Peer Review

Elementary Differential Equations with Boundary Value Problems

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Reviewed:: Jun 4, 2018 by Mathematics

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Overview:: Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. An elementary text can’t be better than its exercises. This text includes 1695 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and definitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 250 completely worked out examples. Where appropriate, concepts and results are depicted in 144 figures. Although I believe that the computer is an immensely valuable tool for learning, doing, and writing mathematics, the selection and treatment of topics in this text reflects my pedagogical orientation along traditional lines. However, I have incorporated what I believe to be the best use of modern technology, so you can select the level of technology that you want to include in your course. The text includes 336 exercises – identified by the symbols C and C/G – that call for graphics or computation and graphics. There are also 73 laboratory exercises – identified by L – that require extensive use of technology. In addition, several sections include informal advice on the use of technology. If you prefer not to emphasize technology, simply ignore these exercises and the advice.
Type of Material:: Open (Access) Textbook
Recommended Uses:: Individual, homework, readings.
Technical Requirements:: Works on any browser or a PDF viewer.
Identify Major Learning Goals:: To serve as the main textbook for a differential equations class
Target Student Population:: Students in an elementary differential equations class
Prerequisite Knowledge or Skills:: Calculus sequence.

Content Quality

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Strengths:: This is a very standard textbook on differential equations that is an OER. It covers all of the material from a standard sophomore level ordinary differential equations class. It comes with a solution manual that contains the solutions to the even exercises. Along with the standard techniques for solving differential equations, it contains several sections on applications such as circuit analysis, damped and undamped motion with and without a forcing function, a differential equations proof of Kepler’s laws, logistics growth, Newton’s law of cooling, and many others. The explanations are thorough and there is a very large selection of exercises to choose from.
Concerns:: Many of the exercises involve very cumbersome calculations. It would be better to have more exercises that demonstrate the point of the technique of the section without having to go through very long calculations. The table of contents has two duplicate sections 2.5 and 2.6, both called Exact Equations. In Chapter 2, more content should be dedicated to the methods of substitution and transformation to cover some additional types of the first order differential equations that can eventually be transformed to separable ones.

Potential Effectiveness as a Teaching Tool

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Strengths:: Being a standard differential equations textbook, this can replace a non-OER textbook and save students hundreds of dollars each. This textbook accomplishes all of the tasks such as introduction, presentation, examples, exercises and solutions to every other homework question. It can very easily serve as the textbook for any standard differential equation class.
Concerns:: None.

Ease of Use for Both Students and Faculty

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Strengths:: The book is in PDF format, so the student can easily access it either online or by downloading it onto a hard drive. There is a table of contents that links to each of the sections, so the students can easily find the topic that they are working on. When the book refers to a prior section or example, there is a link to it so students can simply navigate to that area by just clicking. The layout is clear and the author makes use of color to highlight important topics and figures.
Concerns:: It would be nice to have either links to interactive visualization tools such as direction field graphs, or even better would be to embed such activities directly into the textbook

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