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