Updated Fall 2007 for the 8th ed. of our text. | Mth 256 Index | Mth 256 Documents | HOME |
Our textbook has been very successful for many years. It has been published in eight editions. Some editions have two versions - with or without the boundary value problems material. I do not have a copy of the first edition, but I believe it came out in 1965 - 42 years ago! I also do not have a 3rd edition though I located one in a used book store. It was so moldy that I began to sneeze when I tried to examine it.
If you are trying to get by with an earlier edition to save a few bucks - well, not so few - you may find the following table useful. The table is also interesting. Most of the changes are seen to be in the first two chapters. Perhaps this is an indication of the authors' attempts to find a good way to lead students into the subject matter by the most efficient path. Also we see that many changes involve sections dealing with applications. This may be an attempt to make the text more approachable to engineering and science students, though it is probably also a response to market pressure calling for more applications.
I have indicated roughly related sections below by coloring the cells. I have not done a very good job. One really needs to divide the text into smaller pieces to compare the different editions.
I do not plan to compare homework problems between the different editions. If you want to work from an earlier edition, you will have to make the comparisons yourself. Perhaps this table will give you a starting point. If you come up with useful comparisons, or comments, please let me know. I may add your remarks below (with credit).
The table does not cover the whole text - just a part of the part used in Mth 256.
| Edition | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
| Copyright Year | 2005 | 2001 | 1997 | 1992 | 1986 | 1977 | 1969 | 1965 |
| Some basic mathematical models; direction fields | 1.1 | 1.1 | - | - | - | - | - | - |
| Ordinary differential equations | - | - | - | - | - | - | 1.1 | - |
| Solutions of some differential equations | 1.2 | 1.2 | - | - | - | - | - | - |
| Classification of differential equations | 1.3 | 1.3 | 1.1 | 1.1 | 1.1 | - | - | - |
| Historical remarks | 1.4 | 1.4 | 1.2 | 1.2 | 1.2 | - | 1.2 | - |
| Linear equations - Integrating factors | 2.1 | - | - | - | - | - | - | - |
| Linear equations with Variable Coefficients | - | 2.1 | - | - | - | - | - | - |
| Linear equations | - | - | 2.1 | 2.1 | 2.1 | - | 2.1 | - |
| Further discussion of linear equations | - | - | 2.2 | 2.2 | 2.2 | - | 2.2 | - |
| Differences between linear and nonlinear equations | 2.4 | 2.4 | 2.4 | 2.4 | - | - | - | - |
| Nonlinear equations | - | - | - | - | 2.3 | - | 2.3 | - |
| Separable equations | 2.2 | 2.2 | 2.3 | 2.3 | 2.4 | - | 2.4 | - |
| Modeling with first order equations | 2.3 | 2.3 | - | - | - | - | - | - |
| Modeling with linear equations | - | - | 2.5 | - | - | - | - | - |
| Applications of first order linear equations | - | - | - | 2.5 | 2.5 | - | - | - |
| Miscellaneous problems and applications | - | - | 2.10 | 2.10 | 2.11 | - | - | - |
| Miscellaneous problems | - | - | - | - | - | - | 2.8 | - |
| Applications of first order equations | - | - | - | - | - | - | 2.9 | - |
| Autonomous equations and population dynamics | 2.5 | 2.5 | - | - | - | - | - | - |
| Population dynamics and some related problems | - | - | 2.6 | 2.6 | 2.6 | - | - | - |
| Some problems in mechanics | - | - | 2.7 | 2.7 | - | - | - | - |
| Elementary mechanics | - | - | - | - | 2.7 | - | 2.10 | - |
| Exact equations and integrating factors | 2.6 | 2.6 | 2.8 | 2.8 | - | - | - | - |
| Exact equations | - | - | - | - | 2.8 | - | 2.5 | - |
| Integrating factors | - | - | - | - | 2.9 | - | 2.6 | - |
| Homogeneous equations | - | - | 2.9 | 2.9 | 2.10 | - | 2.7 | - |
| Numerical approximations: Euler's method | 2.7, 8.1 | 2.7, 8.1 | - | - | - | - | - | - |
| The existence and uniqueness theorem | 2.8 | 2.8 | 2.11 | 2.11 | 2.12 | - | 2.11 | - |
| The existence theorem from a more modern viewpoint | - | - | - | - | - | - | 2.12 | - |
| First order difference equations | - | 2.9 | 2.12 | 2.12 | - | - | - | - |
| Introduction (chapter) | - | - | - | - | 3.1 | - | 3.1 | - |
| Homogeneous equations with constant coefficients | 3.1 | 3.1 | 3.1 | 3.1 | 3.5 | - | 3.5 | - |
| Fundamental solutions of linear homogeneous equations | 3.2 | 3.2 | 3.2 | 3.2 | 3.2 | - | 3.2 | - |
| Linear independence and the Wronskian | 3.3 | 3.3 | 3.3 | 3.3 | - | - | - | - |
| Linear independence | - | - | - | - | 3.3 | - | 3.3 | - |
| Complex roots and the characteristic equation | 3.4 | 3.4 | 3.4 | 3.4 | - | - | - | - |
| Complex roots | - | - | - | - | 3.5.1 | - | 3.5.1 | - |
| Repeated roots; reduction of order | 3.5 | 3.5 | 3.5 | 3.5 | - | - | - | - |
| Reduction of order | - | - | - | - | 3.4 | - | 3.4 | - |
| The nonhomogeneous problem | - | - | - | - | 3.6 | - | - | - |
| Nonhomogeneous equations; method of undetermined coefficients | 3.6 | 3.6 | 3.6 | 3.6 | - | - | - | - |
| The method of undetermined coefficients | - | - | - | - | 3.6.1 | - | 3.6.1 | - |
| Variation of parameters | 3.7 | 3.7 | 3.7 | 3.7 | - | - | - | - |
| The method of variation of parameters | - | - | - | - | 3.6.2 | - | 3.6.2 | - |
| Mechanical and electrical vibrations | 3.8 | 3.8 | 3.8 | 3.8 | - | - | - | - |
| Mechanical vibrations | - | - | - | - | 3.7 | - | 3.7 | - |
| Free vibrations | - | - | - | - | 3.7.1 | - | 3.7.1 | - |
| Forced vibrations | 3.9 | 3.9 | 3.9 | 3.9 | 3.7.2 | - | 3.7.2 | - |
| Electrical networks | - | - | - | - | 3.8 | - | 3.8 | - |
| Introduction (chapter) | - | - | - | - | 5.1 | - | 5.1 | - |
| General theory of nth order linear equations | 4.1 | 4.1 | 4.1 | 4.1 | 5.2 | - | 5.2 | - |
| Homogeneous equations with constant coefficients | 4.2 | 4.2 | 4.2 | 4.2 | 5.3 | - | 5.3 | - |
| The method of undetermined coefficients | 4.3 | 4.3 | 4.3 | 4.3 | 5.4 | - | 5.4 | - |
| The method of variation of parameters | 4.4 | 4.4 | 4.4 | 4.4 | 5.5 | - | 5.5 | - |
| Introduction. Definition of the Laplace transform | - | - | - | - | - | - | 6.1 | - |
| Definition of the Laplace transform | 6.1 | 6.1 | 6.1 | 6.1 | 6.1 | - | - | - |
| Solution of initial value problems | 6.2 | 6.2 | 6.2 | 6.2 | 6.2 | - | 6.2 | - |
| Step functions | 6.3 | 6.3 | 6.3 | 6.3 | 6.3 | - | 6.3 | - |
| Differential equations with discontinuous forcing functions | 6.4 | 6.4 | 6.4 | 6.4 | 6.3.1 | - | 6.3.1 | - |
| Impulse functions | 6.5 | 6.5 | 6.5 | 6.5 | 6.4 | - | 6.4 | - |
| The convolution integral | 6.6 | 6.6 | 6.6 | 6.6 | 6.5 | - | 6.5 | - |
| General discussion and summary | - | - | - | - | - | - | 6.6 | - |
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