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- https://math.libretexts.org/Bookshelves/Analysis/Supplemental_Modules_(Analysis)/Ordinary_Differential_Equations/2%3A_First_Order_Differential_Equations/2.7%3A_Exact_Differential_EquationsThat is if a differential equation can be written in a specific form, then we can seek the original function f(x,y) (called a potential function). A differential equation with a potential function is...That is if a differential equation can be written in a specific form, then we can seek the original function f(x,y) (called a potential function). A differential equation with a potential function is called exact. If you have had vector calculus, this is the same as finding the potential functions and using the fundamental theorem of line integrals.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.11%3A_Exact_EquationsThis page discusses exact differential equations, their solutions, and the concept of potential functions in physics, emphasizing the total derivative's role. It illustrates the Poincaré Lemma, which ...This page discusses exact differential equations, their solutions, and the concept of potential functions in physics, emphasizing the total derivative's role. It illustrates the Poincaré Lemma, which connects local potential functions to exact equations, and addresses the use of integrating factors to solve non-exact equations.
- https://math.libretexts.org/Bookshelves/Analysis/Complex_Variables_with_Applications_(Orloff)/07%3A_Two_Dimensional_Hydrodynamics_and_Complex_Potentials/7.04%3A_Complex_PotentialsWe’ll start by seeing that every complex analytic function leads to an irrotational, incompressible flow. Then we’ll go backwards and see that all such flows lead to an analytic function. We will lear...We’ll start by seeing that every complex analytic function leads to an irrotational, incompressible flow. Then we’ll go backwards and see that all such flows lead to an analytic function. We will learn to call the analytic function the complex potential of the flow.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_IV%3A_Multivariable_Calculus/03%3A_Vector_Calculus/3.10%3A_Chapter_3_Review_ExercisesThis page contains mathematical exercises on vector fields, focusing on whether they are conservative, evaluating integrals, and applying theorems like Green's and the divergence theorem. It includes ...This page contains mathematical exercises on vector fields, focusing on whether they are conservative, evaluating integrals, and applying theorems like Green's and the divergence theorem. It includes questions on proofs and the properties of divergence and curl. Authored by Gilbert Strang and Edwin Herman, the content is available under a Creative Commons license.
