Fourier Analysis and Boundary Value ProblemsFourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics. A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.
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Contents
| 1 | |
| 23 | |
| 84 | |
CHAPTER 4 GENERALIZED FOURIER SERIES | 133 |
CHAPTER 5 THE WAVE EQUATION | 165 |
CHAPTER 6 ORTHOGONAL SYSTEMS | 207 |
CHAPTER 7 FOURIER TRANSFORMS | 237 |
CHAPTER 8 LAPLACE TRANSFORMS | 266 |
CHAPTER 10 BOUNDARY VALUE PROBLEMS WITH CIRCULAR SYMMETRY | 351 |
CHAPTER 11 BOUNDARY VALUE PROBLEMS WITH SPHERICAL SYMMETRY | 410 |
CHAPTER 12 DISTRIBUTIONS AND GREENS FUNCTIONS | 451 |
APPENDIX A UNIFORM CONVERGENCE | 506 |
APPENDIX B IMPROPER INTEGRALS | 518 |
APPENDIX C TABLES OF FOURIER AND LAPLACE TRANSFORMS | 535 |
APPENDIX D HISTORICAL BIBLIOGRAPHY | 539 |
Index | 543 |