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Applied Partial Differential Equations [Logan] - mklabgr - 09-03-2026
Applied Partial Differential Equations
Author: J. David Logan
Publication date: 5 December 2014 (eBook; © 2015 edition)
Publisher: Springer Cham
Applied Partial Differential Equations is a concise undergraduate introduction to partial differential equations (PDEs) aimed primarily at students of mathematics, engineering, and the physical sciences. Rather than emphasizing abstract existence and uniqueness theory, Logan develops PDEs from the physical and biological models that produce them, explaining how equations such as the heat, wave, and diffusion equations arise and how their solutions should be interpreted. The book covers PDEs on both bounded and unbounded domains and introduces core techniques including separation of variables, Fourier series and orthogonal expansions, Laplace transforms, Sturm–Liouville problems, and related boundary-value methods.
A distinctive feature is the strong connection between mathematics and applications. After introducing the physical origins of PDEs, the text develops solution methods for problems on infinite domains and bounded regions, followed by orthogonal expansions and applications to the life sciences. Topics include diffusion and transport processes, population models, and equations used in mathematical biology. The presentation deliberately emphasizes motivation, computational techniques, interpretation, and worked examples rather than a highly formal theoretical treatment.
The third edition significantly expands the numerical side of the subject. It introduces computational approaches including finite-difference methods, the Crank–Nicolson scheme, stability analysis, iterative techniques such as Gauss–Seidel, and the finite-element method, with numerical calculations implemented in MATLAB. Additional worked examples and more routine exercises make it particularly suitable for a one-semester introductory PDE course. The book therefore provides a useful bridge between classical analytic methods and the numerical techniques required for PDEs that cannot be solved explicitly.
Key takeaways
- Provides a compact introduction to the principal PDEs of mathematical physics and the methods used to solve them.
- Strong emphasis on applications and mathematical modelling, including problems from biology.
- Covers essential tools such as Fourier methods, Sturm–Liouville theory, separation of variables and transforms.
- The third edition gives increased attention to numerical PDE methods and MATLAB computation, including finite elements.
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