Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
Catalogue Display
Catalogue Display
Differential Equations and Their Applications: An Introduction to Applied Mathematics /
.
Bookmark this Record
Catalogue Record 46507
.
.
Author info on Wikipedia
.
.
LibraryThing
.
.
Google Books
.
.
Amazon Books
.
Catalogue Information
Catalogue Record 46507
.
Reviews
Catalogue Record 46507
.
British Library
Resolver for RSN-46507
Google Scholar
Resolver for RSN-46507
WorldCat
Resolver for RSN-46507
Catalogo Nazionale SBN
Resolver for RSN-46507
GoogleBooks
Resolver for RSN-46507
ICTP Library
Resolver for RSN-46507
.
Share Link
Jump to link
Catalogue Information
Field name
Details
Dewey Class
515
Title
Differential Equations and Their Applications ([EBook] :) : An Introduction to Applied Mathematics / / by Martin Braun.
Author
Braun, Martin
Other name(s)
SpringerLink (Online service)
Edition statement
3rd Edition.
Publication
New York, NY : : Springer New York : : Imprint: Springer, , 1983.
Physical Details
XIII, 546 p. : online resource.
Series
Applied mathematical sciences
ISBN
9781468401646
Summary Note
There are three major changes in the Third Edition of Differential Equations and Their Applications. First, we have completely rewritten the section on singular solutions of differential equations. A new section, 2.8.1, dealing with Euler equations has been added, and this section is used to motivate a greatly expanded treatment of singular equations in sections 2.8.2 and 2.8.3. Our second major change is the addition of a new section, 4.9, dealing with bifurcation theory, a subject of much current interest. We felt it desirable to give the reader a brief but nontrivial introduction to this important topic. Our third major change is in Section 2.6, where we have switched to the metric system of units. This change was requested by many of our readers. In addition to the above changes, we have updated the material on population models, and have revised the exercises in this section. Minor editorial changes have also been made throughout the text. New York City November. 1982 Martin Braun Preface to the First Edition This textbook is a unique blend of the theory of differential equations and their exciting application to "real world" problems. First, and foremost, it is a rigorous study of ordinary differential equations and can be fully understood by anyone who has completed one year of calculus. However, in addition to the traditional applications, it also contains many exciting "real life" problems. These applications are completely self contained.:
Contents note
1 First-order differential equations -- 1.1 Introduction -- 1.2 First-order linear differential equations -- 1.3 The Van Meegeren art forgeries -- 1.4 Separable equations -- 1.5 Population models -- 1.6 The spread of technological innovations -- 1.7 An atomic waste disposal problem -- 1.8 The dynamics of tumor growth, mixing problems, and orthogonal trajectories -- 1.9 Exact equations, and why we cannot solve very many differential equations -- 1.10 The existence-uniqueness theorem; Picard iteration -- 1.11 Finding roots of equations by iteration -- 1.12 Difference equations, and how to compute the interest due on your student loans -- 1.13 Numerical approximations; Euler’s method -- 1.14 The three term Taylor series method -- 1.15 An improved Euler method -- 1.16 The Runge-Kutta method -- 1.17 What to do in practice -- 2 Second-order linear differential equations -- 2.1 Algebraic properties of solutions -- 2.2 Linear equations with constant coefficients -- 2.3 The nonhomogeneous equation -- 2.4 The method of variation of parameters -- 2.5 The method of judicious guessing -- 2.6 Mechanical vibrations -- 2.7 A model for the detection of diabetes -- 2.8 Series solutions -- 2.9 The method of Laplace transforms -- 2.10 Some useful properties of Laplace transforms -- 2.11 Differential equations with discontinuous right-hand sides -- 2.12 The Dirac delta function -- 2.13 The convolution integral -- 2.14 The method of elimination for systems -- 2.15 Higher-order equations -- 3 Systems of differential equations -- 3.1 Algebraic properties of solutions of linear systems -- 3.2 Vector spaces -- 3.3 Dimension of a vector space -- 3.4 Applications of linear algebra to differential equations -- 3.5 The theory of determinants -- 3.6 Solutions of simultaneous linear equations -- 3.7 Linear transformations -- 3.8 The eigenvalue-eigenvector method of finding solutions -- 3.9 Complex roots -- 3.10 Equal roots -- 3.11 Fundamental matrix solutions; eAt -- 3.12 The nonhomogeneous equation; variation of parameters -- 3.13 Solving systems by Laplace transforms -- 4 Qualitative theory of differential equations -- 4.1 Introduction -- 4.2 Stability of linear systems -- 4.3 Stability of equilibrium solutions -- 4.4 The phase-plane -- 4.5 Mathematical theories of war -- 4.6 Qualitative properties of orbits -- 4.7 Phase portraits of linear systems -- 4.8 Long time behavior of solutions; the Poincaré-Bendixson Theorem -- 4.9 Introduction to bifurcation theory -- 4.10 Predator-prey problems; or why the percentage of sharks caught in the Mediterranean Sea rose dramatically during World War I -- 4.11 The principle of competitive exclusion in population biology -- 4.12 The Threshold Theorem of epidemiology -- 4.13 A model for the spread of gonorrhea -- 5 Separation of variables and Fourier series -- 5.1 Two point boundary-value problems -- 5.2 Introduction to partial differential equations -- 5.3 The heat equation; separation of variables -- 5.4 Fourier series -- 5.5 Even and odd functions -- 5.6 Return to the heat equation -- 5.7 The wave equation -- 5.8 Laplace’s equation -- Appendix A -- Appendix B -- Appendix C -- Answers to odd-numbered exercises.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4684-0164-6
Links to Related Works
Subject References:
Analysis
.
Analysis (Mathematics)
.
Applications of Mathematics
.
Applied mathematics
.
Differential Equations
.
Engineering mathematics
.
Mathematical analysis
.
Mathematics
.
Ordinary differential equations
.
Authors:
Braun, Martin
.
Corporate Authors:
SpringerLink (Online service)
.
Series:
Applied mathematical sciences
.
Classification:
515
.
.
ISBD Display
Catalogue Record 46507
.
Tag Display
Catalogue Record 46507
.
Related Works
Catalogue Record 46507
.
Marc XML
Catalogue Record 46507
.
Add Title to Basket
Catalogue Record 46507
.
Catalogue Information 46507
Beginning of record
.
Catalogue Information 46507
Top of page
.
Download Title
Catalogue Record 46507
Export
This Record
As
Labelled Format
Bibliographic Format
ISBD Format
MARC Format
MARC Binary Format
MARCXML Format
User-Defined Format:
Title
Author
Series
Publication Details
Subject
To
File
Email
Reviews
This item has not been rated.
Add a Review and/or Rating
46507
1
46507
-
2
46507
-
3
46507
-
4
46507
-
5
46507
-
Quick Search
Search for