Elementary Differential Equations with Boundary Value Problems
William Trench, Trinity University
Pub Date: 2013
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The text gives a very thorough treatment of the topics in a traditional beginning course in ODE. read more
The text gives a very thorough treatment of the topics in a traditional beginning course in ODE.
The book is carefully written.
The topics are completely in line with the topics in the traditional course such as our Engineering Math IV Differential Equations. I don't envision changes in the basic material any time soon.
The book is very well written. The most difficult thing for an instructor will be in selection the portions of the text to include in a course. There is more there than can be carefully treated in one course.
The book is carefully written in the standard mathematical style.
The book was not written as electronic materials. While the .pdf production is beautiful and does have numerous hyperlinks, it is one long scroll...
The book is very well organized mathematically.
As a .pdf of a print book, the eBook is beautiful. But it is not modular and there is no "back" button for links. This is a general weakness of this technology.
It's fine. The questions here should have been: How's the math? and How are the applications? At a student level, the mathematical presentation is pretty good. Some instructors may want it to include proofs of things like existence and uniqueness, but I'd say the author made sound choices of what to omit and what to include.
I didn't notice anything culturally sensitive.
This is a good book for the intended course, but I think most students would want it printed.
Table of Contents
Chapter 1: Introduction
Chapter 2: First Order Equations
Chapter 3: Numerical Methods
Chapter 4: Applications of First Order Equations
Chapter 5: Linear Second Order Equations
Chapter 6: Applications of Linear Second Order Equations
Chapter 7: Series Solutions of Linear Second Order Equations
Chapter 8: Laplace Transforms
Chapter 9: Linear Higher Order Equations
Chapter 10: Linear Systems of Differential Equations
Chapter 11: Boundary Value Problems and Fourier Expansions
Chapter 12: Fourier Solutions of Partial Differential Equations
Chapter 13: Boundary Value Problems for Second Order Linear Equations
About the Book
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.
About the Contributors
William F. Trench, PhD. Andrew G. Cowles Distinguished Professor, Trinity University (Retired).