Linear Partial Differential E Book Free Download

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Linear Partial Differential
Equations and Fourier Theory
Marcus Pivato


Table of Contents 

I  Motivating examples and major applications

1 Heat and diffusion

2 Waves and signals

3 Quantum mechanics

II  General theory

4 Linear partial differential equations

5 Classification of PDEs and problem types
   
III  Fourier series on bounded domains

6 Some functional analysis

7 Fourier sine series and cosine series

8 Real Fourier series and complex Fourier series

9 Multidimensional Fourier series

10 Proofs of the Fourier convergence theorems

IV  BVP solutions via eigenfunction expansions

11 Boundary value problems on a line segment

12 Boundary value problems on a square

13 Boundary value problems on a cube

14 Boundary value problems in polar coordinates

15 Eigenfunction methods on arbitrary domains

V  Miscellaneous solution methods

16 Separation of variables

17 Impulse-response methods

18 Applications of complex analysis

VI  Fourier transforms on unbounded domains

19 Fourier transforms

20 Fourier transform solutions to PDEs



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