Differential Equations

1. Front Matter

   Pages i-xi

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2. Introduction

   • Viorel Barbu

   Pages 1-28

3. Existence and Uniqueness for the Cauchy Problem

   • Viorel Barbu

   Pages 29-77

4. Systems of Linear Differential Equations

   • Viorel Barbu

   Pages 79-121

5. Stability Theory

   • Viorel Barbu

   Pages 123-159

6. Prime Integrals and First-Order Partial Differential Equations

   • Viorel Barbu

   Pages 161-199

7. Back Matter

   Pages 201-224

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This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner.


Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations.


Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.

• Cauchy problem
• Lyapunov stability
• variational inequality
• variational existence
• variational uniqueness
• optimal control
• Hamilton Jacobi equation
• prime integral
• harmonic oscillator
• ordinary differential equations
• partial differential equations

“This book provides a thorough and mathematically rigorous presentation of the basic theory of differential equations. … The author has a style and approach that makes the book quite readable. There is, also, given explanatory and motivational material, associated with carefully chosen examples and exercises (with hints). This is an excellent book … by means of which an undergraduate student can be introduced to ordinary and partial differential equations.” (George Karakostas, zbMATH 1370.34001, 2017)

• Department of Mathematics, Alexandru Ioan Cuza University , Iasi, Romania

  Viorel Barbu

Viorel Barbu is Professor of Mathematics at the Alexandru Ioan Cuza University of Iasi, Romania, and member of the Romanian Academy and the European Academy of Sciences. He is the author of several monographs and textbooks on partial differential equations, optimal control, nonlinear analysis, and optimization theory.

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