Charles E. Roberts Jr. – författare

This book is written to innovate the standard course and to modernize it. There has been a dramatic change in the past century in how solutions to differential equations are calculated. However, the way the topic has been taught in introductory courses has barely changed to reflect these advances, which leaves students at a disadvantage.Elementary Differential Equations, Third Edition builds on the previous editions, continuing to innovate with the addition of a new topic: combinatorics. The goal is to assist instructors as they facilitate new teaching methods and utilize the latest technology and to provide flexibility in presenting a new topic to encourage students to explore mathematics and not only its applications.The text is designed to help instructors who want to use computers in their classrooms. It accomplishes this by emphasizing and integrating computers. Many examples and exercises included in the text require the use of computer software to solve problems. It should be noted that since instructors use their own preferred software, this book has been written to be independent of any specific software package.Features: Focuses on numerical methods and computing to generate solutions Features extensive coverage of nonlinear differential equations and nonlinear systems Contains a wider variety of non-mathematical models than any competing textbook In the new Chapter 11, readers will learn notions of set partitions, graphs, and rooted trees, the concept of exponential generating functions, and see how differential equations can be surprisingly useful in solving complex counting problems The third edition continues to serve as an excellent introductory textbook for undergraduate students majoring in applied mathematics, computer science, various engineering disciplines, and other sciences. They also will find that the textbook will aid them greatly in their professional careers because of its instructions on how to use computers to solve equations.

This book is written to innovate the standard course and to modernize it. There has been a dramatic change in the past century in how solutions to differential equations are calculated. However, the way the topic has been taught in introductory courses has barely changed to reflect these advances, which leaves students at a disadvantage.Elementary Differential Equations, Third Edition builds on the previous editions, continuing to innovate with the addition of a new topic: combinatorics. The goal is to assist instructors as they facilitate new teaching methods and utilize the latest technology and to provide flexibility in presenting a new topic to encourage students to explore mathematics and not only its applications.The text is designed to help instructors who want to use computers in their classrooms. It accomplishes this by emphasizing and integrating computers. Many examples and exercises included in the text require the use of computer software to solve problems. It should be noted that since instructors use their own preferred software, this book has been written to be independent of any specific software package.Features: Focuses on numerical methods and computing to generate solutions Features extensive coverage of nonlinear differential equations and nonlinear systems Contains a wider variety of non-mathematical models than any competing textbook In the new Chapter 11, readers will learn notions of set partitions, graphs, and rooted trees, the concept of exponential generating functions, and see how differential equations can be surprisingly useful in solving complex counting problems The third edition continues to serve as an excellent introductory textbook for undergraduate students majoring in applied mathematics, computer science, various engineering disciplines, and other sciences. They also will find that the textbook will aid them greatly in their professional careers because of its instructions on how to use computers to solve equations.

This book is written to innovate the standard course and to modernize it. There has been a dramatic change in the past century in how solutions to differential equations are calculated. However, the way the topic has been taught in introductory courses has barely changed to reflect these advances, which leaves students at a disadvantage. Elementary Differential Equations, Third Edition builds on the previous editions, continuing to innovate with the addition of a new topic: combinatorics. The goal is to assist instructors as they facilitate new teaching methods and utilize the latest technology and to provide flexibility in presenting a new topic to encourage students to explore mathematics and not only its applications. The text is designed to help instructors who want to use computers in their classrooms. It accomplishes this by emphasizing and integrating computers. Many examples and exercises included in the text require the use of computer software to solve problems. It should be noted that since instructors use their own preferred software, this book has been written to be independent of any specific software package. Features:Focuses on numerical methods and computing to generate solutionsFeatures extensive coverage of nonlinear differential equations and nonlinear systemsContains a wider variety of non-mathematical models than any competing textbookIn the new Chapter 11, readers will learn notions of set partitions, graphs, and rooted trees, the concept of exponential generating functions, and see how differential equations can be surprisingly useful in solving complex counting problemsThe third edition continues to serve as an excellent introductory textbook for undergraduate students majoring in applied mathematics, computer science, various engineering disciplines, and other sciences. They also will find that the textbook will aid them greatly in their professional careers because of its instructions on how to use computers to solve equations.

This successful book has one goal: to help students develop the necessary skills to write clear, correct, and concise proofs. The beautiful proofs found in this new edition will encourage many students to study higher mathematics. Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs. The third edition includes a new Chapter 10, Proofs from Combinatorics. This unique chapter, authored by Prof. Bóna, offers instructors a choice to include coverage of combinatorics, which, for many students in this course, might be an introduction. Readers will encounter counting arguments, combinatorial proofs of identities, and proofs from graph theory. In this chapter, many of the exercises introduce classic material that is not covered in the text. This helps the instructor spend more time on combinatorics if the instructor prefers to do so. The first two editions of this successful textbook were authored by Charles E. Roberts Jr.. Miklós Bóna picks up his legacy with this revision and a new revision of Roberts' Elementary Differential Equations (CRC Press), now in its third edition.