Differential Equations Books

ODEs, PDEs, and dynamical systems - from introductory courses to advanced analysis — Recommended Reading

Differential equations are the language of continuous change and are central to physics, engineering, biology, and economics. These books cover both ordinary and partial differential equations from introductory through research levels.

Introductory ODEs

Standard undergraduate textbooks on ordinary differential equations.

BookAuthorYearLevelDescription
Elementary Differential Equations and Boundary Value Problems
11th Edition, Wiley		William E. Boyce, Richard C. DiPrima, Douglas B. Meade2017IntermediateThe standard undergraduate ODE textbook. Clear exposition of first-order equations, linear equations, Laplace transforms, and systems.
Differential Equations and Their Applications
4th Edition, Springer		Martin Braun1993IntermediateApplication-focused ODE textbook with interesting models from biology, economics, and physics.
Ordinary Differential Equations
Dover		Morris Tenenbaum, Harry Pollard1985Intermediate-AdvancedClassic comprehensive ODE textbook, now affordable in Dover reprint.

Advanced ODEs and Dynamical Systems

Qualitative theory, stability, and dynamical systems.

BookAuthorYearLevelDescription
Differential Equations, Dynamical Systems, and an Introduction to Chaos
3rd Edition, Academic Press		Morris W. Hirsch, Stephen Smale, Robert L. Devaney2012AdvancedModern classic covering linear systems, stability, bifurcations, and chaos. Strong geometric viewpoint.
Nonlinear Dynamics and Chaos
2nd Edition, Westview Press		Steven H. Strogatz2014Intermediate-AdvancedBeloved introduction to nonlinear dynamics with remarkable pedagogy. Physical intuition meets mathematical rigor.
Ordinary Differential Equations
MIT Press		V.I. Arnold1973AdvancedGeometric, coordinate-free treatment of ODEs by the great Russian mathematician.

Partial Differential Equations

PDE textbooks from introductory through research level.

BookAuthorYearLevelDescription
Partial Differential Equations
2nd Edition, AMS		Lawrence C. Evans2010AdvancedThe standard graduate PDE textbook. Rigorous treatment of the major classes of PDEs, Sobolev spaces, and weak solutions.
Partial Differential Equations: An Introduction
2nd Edition, Wiley		Walter A. Strauss2007Intermediate-AdvancedClear introduction to PDEs suitable for advanced undergraduates and early graduate students.
An Introduction to Partial Differential Equations
2nd Edition, Cambridge University Press		Yehuda Pinchover, Jacob Rubinstein2005Intermediate-AdvancedAccessible but rigorous introduction.

Numerical Methods for Differential Equations

Computational approaches to solving differential equations.

BookAuthorYearLevelDescription
Numerical Solution of Ordinary Differential Equations
Wiley		Kendall Atkinson, Weimin Han, David Stewart2009AdvancedRigorous treatment of numerical ODE methods including Runge-Kutta and multistep methods.
Finite Difference Methods for Ordinary and Partial Differential Equations
SIAM		Randall J. LeVeque2007AdvancedModern treatment of finite difference methods with excellent error analysis.
Spectral Methods in MATLAB
SIAM		Lloyd N. Trefethen2000AdvancedCompact, readable introduction to spectral methods with MATLAB code.

Applications and Specialized Topics

Applied DE texts for physics, engineering, and other sciences.

BookAuthorYearLevelDescription
Elementary Differential Equations
10th Edition, Wiley		William E. Boyce2012IntermediateClassic applied text with physical applications.
Partial Differential Equations in Action
2nd Edition, Springer		Sandro Salsa2015AdvancedModern applied PDE text with emphasis on modeling.
Mathematical Methods for Physicists
7th Edition, Academic Press		George B. Arfken, Hans J. Weber, Frank E. Harris2012AdvancedComprehensive mathematical methods reference for physicists with extensive DE coverage.