Partial Differential Equations
by Lawrence C. Evans · first published 2010
83% recommend17% neutral
Why HN recommends it
Comprehensive graduate-level coverage of partial differential equations, often named as the standard reference for people moving into PDE theory or functional analysis. Suits students and working mathematicians.
Summarised by Claude from recommending comments
"This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including: a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, and a significantly expanded bibliography."--Publisher's description.
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…this article mentions is a way to work around things, but nowhere near an undergraduate degree in mathematics. I'm astonished that the PDE section has such books, they look like the calculus aspect of partial differential equations. A more appropriate book would be L. C. Evans' Partial Differential Equations. Same with ODEs, no mention of Barreira's or Coddington & Levinson's books.
on “So you want to study mathematics” ↗…problems concerning aerospace applications and they mostly use a simplified form of the Navier-Stokes equations together with some elasticity assumptions. [0] Fluid Structure Interacion, Morand-Ohayon. [1] Partial Differential Equations, Evans.
on “Poisson's Equation” ↗Absolutely, if you're looking for advanced books on differential equations, I'd recommend "Partial Differential Equations" by Lawrence C. Evans for a comprehensive coverage of PDEs. For a more specialized focus on Ordinary Differential Equations, "Ordinary Differential Equations" by Vladimir I. Arnold is a fantastic choice.…
on “Ask HN: Can you suggest advanced books on all type differential equations?” ↗…Topology (James Munkres) - Calculus On Manifolds (Michael Spivak) - Principles of Mathematical Analysis (Walter Rudin) - Real and Complex Analysis (Walter Rudin) - Functional Analysis (Walter Rudin) - Partial Differential Equations (Lawrence Evans) - Analysis On Manifolds (James Munkres) - Abstract Algebra (David Dummit and Richard Foote) - Algebraic Topology (Allen Hatcher) - Introduction to Smooth Manifolds (John Lee) - Foundations…
on “Mathematician's anger over his unread 500-page proof” ↗re book recommendation: Lawrence Evans's book Partial Differential Equations. Functional analysis etc.
on “Approximating a solution that doesn't exist (2009)” ↗…explicitly ran into anything about discrete differential geometry, but that doesn't mean it wasn't there all along, lurking beneath (or perhaps above?) my level of understanding. some reading: Evans -- Partial Differential Equations, Wendland -- Scattered Data Approximation, Wahba -- Spline models for observational data .
on “Discrete Differential Geometry: An Applied Introduction [pdf]” ↗…Single variable calculus - Multivariable calculus, vector calculus - Linear algebra - Tensor calculus - Real analysis (see Walther Rudin) - Complex analysis - Ordinary differential equations - Partial differential equations - Abstract algebra - Differential geometry
on “Ask HN: Best books to self study undergrad level mathematics?” ↗