Tue. Jul 5th, 2022

Introduction: What is the course about? And why do you need it?

This is a first course in differential equations and modeling applications that introduces principles of modeling and analysis for linear, nonlinear, dynamical, and global models. The 11th edition has been carefully revised to keep up with the many advances in modeling over recent years – while maintaining the book’s position as a clear and concise introduction to differential equations and their applications. The purpose of this article is to inform readers of the new material and organization.
The main goal of this book (and its companion to be published next year) is to provide a foundation for modeling and analysis. The book covers all aspects of modeling and analysis, including optimization, design, control and computation, linear algebra and differential equations, reliability engineering, manufacturing, finance, etc. It emphasizes comparison-based reasoning (e.g., the importance of fundamentals) over mathematical preamble.
The book has three parts: Part I covers modeling principles and their application to optimization, design, control, and computing; Part II covers linear algebra and differential equations; Part III covers reliability engineering and manufacturing. The book’s companion volume (to be published in 2018) will cover the remaining topics: finance, regulation, sustainability and cyber security.
The book covers all aspects of modeling including optimization, design, control and computing; linear algebra and differential equations; reliability engineering; manufacturing (and its applications to finance as well). The book emphasizes comparison-based reasoning (putting off mathematics until later, instead getting the fundamental principles first and foremost) over mathematical preamble.

a first course in differential equations with modeling applications 11th edition pdf
a first course in differential equations with modeling applications 11th edition pdf

What are the Books that You Recommend?

The book has been reviewed and adopted by the American Mathematical Society, Dalhousie University, Massachusetts Institute of Technology, Northwestern University , Princeton University. The book is written in a clear and concise style, with abundant exercises, examples and explanatory illustrations.
This textbook is suitable for advanced undergraduate or graduate level courses in differential equations. The material can be used in conjunction with a course of calculus and linear algebra. Anyone wishing to learn the subject thoroughly; teachers of mathematics; people who have to deal with differential equations in their work such as physicists, engineers, actuaries, statisticians and many others will find this book an indispensable guide.
Excerpt from Book:
Introduction to Differential Equations: Method of Frobenius and Other Generalizations (Pure and Applied Mathematics)

a first course in differential equations with modeling applications 11th edition pdf
a first course in differential equations with modeling applications 11th edition pdf

How to Choose a Book on Differential Equations

This book is a clear event-driven text. The book first explains the basics and then builds up to more advanced topics. The book is well structured with each chapter having a topic list and review questions in addition to the problems. This book gives in-depth coverage of each topic and has an extensive bibliography for those students who wish to pursue their studies further. The book’s text and supporting material is now based on Mathematica . [ Background material regarding Mathematica can be found at: Mathematica: Programmable Computational Tools for Students. ]
This book is a clear event-driven text. The book first explains the basics and then builds up to more advanced topics. The book is well structured with each chapter having a topic list and review questions in addition to the problems. This book gives in-depth coverage of each topic and has an extensive bibliography for those students who wish to pursue their studies further. The book’s text and supporting material is now based on . [ Background material regarding Mathematica can be found at: Mathematica: Programmable Computational Tools for Students. ]
This book is a clear event-driven text. The book first explains the basics and then builds up to more advanced topics. The book is well structured with each chapter having a topic list and review questions in addition to the problems. This book gives in-depth coverage of each topic and has an extensive bibliography for those students who wish to pursue their studies further. The book’s text and supporting material is now based on . [ Background material regarding Mathematica can be found at: Mathematica: Programmable Computational Tools for Students. ]

a first course in differential equations with modeling applications 11th edition pdf
a first course in differential equations with modeling applications 11th edition pdf

What is the Difference Between These Two Books?

The first book, A First Course in Differential Equations with Modeling Applications, is a clear event-driven text. The book first explains the basics and then builds up to more advanced topics. The book is well structured with each chapter having a topic list and review questions in addition to the problems. This book gives in-depth coverage of each topic and has an extensive bibliography for those students who wish to pursue their studies further.
The second book, The Second Course in Differential Equations with Applications, is a more traditional approach to differential equations. Unlike the first book which gives general coverage of all differential equations, the second book has chapters dedicated to particular classes of differential equations. The chapters are well written and outline the key concepts from a given class so that there isn’t much material that needs to be learned before being able to move on to another topic. There are occasional mentions of modeling applications in each chapter which help tie the math topics together into a cohesive whole.
Both books are well written and do a good job at explaining the concepts. The first book is more geared toward the student who just wants to learn differential equations with some mathematical rigor attached, while the second book is geared more toward the student who will use differential equations in an applied context.

a first course in differential equations with modeling applications 11th edition pdf
a first course in differential equations with modeling applications 11th edition pdf

What are the Best Books for Interspersal Differential Equations?

Mathematical Methods for Physicists by Steven G. Krantz is an excellent book [for those who like schoolbooks] and can be used as a supplement. The book has been reviewed and adopted by the American Mathematical Society, Dalhousie University, Massachusetts Institute of Technology, Northwestern University , Princeton University. If you like those books : Mathematical Methods for Physicists, then you will also like the book by W. Murray and M. Muller-Kirsten called Advanced Calculus for Scientists and Engineers .
P. Tucker is a professor at the Department of Mathematics, University of Rochester : http://www.math.rochester.edu/tucker/ [to read more about him]
Differential equations [and Linear Algebra] can be approached in many ways, depending on your interest and background. If you are coming from the world of physics, it is likely that you will want differential equations to help with your research, and in that case there are several excellent books out there to help get you started.

a first course in differential equations with modeling applications 11th edition pdf
a first course in differential equations with modeling applications 11th edition pdf