Skip to main content Accessibility help
×
  1. Home
  2. Browse subjects
  3. Mathematics
  4. Abstract analysis
  5. Content listing

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

26079 results in Abstract analysis

Page 894 of 1304

  • Introduction

  • James C. Robinson, University of Warwick
  • Book:
    An Introduction to Ordinary Differential Equations
    Published online:
    05 September 2012
    Print publication:
    08 January 2004, pp 1-2

  • Summary

    Differential equations date back to the mid-seventeenth century, when calculus was discovered independently by Newton (c. 1665) and Leibniz (c. 1684). Modern mathematical physics essentially started with Newton's Principia (published in 1687) in which he not only developed the calculus but also presented his three fundamental laws of motion that have made the mathematical modelling of physical phenomena possible.

    Historically, advances in the theory of differential equations have come from the insights gained when trying to treat specific physical models. Despite this somewhat piecemeal development, the subject has become a well-defined and coherent area of mathematics. This book adopts a theoretical point of view, developing the theory to the point at which it can no longer be described as ‘basic differential equations’ and is about to become entangled with more advanced topics from the theory of dynamical systems. Of course, applications are used throughout to serve as motivation and illustration, but the emphasis is on a clean presentation of the mathematics.

    You may find that some of the problems covered in the first few chapters are already familiar. The methods of solving these problems are well established, and you may be well practised at applying them. However, we will take care here to show why these methods work; giving proper justification of the methods can take some time, but as mathematicians we should not be satisfied merely with a set of ‘recipes’.

Page 894 of 1304