Perturbation Theory (UMAP)

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. INTRODUCTION

2. ASYMPTOTIC SERIES

3. INTRODUCTORY EXAMPLE AND COMMENTS ON ASYMPTOTICS

4. NONLINEAR DIFFERENTIAL EQUATIONS AND THE PERTURBATION PROBLEM

5. EXAMPLE OF A REGULAR PERTURBATION PROBLEM

6. THE PROBLEM OF EXTENDING A REGION OF VALIDITY

7. CONCLUDING REMARKS

8. TEST PROBLEM AND COMMENTARY

9. REFERENCES

10. ANNOTATED BIBLIOGRAPHY

11. ANSWERS AND SOLUTIONS TO EXERCISES

APPENDIX A

APPENDIX B