 Ordinary
Differential Equations:Methods and Applications by WT Ang and YS Park |
Here is a concise elementary course in
ordinary differential equations. The
focus is on methods of solution and applications rather than
theoretical analyses.
Applications drawn mainly
from dynamics,
population biology and electric circuit theory are used to show how
ordinary differential equations appear in the formulation of problems
in science and engineering.
The calculus needed to comprehend this course is rather elementary,
involving differentiation, integration and power series
representation
of only real functions of one variable.
If you would like to create a hyperlink to this webpage or bookmark it, please use the following URL:
www.ntu.edu.sg/home/mwtang/odesite.htm
Tell a friend about this site!
Brief Description of the Course
TOC, Preface and Chapters ( Chapters 1, 4 and 5 are available for browsing)
The Complete Course
Errata updated 16 Jan 2009
About the Authors
Contact Us
| This
course is now available in paperback, details as follows: WT Ang and YS Park, Ordinary Differential Equations: Methods and Applications, Universal Publishers, Boca Raton, USA, 2008, 200 pages. Book cover. To find out more, visit Universal Publishers or online bookstores such as Amazon (USA, UK, Japan, Canada, France and Germany) and Barnes and Noble. Or do a Google book search. The e-book version of the course (in  ) is available
at a reasonably low price at
Powell's Books.Chapters for browsing! Chapters 1, 4 and 5 can be downloaded here. |
You may also interested in "A Beginner's Course in Boundary Element Methods" by WT Ang?
Brief
Description of the Course
Here is an introductory course in ordinary differential equations for junior undergraduate students in applied mathematics, science and engineering. The focus is on methods of solution and applications rather than theoretical analyses. Applications drawn mainly from dynamics, population biology and electric circuit theory are used to show how ordinary differential equations appear in the formulation of problems in science and engineering.
The calculus required to comprehend this course is rather elementary, involving differentiation, integration and power series representation of only real functions of one variable. A basic knowledge of complex numbers and their arithmetic is also assumed, so that elementary complex functions which can be used for working out easily the general solutions of certain ordinary differential equations can be introduced. The pre-requisites just mentioned aside, the course is mainly self-contained.
Exercises are set not only to test the understanding of students but sometimes also to impart additional insights into the materials studied. Suggested solutions to all the exercises are given at the end of the chapters. To promote the use of this course for self-study, the solutions provided are by and large complete with details.
WT Ang and YS Park
10 July 2008
Table of Contents, Preface and ChaptersHere is an introductory course in ordinary differential equations for junior undergraduate students in applied mathematics, science and engineering. The focus is on methods of solution and applications rather than theoretical analyses. Applications drawn mainly from dynamics, population biology and electric circuit theory are used to show how ordinary differential equations appear in the formulation of problems in science and engineering.
The calculus required to comprehend this course is rather elementary, involving differentiation, integration and power series representation of only real functions of one variable. A basic knowledge of complex numbers and their arithmetic is also assumed, so that elementary complex functions which can be used for working out easily the general solutions of certain ordinary differential equations can be introduced. The pre-requisites just mentioned aside, the course is mainly self-contained.
Exercises are set not only to test the understanding of students but sometimes also to impart additional insights into the materials studied. Suggested solutions to all the exercises are given at the end of the chapters. To promote the use of this course for self-study, the solutions provided are by and large complete with details.
WT Ang and YS Park
10 July 2008
This
course comprises six chapters. The chapters are as described
below.
Chapters 1, 4 and 5 are available in for browsing.
Table
of Contents (Read
to find out what is inside the course)
Preface (Read to have a general overview of the
course)
Chapter 1: Basic Concepts
Chapter 1 gives the basic concepts of ordinary differential equations, explaining what an ordinary differential equation is and what is involved in solving such an equation. It also illustrates how ordinary differential equations can be derived from physical laws or basic principles for two specific examples of problems.
Download Chapter
1 in PDF.
Chapter 2: First Order Ordinary Differential Equations
In Chapter 2, methods of solution are given for some first order ordinary differential equations. The equations studied include those which can be written in separable form, those which are linear and the nonlinear Bernoulli differential equation. Mathematical models which describe population growth are given as examples of applications involving first order ordinary differential equations.
Chapter 3: Second Order Linear Ordinary Differential Equations
In Chapter 3, the mathematical theory for constructing general solutions of second order linear ordinary differential equations is studied. It is applied to obtain general solutions of second order linear ordinary differential equations with constant coefficients and the Euler-Cauchy equations. Also discussed is the extension of the theory to higher order linear ordinary differential equations.
Chapter 4: Circuits and Springs
Chapter 4 shows how linear ordinary differential equations with constant coefficients arise in the formulation of problems involving electric circuits and spring-mass systems. Specific examples of problems are solved.
Download Chapter
4 in PDF.
Chapter 5: Series Solutions
Chapter 5 introduces the power series method and the Frobenius method for deriving series solutions of rather general homogeneous second order linear ordinary differential equations. The methods studied can be applied to solve some well known ordinary differential equations in mathematical physics, such as the Legendre's equation and the Bessel's equation, giving rise to particular special functions, but those equations and the associated special functions are not examined in this course.
Download Chapter
5 in PDF.
Chapter 6: Numerical methods
Chapter 6 describes some simple numerical methods for solving first and second order ordinary differential equations. For a particular example of applications, the second order nonlinear ordinary differential equation which governs the motion of a swinging pendulum is solved numerically.
The Complete Course
The complete course is published by Universal Publishers (in USA). It is available in paperback [further details at Universal Publishers or at Amazon (USA, UK, Japan, Canada, France and Germany) or at Barnes and Noble].
The e-book version of the course (in ) is
available
at a reasonably low price at
Powell's Books.
Errata
We are posting here an errata (last updated on 16 January 2009) for the book "Ordinary Differential Equations: Methods and Applications" published by Universal Publishers. It will be updated if and when we find any error or inaccurate statement in the book. If you discover any mistake (even a very small one) or if you wish to be informed of any update in the errata (assuming that you possess a copy of the book), please let us know. You may write us using this e-mail form or at the following e-mail address:
About the Authors
WT Ang and YS Park graduated from the University of Adelaide, Australia, with PhD and Master of Mathematical Sciences degrees respectively. Both authors have considerable experience in tertiary teaching of applied and engineering mathematics.
Contact Us
Comments, suggestions and queries are always welcome. Please let us know if you would like to be kept informed on updates on this course, such as posting of errata sheet (if any). You may write us using this e-mail form or at the following e-mail address:
Chapters 1, 4 and 5 are available in
for browsing.Table
of Contents (Read
to find out what is inside the course)Preface (Read to have a general overview of the
course)Chapter 1: Basic Concepts
Chapter 1 gives the basic concepts of ordinary differential equations, explaining what an ordinary differential equation is and what is involved in solving such an equation. It also illustrates how ordinary differential equations can be derived from physical laws or basic principles for two specific examples of problems.
Download Chapter
1 in PDF.Chapter 2: First Order Ordinary Differential Equations
In Chapter 2, methods of solution are given for some first order ordinary differential equations. The equations studied include those which can be written in separable form, those which are linear and the nonlinear Bernoulli differential equation. Mathematical models which describe population growth are given as examples of applications involving first order ordinary differential equations.
Chapter 3: Second Order Linear Ordinary Differential Equations
In Chapter 3, the mathematical theory for constructing general solutions of second order linear ordinary differential equations is studied. It is applied to obtain general solutions of second order linear ordinary differential equations with constant coefficients and the Euler-Cauchy equations. Also discussed is the extension of the theory to higher order linear ordinary differential equations.
Chapter 4: Circuits and Springs
Chapter 4 shows how linear ordinary differential equations with constant coefficients arise in the formulation of problems involving electric circuits and spring-mass systems. Specific examples of problems are solved.
Download Chapter
4 in PDF.Chapter 5: Series Solutions
Chapter 5 introduces the power series method and the Frobenius method for deriving series solutions of rather general homogeneous second order linear ordinary differential equations. The methods studied can be applied to solve some well known ordinary differential equations in mathematical physics, such as the Legendre's equation and the Bessel's equation, giving rise to particular special functions, but those equations and the associated special functions are not examined in this course.
Download Chapter
5 in PDF.Chapter 6: Numerical methods
Chapter 6 describes some simple numerical methods for solving first and second order ordinary differential equations. For a particular example of applications, the second order nonlinear ordinary differential equation which governs the motion of a swinging pendulum is solved numerically.
The Complete Course
The complete course is published by Universal Publishers (in USA). It is available in paperback [further details at Universal Publishers or at Amazon (USA, UK, Japan, Canada, France and Germany) or at Barnes and Noble].
The e-book version of the course (in
) is
available
at a reasonably low price at
Powell's Books.Errata
We are posting here an errata (last updated on 16 January 2009) for the book "Ordinary Differential Equations: Methods and Applications" published by Universal Publishers. It will be updated if and when we find any error or inaccurate statement in the book. If you discover any mistake (even a very small one) or if you wish to be informed of any update in the errata (assuming that you possess a copy of the book), please let us know. You may write us using this e-mail form or at the following e-mail address:
About the Authors
WT Ang and YS Park graduated from the University of Adelaide, Australia, with PhD and Master of Mathematical Sciences degrees respectively. Both authors have considerable experience in tertiary teaching of applied and engineering mathematics.
Contact Us
Comments, suggestions and queries are always welcome. Please let us know if you would like to be kept informed on updates on this course, such as posting of errata sheet (if any). You may write us using this e-mail form or at the following e-mail address: