Differential Equations and Their Applications

1. Front Matter

   Pages i-xiii

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2. First-order differential equations

   • Martin Braun

   Pages 1-124

3. Second-order linear differential equations

   • Martin Braun

   Pages 125-261

4. Systems of differential equations

   • Martin Braun

   Pages 262-369

5. Qualitative theory of differential equations

   • Martin Braun

   Pages 370-473

6. Separation of variables and Fourier series

   • Martin Braun

   Pages 474-511

7. Back Matter

   Pages 512-546

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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 Martin Braun Nooember, 1982 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.

• Fourier series
• applied mathematics
• bifurcation
• calculus
• differential equation
• ordinary differential equation

• Department of Mathematics, Queens College, City University of New York, Flushing, USA

  Martin Braun

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