Linear partial differential equations and Fourier theory
Do you want a rigorous book that remembers where PDEs come from and what they look like? This highly visual introduction to linear PDEs and initial/boundary value problems connects the math to physical reality, all the time providing a rigorous mathematical foundation for all solution methods. Reade...
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| Format: | eBook |
| Language: | English |
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Cambridge
Cambridge University Press
2010
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| Collection: | Cambridge Books Online - Collection details see MPG.ReNa |
Table of Contents:
- Suggested 12-week syllabus
- Heat and diffusion
- Waves and signals
- Quantum mechanics
- Linear partial differential equations
- Classification of PDEs and problem types
- Some functional analysis
- Fourier sine series and cosine series
- Real Fourier series and complex Fourier series
- Multidimensional Fourier series
- Proofs of the Fourier convergence theorems
- Boundary value problems on a line segment
- Boundary value problems on a square
- Boundary value problems on a cube
- Boundary value problems in polar coordinates
- Eigenfunction methods on arbitrary domains
- Separation of variables
- Impulse-response methods
- Applications of complex analysis
- Fourier transforms
- Fourier transform solutions to PDEs
- Appendix A: Sets and functions
- Appendix B: Derivatives
- notation
- Appendix C: Complex numbers
- Appendix D: Coordinate systems and domains
- Appendix E: Vector calculus
- Appendix F: Differentiation of function series
- Appendix G: Differentiation of integrals
- Appendix H: Taylor polynomials