Logan, J. David
Applied Partial Differential Equations
- 3rd ed.
- New York: Springer, 2015.
- 289p.
1: The Physical Origins of Partial Differential Equations.-
1.1 PDE Models.-
1.2 Conservation Laws.-
1.3 Diffusion.-
1.4 Diffusion and Randomness.-
1.5 Vibrations and Acoustics.-
1.6 Quantum Mechanics*.-
1.7 Heat Conduction in Higher Dimensions.-
1.8 Laplace's Equation.-
1.9 Classification of PDEs.-
2. Partial Differential Equations on Unbounded Domains.-
2.1 Cauchy Problem for the Heat Equation.-
2.2 Cauchy Problem for the Wave Equation.-
2.3 Well-Posed Problems.-
2.4 Semi-Infinite Domains.-
2.5 Sources and Duhamel's Principle.-
2.6 Laplace Transforms.-
2.7 Fourier Transforms.-
3. Orthogonal Expansions.-
3.1 The Fourier Method.-
3.2 Orthogonal Expansions.-
3.3 Classical Fourier Series.-
4. Partial Differential Equations on Bounded Domains.-
4.1 Overview of Separation of Variables.-
4.2 Sturm-Liouville Problems -
4.3 Generalization and Singular Problems.-
4.4 Laplace's Equation.-
4.5 Cooling of a Sphere.-
4.6 Diffusion inb a Disk.-
4.7 Sources on Bounded Domains.-
4.8 Poisson's Equation*.-
5. Applications in the Life Sciences.-
5.1 Age-Structured Models.-
5.2 Traveling Waves Fronts.-
5.3 Equilibria and Stability.
9783319124926
Differential equations, Partial
Mathematics
515.353 / LOG/A