A Modern Introduction to Differential Equations 2nd Edition by Henry J. Ricardo (PDF)

Description

A Modern Introduction to Differential Equations, Second Edition, provides an introduction to the basic concepts of differential equations.The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical, and numerical aspects of first-order equations, including slope fields and phase lines. The discussions then cover methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients; systems of linear differential equations; the Laplace transform and its applications to the solution of differential equations and systems of differential equations; and systems of nonlinear equations. Each chapter concludes with a summary of the important concepts in the chapter. Figures and tables are provided within sections to help students visualize or summarize concepts. The book also includes examples and exercises drawn from biology, chemistry, and economics, as well as from traditional pure mathematics, physics, and engineering.This book is designed for undergraduate students majoring in mathematics, the natural sciences, and engineering. However, students in economics, business, and the social sciences with the necessary background will also find the text useful.

User’s Reviews

Editorial Reviews: Review An accessible introductory differential equations textbook for the one-semester course. About the Author Henry J. Ricardo works at Medgar Evers College of the City University of New York in Brooklyn, USA.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The text book does NOT include enough worked out problems…it explains concepts then the questions are worded differently and are very difficult to do if you were to depend on just the text. I bought this book because it is required by my professor but as far as the homework problems go (assigned problems from the book) I only have used the book to solve 10% of the problems…to solve the rest I had to read lessons online and watch youtube videos to understand the concepts. This review is obviously coming from a student who is still new to this subject not somebody who’s been studying math all their life. But compared to the other math texts I’ve used in the past, this is by far the least useful and the least informative.

⭐This book was just okay as a reference for Diff Eq. I originally was looking for a text with more worked problems but this book takes the approach of utilizing computational software in conjunction with the text.

⭐I found this book to be of limited usefulness primarily because it falls into the same trap that seemingly all math textbooks in the US have; over dependance on technology. Over and over again the author tells you to use the mathematic software package of your choice to explore slope fields of some equation. I really don’t care about the slope field, maybe I will after I understand how to find particular solutions to nonhomogenous equations (which was not explained well at all imho). Overall, the text doesn’t spend alot of time explaining things, and when it does it’s not very enlightening. I found the problem sets lacking and the solutions manual wasn’t much help. A much better book is the Dover Ordinary Differential Eqn book by Tannenbaum. First published in 1964 (iirc) it’s a far superior book.

⭐I took ODE class 15 years ago and never had to use it in practice. Now, due to a nature of work I have to go back and refresh my knowledge. This is excellent book for student or anyone who wants to understand how to solve and apply differential equations in real life.My old professor used dry, formal approach to just manipulate equations and never really taught real life use cases.Unlike most of textbooks I’ve seen, this book is self contained, no question is left unanswered. I mean really no question.If topic is not covered in the main text, author provides all the necessary information in appendix, you will even find introduction to vector algebra and complex numbers. You will never see vague explanation or do it yourself calculation for any formula derivation that is not trivial.Excellent work. I wish I had a chance to use this textbook long time ago when I took my ODE class.

⭐Off course, what else can anyone expect from the mind of Dr. Ricardo??? I just wish he had already published this book when I was still in my Undergraduate years as a Physics Major. Or perhaps even better: When I used to sit in his classroom. I owe my mathematical skills to the same teaching techniques I see when I read his book: The ability of Dr. Ricardo to explain complex subjects in a simple way, so different from many other instructors, especially at the undergraduate level. That is, not only the ability to get students to see the practical application of mathematical concepts, but to motivate them to do interesting work. I took my differential equations with another teacher, using the De Prima textbook, (a classic) long before Dr. Ricardo published his work. Nevertheless, I just purchased his book, it is part of my library and will remain there as a source of teaching ideas. Reading his work was like if I was still seating at his calculus class.Also recommended: De Prima: ‘Differential Equations and Boundary Value Problems’ Powers: ‘Boundary Value Problems’ Tromba: ‘Vector Calculus’ Arfken: ‘Mathematical Methods For Physicists’

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