# Mth 256 Documents

Last updated November 30 2007

This page lists old tests, notes, Maple worksheets, sample problems, etc., for Mth 256. You may find this material useful for studying. Expect some overlaps in the various files. Eventually very old files will dribble off the bottom.

Many of the documents are in Portable Document Format (PDF) or are Maple worksheets (MWS). PDF files are "Portable Document Files." You can use the free Adobe Acrobat Reader, available at http://www.adobe.com, to view or print PDF files. The Acrobat Reader plug-in is installed in the browser(s) on many campus computers. There are many other software packages for reading PDF files. Maple Worksheets require Maple to be useful.

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Homework (for text edition 8)

2007 Fall Mth 256 Exam
PDF, 61 KB, 8 pages, 15 problems
In addition to 15 multiple choice problems the final exam has 4 useful tables occupying 3 pages. The actual test is 5 pages. The following table shows the problem number, the correct answer and the number of people who chose it, the number of people who chose each proposed answer, A - E, and the topic of the problem. As you can see, for most problems the correct answer was the most popular choice. The exceptions are problems 5 and 6. Note also that problem 7 was difficult for many people.
 Que Ans A B C D E Topic 1 B - 45 38 45 9 5 4 undetermined coefficients 2 C - 41 3 26 41 28 3 undetermined coefficients 3 C - 52 10 11 52 24 4 initial value problem 4 D - 50 15 13 17 50 6 variation of parameters 5 A - 18 18 35 26 18 5 variation of parameters 6 A - 13 13 49 21 17 1 amplitude of steady state, driven dissipative spring 7 E - 31 29 16 21 4 31 harmonic oscillator, magnitude of solution 8 A - 90 90 5 1 1 4 Laplace transform 9 D - 74 2 8 10 74 7 inverse Laplace transform 10 C - 80 7 8 80 4 2 IVP via Laplace transform 11 A - 71 71 7 6 12 5 IVP via Laplace transform 12 A - 59 59 38 2 1 1 Laplace transform of unit step 13 C - 46 9 25 46 17 8 Newton's law of heating-cooling, cold beer 14 B - 37 11 37 26 16 9 Torricelli-Borda draining a tank 15 A - 90 90 1 0 3 5 Laplace transform, IVP with Dirac delta
2007 Fall Mth 256 Midterm Test
PDF 1300 version, 35 KB, 4 pages, 11 problems
PDF 1500 version, 35 KB, 4 pages, 11 problems
The answers are:
1300: C / A C C B / C D D C / 2.0625 oz/gal
1500: D / B A A B / D C D D / 2.0625 oz/gal
2007 Fall Mth 256 Time of Death Example
PDF, 19 KB, 1 page
This example uses Newton's Law of Cooling to determine the time of death of a cadaver. In reality the situation is more complex but at least now you'll have a reason to think about differential equations when watching a murder mystery movie.
2006 Fall Mth 256 Test Format Sample
PDF, 21 KB, 2 pages
Here is the cover page for our mid-term test. Please read the instructions before coming to class to save a bit of time. Ignore any statements about the number of problems. I just chose some random numbers!
2006 Fall Mth 256 Complex Numbers - Early History
PDF, 13 KB, 2 pages
This is a brief and very sketchy early history of complex numbers.
2006 Fall Mth 256 Three Week Review
PDF, 47 KB, 8 pages, 27 problems
Here are a few sample problems with Maple generated answers. The actual test problems will be similar to some of these problems but will be in multiple-choice-answer format.
2006 Winter Mth 256 Final Exam
PDF, (Lost - to be posted after being found.)
2006 Winter Mth 256 Midterm Test
PDF, 37 KB, 4 pages, 8 problems
PDF large print, 39 KB, 6 pages, 8 problems
Multiple-choice answers, 10 points each: 1=C, 2=B, 3=A, 4=D, 5=D, 6=A, 7=E (31/4). Partial credit for problems 2 and 3, 8 points for 2=A and for 3=D. For problem number 8 the answer is 1.10119 oz/gal and partial credit was allowed for some correct work.
2004 Winter Mth 256 Final Exam
PDF, 65 KB, 6 pages, 12 problems
Multiple-choice exam.
2004 Winter Mth 256 Laplace Transform table from the final exam
PDF, 45 KB, 2 pages
This is the actual Laplace transform table that will be supplied with the final exam. Be sure that you understand how to use it.
2004 Winter Mth 256 Test 2
PDF, 38 KB, 3 pages, 4 problems
2004 Winter Mth 256 Test 1
PDF, 40 KB, 3 pages, 8 problems
2004 Winter Mth 256 Sample Problems - second set
PDF, 55 KB, 5 pages
Here are 24 problems dealing with variation of parameters and the method of undetermined coefficients.
2004 Winter Mth 256 Applied Differential Equations Problem Collection
PDF, 72 KB, 9 pages
Version 20040123. This collection of problems will be updated fairly frequently during the quarter. The problems are mostly multiple-choice problems and are organized by topic. Many of the problems, though perhaps not all, are suitable test problems.
2002 Winter Mth 256 Applied Differential Equations Test 2, version a
PDF, 34 KB, 3 pages, 10 problems
2002 Winter Mth 256 Applied Differential Equations Sample (partial) Test
PDF, 30 KB, 1 page, 3 problems

2002 Winter Mth 256 Variation of Parameters and Duhamel's Principle
PDF, 48 KB, 4 pages
MWS, 13 KB, Maple Worksheet

2002 Winter Mth 256 Method of Undetermined Coefficients - sample problems
PDF, 46 KB, 4 pages, 10 problems
MWS, 12 KB, Maple Worksheet
2002 Winter Mth 256 Applied Differential Equations Test 1
PDF, 33 KB, 2 pages, 8 problems, test version a
PDF, 33 KB, test version z
2002 Winter Mth 256 Applied Differential Equations Sample Test Problems
PDF, 20KB, 1 page, 4 problems
2002 Winter Mth 256 Integrating Factors and Exact ODE
PDF, 63 KB, 9 pages, 12 problems
MWS, 25 KB, Maple Worksheet
2002 Winter Mth 256 Euler Method for First Order ODE
PDF, 76 KB, 7 pages
MWS, 30 KB, Maple Worksheet
2002 Winter Mth 256 Linear First Order ODEs
PDF, 33 KB, 2 pages, 12 problems
MWS, 14 KB, Maple Worksheet Drill problems with answers provided by Maple.
2002 Winter Mth 256 Separable First Order ODEs
PDF, 43 KB, 1 page, 6 problems
MWS, 17 KB, Maple Worksheet Drill problems with answers provided by Maple.
2001 Winter Mth 256 Applied Differential Equations Final Exam
PDF, 108 KB, 6 pages, 12 problems
2001 Winter Mth 256 Applied Differential Equations Sample Final Exam Problems
PDF, 101 KB, 4 pages, 6 problems
2001 Winter Mth 256 Applied Differential Equations Midterm Exam
PDF, 61 KB, 4 pages, 4 problems
2001 Winter Mth 256 Applied Differential Equations Sample Problems
PDF, 43 KB, 2 pages, 34 problems
2001 Winter Mth 256 Model Problems - Mixing Problems
PDF, 35 KB, 1 page, 3 problems
2001 Winter Mth 256 Model Problems - Drug Dosage
PDF, 33 KB, 1 page, 3 problems
2001 Winter Mth 256 Model Problems - Rocket Equation
PDF, 36 KB, 1 page, 3 problems
2001 Winter Mth 256 Model Problems - Newton's Law of Cooling
PDF, 39 KB, 1 page, 2 problems
2001 Winter Mth 256 Model Problems - Bouyancy, drag and acceleration of gravity
PDF, 36 KB, 1 page, 2 problems
2001 Winter Mth 256 Model Problems - Parachute problems
PDF, 39 KB, 1 page, 3 problems
2001 Winter Mth 256 Model Problems - Borda-Torricelli principle examples
PDF, 42 KB, 1 page, 5 problems
2001 Winter Mth 256 Model Problems - Euler's method for a first order IVP
PDF, 35 KB, 1 page, 1 problem
2001 Winter Mth 256 Laplace Transform in Maple
PDF, 52 KB, 4 pages
MWS, 11 KB, Maple Worksheet
This Worksheet illustrates how to solve (linear) initial value problems by using the Laplace transform. Maple is useful here by eliminating the large amounts of (simple, but overwhelming) algebra needed when doing transform problems by hand.
2001 Winter Mth 256 Differential Equations with Maple
PDF, 211 KB, 10 pages
MWS, 46 KB, Maple Worksheet
This worksheet illustrates how to solve differential equations in Maple, how to extract pieces of the data structure that Maple returns and a bit of plotting. It is just a short introduction!
2000 Fall Mth 256 Laplace Transform table
PDF, 54 KB, 2 pages
2000 Fall Mth 256 Linear differential equations with Dirac-delta and Heaviside terms: Examples
PDF, 84 KB, 6 pages
MWS, 29 KB, Maple Worksheet
2000 Fall Mth 256 Newton's Law of Cooling - examples
PDF, 110 KB, 3 pages
MWS, 17 KB, Maple Worksheet
We solve two problems illustrating Newton's law of cooling. We note the system temperature tracks the ambient, but with a time delay and with reduced amplitude of fluctuation.
2000 Fall Mth 256 Applied Differential Equations Archive
PDF, 84 KB, 8 pages, 18 problems
Two tests and the final exam.
1997 Spring Mth 256 Applied Differential Equations Archive
PDF, 162 KB, 36 pages, 183 problems
This archive contains 164 sample problems, two tests and the final exam.
1996 Summer Mth 256 Applied Differential Equations Archive
PDF, 33 KB, 5 pages, 15 problems
Three tests.
1996 Spring Mth 256 Applied Differential Equations Archive
PDF, 46 KB, 7 pages, 19 problems
Two tests, final exam, Laplace transform table
1995 Spring Mth 256 Applied Differential Equations Archive
PDF, 91 KB, 9 pages, 25 problems
Five tests, final exam, Mothers' weekend test (fun), Laplace transform table
1995 Winter Mth 256 Applied Differential Equations Archive
PDF, 158 KB, 25 pages, 141 problems
Sample problems by topic from CRUM1994, two tests, final exam.
1994 Fall Mth 256 Applied Differential Equations CRUM Report
PDF, 123 KB, 15 pages, 123 problems
Applied differential equations equations course description. Most parts of the course are illustrated by typical test or homework problems.
1994 Summer Mth 256 Applied Differential Equations Archive
PDF, 88 KB, 9 pages, 54 problems
Sample problems, two tests.
1994 Winter Mth 256 Applied Differential Equations Archive
PDF, 111 KB, 12 pages, 69 problems
Sample problems, two tests, final exam.
1993 Summer Mth 256 Applied Differential Equations Archive
PDF, 87 KB, 7 pages, 45 problems
Sample problems, three tests.
1992 Summer Mth 256 Applied Differential Equations Archive
PDF, 84 KB, 7 pages, 48 problems
Six tests.
1992 Spring Mth 256 Applied Differential Equations Archive
PDF, 70 KB, 4 pages, 28 problems
Two tests, final exam, make-up exam.
1992 Winter Mth 256 Applied Differential Equations Archive
PDF, 90 KB, 7 pages, 47 problems
Sample problems, two tests, final exam.

Copyright © 1992-2004 Bent E. Petersen. The documents and the Maple worksheets described here, may be used, copied and distributed freely, entire and intact, for any educational noncommercial purpose, but may not be distributed in an altered form. If you want to improve on anything, which certainly can be done, then please write your own version(s).