Ordinary differential equations with applications Besides giving rigorous proofs for basic theorems of ODE it also provides numerous examples arising from physical and biological science for readers to understand the theorems and their applications Exercises are given at the end of each chapter for the reader to practice; some are challenging This is also a good textbook for students aiming for applied mathematics with applications in Engineering Some knowledge in Nonlinear Analysis in which we think is necessary for the students is presented in the book For oscillatory solutions which occur in nature we introduce the Poincare Bendixson Theorem and its applications Monotone Dynamical Systems especially three dimensional competitive systems and Hopf bifurcations in n dimensional space This text also provides a friendly introduction to Hamiltonian systems written by co author Kuo Chang Chen an expert in celestial mechanics