Mth 256 Applied Differential Equations
Fall 2007
Sample problems

Last updated November 30 2007

Final exam
10428 MWF 1300 - 86 - Phar 305 W 1600-1750
13157 MWF 1500 - 44 - Kidd 364 W 1600-1750

The final exam has 15 problems, all multiple-choice. Each problem is worth 12 points independently of its difficulty, so try not to get hung up on a difficult problem. It will be a challenge to do all the problems in the alloted 110 minutes, so look over all the problems before doing any. I have appended a table of Laplace transforms and a short table of integrals to the exam.

Section:   010 CRN 10428 020 CRN 13157
Lectures:   MWF 1300-1350 MWF 1500-1550
Locations Kidder 364 Kidder 364
GTA email: Dean Wills Kyle Hickmann
GTA webpages:     //web.mac.com/deancwills/Main/256.html //oregonstate.edu/~hickmank/MTH256_F07/MTH256_F07.htm
GTA Offices:     Kidder 262 Kidder 324
Recitations: R 1000, 1100, 1200     R 1400, 1500, 1600
Enrolment 94 / 96 (2007/09/22) 42 / 89 (2007/09/22) Lots of room!
Lecturer: Bent Petersen
Office: Kidder 296
Phone: (541) 737-5163

Phone messages are likely to be ignored. Use email!

Textbook

William E. Boyce and Richard C DiPrima,
Elementary Differential Equations and Boundary Value Problems,
8th ed., John Wiley & Sons, Inc., 2005

We have used the Boyce and DiPrima text for many years. You may find a cheaper older edition perfectly satisfactory, especially the 7th ed. See the many editions of Boyce and DiPrima for a comparison of editions.

Contact Information and Office Hours
Assignments, Documents, Sample Problems, Old Tests, etc.
Where are the Answers?
Maple Notes
Grade Information by Email
Homework (for text edition 8)
Class Record
Test Information
Textbook
Prerequisites
Course Description
Course Syllabus
Calculators
Grade Distribution
OSU Fall 2007 Official Exam Schedule

Official Description

The current official description of Mth 256 appears to be:

(Winter 2006) First order linear and nonlinear equations, and second order linear equations. Applications to electric circuits and mechanical oscillators. Introduction to the Laplace transform and higher order equations. Solution methods and applications appropriate for science and engineering. (Familiarity with complex numbers and Euler's identities is highly desirable.) PREREQ: MTH 254 or instructor approval required. OTHER PREREQS: MTH 254 or instructor approval required.

The description used to be:

First order linear and nonlinear equations, and second order linear equations. Applications to electrical circuits and mechanical oscillators. Introduction to the Laplace transform and higher order equations. Introduction to linear systems of differential equations, eigenvalues and normal modes. Related matrix and linear algebra concepts. Solution methods and applications appropriate for science and engineering.

This description is overly ambitious and, in fact, I don't believe we ever covered all the material in a single quarter. However if there is sufficient time, I may add some of the material on systems to our course.

Prerequisites

Most of the first year of calculus is used in differential equations. Note calculus is used not just to solve sample problems, but also is essential for understanding the course. If you have to think too much about the mechanics of calculus, you will have difficulty understanding differential equations. The following topics are particularly important. In addition, it will be useful to know a little bit about complex numbers, and to know some concepts from linear algebra.

Syllabus

Chapter 1 and Section 8.1 Introduction, geometrical and numerical ideas
Chapter 2 (omit 2.9) First order differential equations
Chapter 3 and 4 simultaneously Differential equations of order 2 and higher
Chapter 6 Laplace transform
(bits of chapter 7) Laplace transform applied to systems of ODE (see the end of section 7.9), and other material, as time allows

Tests

There may be some quizzes, homework or other assignments in the recitations. In addition we will have two major tests. Your grade will be computed based on the following table.

Grade distribution

Recitation activities In-Class Test (midterm) Final Exam
15 % 25 % 60 %

In-class Test

Class Time Test Date Test Length Location
1300 Wed Oct 31 50 min In class
1500 Wed Oct 31 50 min In class

Final exam

Class Time Exam Date Exam Time Exam Length Location
1300 Wed Dec 5 1600 110 min TBA
1500 Wed Dec 5 1600 110 min TBA

We will have a group exam Wednesday at 4 PM. Both classes will take the exam at the same time (and possibly in the same place - TBA).

You may use a single 8.5 by 11 inch (21.6 by 27.9 cm) notesheet, or smaller, prepared in advance, to bolster your memory on the tests. You may write on both sides of your notesheet. Notesheets may not be shared. If you don't prepare a notesheet in advance you will have to do without a notesheet.

In view of the size of the class, the tests will consists mostly, or entirely, of multiple-choice problems. Be sure you work very carefully.

If you do fairly well on the midterm and then miss the final exam, your grade will be I (incomplete). If you do poorly on the midterm and then miss the final exam, your grade will be F. In order to obtain a W you must formally withdraw from the course in accord with institutional rules.

You must return both the scantron and the entire exam. Failure to return either may result in a grade of 0.

Calculators

You may use a simple graphics calculator (not a laptop nor a palmtop, etc.) on tests. I will expect that you have at the very least a scientific calculator. Note your calculator will need to be in radians mode (not degrees). Questions about calculators will not be answered during tests. You must know how to use your own calculator.

Because many calculators are capable of solving fairly elaborate problems you should expect that test problems may be a little bit indirect, at least in some cases, and require a modicum of thought.

Calculators may not be shared during tests.

Class Record

This record is a bit sketchy, but you may find it useful if you miss a few classes. Each entry below is a record of what we actually did in class, or occasionally, what I plan to do in class.
Mon week 1, Sep 24
Discusion of course - tests, homework, etc. Definition of differential equations. Examples: Newton's law of cooling, Parachute equation.
Wed week 1, Sep 26
Section 2.1: Linear ODE of order 1. The method of the integrating factor. Example: Newton's law of cooling - heating of a building by the sun - see problem 18 in section 2.3, page 63.
Fri week 1, Sep 28
Section 2.1 and 2.3: Numerous examples of the method of the integrating factor for first-order ODE. Discussion of mixing problems.
Mon week 2, Oct 1
Sections 2.2 and 2.3: Separable ODE. Parachute equation
Wed week 2, Oct 3
Section 2.3: Examples. Finished parachute equation. Discussed some special second order ode, time-invariant (autonomous) and space invariant ode (see problems 36 - 51 for section 2.9). Discussed projectile equation (a canon on a spherical airless planet).
Fri week 2, Oct 5
Section 2.5-2.6: Autonomous first order ODE. Population models, especially Malthusian and logistic models. We started to discuss exact ode and integrating factors.
Mon week 3, Oct 8
Section 2.6 exact ode and integrating factors.
Wed week 3, Oct 10
Section 2.6 integrating factors. Section 2.8 Picard iteration.
Fri week 3, Oct 12
Section 2.8 Picard iteration continued. Section 1.1 direction fields. Section 2.7, 8.1 Numerical approximation by Euler's method.
Mon week 4, Oct 15
2.8 Existence and uniqeness. Higher order ODE and systems of ODE - Cauchy initial value problem.
Wed week 4, Oct 17
Section 3.1, 3.2 and 4.1 Second and higher linear ODE.
Fri week 4, Oct 19
Section 3.2, 3.5 and 4.2. Linear ODE with multiple real characteric roots. Lots of examples.
Mon week 5, Oct 22
Section 3.4 and 4.2: Complex numbers. Complex characteristic roots. Complex exponential.
Wed week 5, Oct 24
Sick - No class!
Fri week 5, Oct 26
Section 3.2 and 3.3: Fundamental solutions. Wronskian.
Mon week 6, Oct 29
  Review
Wed week 6, Oct 31
  Mid-term test
Fri week 6, Nov 2
Section 3.6, 3.7 and 4.4: Nonhomogeneous equations. Variation of parameters
Mon week 7, Nov 5
Section 3.7, 3.6, 4.4 and 4.3: Variation of parameters and undetermined coefficients
Wed week 7, Nov 7
Section 3.6 and 4.3: Undetermined coefficients
Fri week 7, Nov 9
Section 3.6 and 4.3: Undetermined coefficients - complex methods
Mon week 8, Nov 12
Section 3.5: Reduction of order.
Wed week 8, Nov 14
Section 3.8: Free vibrations.
Fri week 8, Nov 16
Section 3.9: Forced vibrations.
Mon week 9, Nov 19
Section 6.1: Laplace transform.
Wed week 9, Nov 21
Section 6.2: Solution of initial value problems using Laplace transform.
Fri week 9, Nov 23
Thanksgiving holiday!
Mon week 10, Nov 26
Section 6.3, 6.4:
Wed week 10, Nov 28
Section 6.4, 6.5, 6.6:
Fri week 10, Nov 30
Review

|  TOP  |  HOME  |  Mth 256 Documents   |