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"Initial value problems" is a specialty category for books that treat ordinary and partial differential equations posed with specified starting conditions — i.e., finding solutions that satisfy given values at an initial time or location. Titles in this category range from introductory textbooks that explain the formulation, existence and uniqueness theorems, and elementary analytic solution techniques, to advanced monographs on qualitative behavior, stability, and long-term dynamics of solutions. Many books emphasize numerical methods (Euler, Runge–Kutta, multistep, stiff solvers), implementation and error analysis, and practical modeling applications in physics, engineering, biology and finance; others cover related topics such as systems of equations, differential-algebraic equations, and initial-boundary value problems for PDEs. Intended readers include undergraduate and graduate students, applied mathematicians, and practitioners seeking rigorous theory or computational tools for solving time-evolution problems.

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