Introduction to differential equations

著者

• Taylor, Michael Eugene

書誌事項

Introduction to differential equations

Michael E. Taylor

（The Sally series, . Pure and applied undergraduate texts ; 14）

American Mathematical Society, c2011

注記

Bibliography: p. 403-405

Includes index

内容説明・目次

内容説明

The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponential and trigonometric functions, which plays a central role in the subsequent development of this chapter. Chapter 2 provides a mini-course on linear algebra, giving detailed treatments of linear transformations, determinants and invertibility, eigenvalues and eigenvectors, and generalized eigenvectors. This treatment is more detailed than that in most differential equations texts, and provides a solid foundation for the next two chapters. Chapter 3 studies linear systems of differential equations. It starts with the matrix exponential, melding material from Chapters 1 and 2, and uses this exponential as a key tool in the linear theory. Chapter 4 deals with nonlinear systems of differential equations. This uses all the material developed in the first three chapters and moves it to a deeper level. The chapter includes theoretical studies, such as the fundamental existence and uniqueness theorem, but also has numerous examples, arising from Newtonian physics, mathematical biology, electrical circuits, and geometrical problems. These studies bring in variational methods, a fertile source of nonlinear systems of differential equations. The reader who works through this book will be well prepared for advanced studies in dynamical systems, mathematical physics, and partial differential equations.

目次

Preface Single differential equations Linear algebra Linear systems of differential equations Nonlinear systems of differential equations Bibliography Index

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB05143833
• ISBN:
  • 9780821852712
• LCCN: 2010037816
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: xii, 409 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QA372
  • DC22 : 515/.35
• 件名:
  • LCSH : Differential equations
  • FREE : Ordinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.). msc
• 親書誌ID:
  • BA8980131X