A toolbox of averaging theorems : ordinary and partial differential equations This primer on averaging theorems provides a practical toolbox for applied mathematicians physicists and engineers seeking to apply the well known mathematical theory to real world problems. With a focus on practical applications the book introduces new approaches to dissipative and Hamiltonian resonances and approximations on timescales longer than 1 ε. Accessible and clearly written the book includes numerous examples ranging from elementary to complex making it an excellent basic reference for anyone interested in the subject. The prerequisites have been kept to a minimum requiring only a working knowledge of calculus and ordinary and partial differential equations (ODEs and PDEs). In addition to serving as a valuable reference for practitioners the book could also be used as a reading guide for a mathematics seminar on averaging methods. Whether youre an engineer scientist or mathematician this book offers a wealth of practical tools and theoretical insights to help you tackle a range of mathematical problems.