Branches of Mathematics
Differential Equations
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A differential equation is an equation that relates one or more unknown functions to their derivatives. In applications the functions typically represent physical quantities and the derivatives their rates of change, so the branch covers ordinary and partial differential equations and the exact, qualitative, and numerical methods used to understand their solutions.
Facts
Central QuestionGiven a rule that governs how a quantity changes rather than the quantity itself, can that quantity be recovered exactly, approximately, or merely shown to exist and be unique? 1 Key DebatePure mathematics and applied mathematics diverge in emphasis within the field: pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics is concerned with finding solutions, either directly or approximately. 1 Cross-Tradition Connections
Sources
1. Differential Equation (Wikipedia)
Wikimedia Foundationlead paragraphQuote, lead paragraph
Pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics is concerned with finding solutions, either directly or approximately.
Dynamical System (Wikipedia)
Wikimedia FoundationAssociated With: Dynamical Systems, lead paragraphQuote, Associated With: Dynamical Systems, lead paragraph
a dynamical system is the description of how a system evolves in time
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