The Generalized Euler-Lagrange Equation
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Abstract: The generalized Euler-Lagrange equation is derived in the context of classical mechanics and classical field theory through the principle of stationary action. The physical relevance of the formula is briefly discussed.
Sequence Operators: From Recurrence Relations to Differential Equations
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Abstract: Sequence operators on series expansions are inverted to obtain a differential equation from a recurrence relation. Common sequences are considered and their associated differential equations are calculated.
Sequence Operators for the Series Expansion of Differential Equations
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Abstract: We present an operator formalism for the solution of ordinary differential equations using series expansion. These operators make it possible to easily map a differential equation into an algebraic equation.
Dual Algebras and Automatic Differentiation
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Abstract: This is a short introduction to dual algebras and their computational application for automatic differentiation.
Time Evolution: From Classical to Quantum
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Abstract: In this article I will introduce the quantum time evolution operator drawing parallels with classical mechanics and continuous transformations.