A Textbook on Ordinary Differential Equations

Prof. Shair Ahmad is a professor of Mathematics at the University of Texas, San Antonio. Prof. Antonio Ambrosetti is full professor of Mathematical Analysis at SISSA, Trieste, Italy.

1 First order linear differential equations.- 2 Theory of first order differential equations.- 3 First order nonlinear differential equations.- 4 Existence and uniqueness for systems and higher order equations.- 5 Second order equations.- 6 Higher order linear equations.- 7 Systems of first order equations.- 8 Qualitative analysis of 2x2 systems and nonlinear second order equations.- 9 Sturm Liouville eigenvalue theory.- 10 Solutions by infinite series and Bessel functions.- 11 Laplace transform.- 12 Stability theory.- 13 Boundary value problems.- 14 Appendix A. Numerical methods.- 15 Answers to selected exercises.

"This is the second edition of an undergraduate introduction to ordinary differential equations suitable for mathematicians and engineers. ... The style is clean and concise with many examples and exercises. Basic results are proven, more involved results are only stated. The new edition features some new exercises and better explanations at various points. So if you are looking for an application oriented introduction which is still concise and rigorous, this book might be just right for you." (G. Teschl, Monatshefte für Mathematik, 2016)

“This is the second edition of an undergraduate introduction to ordinary differential equations suitable for mathematicians and engineers. … The style is clean and concise with many examples and exercises. Basic results are proven, more involved results are only stated. The new edition features some new exercises and better explanations at various points. So if you are looking for an application oriented introduction which is still concise and rigorous, this book might be just right for you.” (G. Teschl, Monatshefte für Mathematik, 2016)