# Perturbation Theory (UMAP)

### Author: Bertram Ross

This module gives a historical and self-contained introduction to the method of solving nonlinear differential equations by expressing their solutions as power series expansions in powers of a small parameter. The basic example is the perturbation problem. Students who read this unit learn an approach to the solution of nonlinear differential equations that is of great importance in mathematical physics and space engineering.** Table of Contents:1. INTRODUCTION2. ASYMPTOTIC SERIES3. INTRODUCTORY EXAMPLE AND COMMENTS ON ASYMPTOTICS4. NONLINEAR DIFFERENTIAL EQUATIONS AND THE PERTURBATION PROBLEM5. EXAMPLE OF A REGULAR PERTURBATION PROBLEM6. THE PROBLEM OF EXTENDING A REGION OF VALIDITY7. CONCLUDING REMARKS8. TEST PROBLEM AND COMMENTARY9. REFERENCES10. ANNOTATED BIBLIOGRAPHY11. ANSWERS AND SOLUTIONS TO EXERCISESAPPENDIX A APPENDIX B **

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