Perturbation methods are old and powerful. Solutions are provided as formulas rather than numbers or pictures, so the skill of the person (or machine!) reading the formula is essential. This unique book presents several classical methods to solve perturbation problems using backward error analysis. This lessens the likelihood of blunders because the method for testing the validity of the answers is uniform. It also demands that the modeler consider the effects of other changes to the data or model equations. For this the concept of a condition number from numerical analysis is used. Perturbation Methods Using Backward Error includes includes a discussion of the impact on science of the idea of perturbation, includes a chapter on the relatively novel renormalization group method, uses computer algebra (via Maple) to ease the computing of symbolic answers, and provides solutions to all exercises.