 26, 34, 40 | 1/16 |

Friday 1/16 | 1.3 | 6 (use any technology), 8, 10, 12, 14, 16 | 1/21 |

Wednesday 1/21 | 1.4 1.3 |
2 (use any technology), 6, 8, 11 In #8, use the given slope field to sketch by hand the Euler's method solution with Δt = 0.2 and y(0) = 0. | 1/23 |

Friday 1/23 | 1.5 | 2, 7, 12, 16, 18 | 1/26 |

Monday 1/26 | 1.6 | 2, 4, 14, 16, 32, 39 | 1/28 |

Wednesday 1/28 | 1.8 | 2, 4, 8, 10, 22, 30 | 2/2 |

Friday 1/30 | Exam 1 | ||

Monday 2/2 | Snow day | ||

Wednesday 2/4 | 2.1 | 1, 2, 8(a,b), 9, 20(a,b) | 2/6 |

Friday 2/6 | 2.2 | 8, 10, 11, 12, 21 | 2/9 |

Monday 2/9 | 2.3 2.4 |
2.3: 2, 5 2.4: 5, 6, 7 | 2/11 |

Wednesday 2/11 | 2.5 | 2, 4(a,b), 6(a,b), 7 | 2/13 |

Friday 2/13 | 2.6 | 3, 4, 5 (use any technology, e.g. Wolfram Alpha) 9 | 1/16 |

Monday 2/16 | 2.7 | 3, 4, 6, 7 | 2/20 |

Wednesday 2/18 | Exam 2 | ||

Friday 2/20 | Snow day | ||

Monday 2/23 | 3.1 | 4, 6, 17, 19, 20, 21 | 2/25 |

Wednesday 2/25 | 3.1 | 24, 26, 28, 32, 33 | 2/27 |

Friday 2/27 | 3.2 | 2, 6, 14, 19 | 3/2 |

Monday 3/2 | 3.3 | 2, 4, 12, 20, 24 | 3/4 |

Wednesday 3/4 | 3.4 | 4, 6, 10, 12, 15 | 3/16 (but do it before the midterm!) |

Friday 3/6 | Exam 3 | ||

Monday 3/16 | 3.5 | 2, 4, 6, 8, 18, 22 | 3/18 |

Wednesday 3/18 | 3.6 | 2, 10, 18, 26 | 3/20 |

Friday 3/20 | 3.7 | 3, 6, 8, 12 | 3/23 |

Monday 3/23 | 3.8 | 4, 16, 19, 20 | 3/25 |

Wednesday 3/25 | 4.1 | 2, 6, 10, 22, 26 | 3/27 |

Friday 3/27 | 4.2 | 4, 8, 14, 17 | 4/1 |

Monday 3/30 | Exam 4 | ||

Wednesday 4/1 | 4.3 | 2, 10, 12, 16, 21 | 4/3 |

Friday 4/3 | 5.1 | 2, 4, 8(a,b), 12(a,b), 30 | 4/6 |

Monday 4/6 | 5.2 | 2, 4, 6, 10, 15 | 4/8 |

Wednesday 4/8 | 5.3 | 1, 2, 9, 10, 12 | 4/10 |

Friday 4/10 | 6.1 | 2, 4, 10, 16, 19, 25 | 4/13 |

Monday 4/13 | 6.2 | 2, 4, 6, 8, 10 | 4/15 |

Wenesday 4/15 | 6.3 | 4, 8, 28, 30, 32 | 4/20 |

Monday 4/20 | 6.3 | 27, 29, 33, 35 | 4/22 |

Wednesday 4/22 | 6.4 | 2, 4, 5, 6, 7 | 4/24 |

Friday 4/224 | 7.1 7.2 |
1(a,b,c,d) (for part (d), use n=20, 40, 60, 80, 100), 6 2, 10 | 4/27 |