Rethinking pedagogy for second-order differential equations: a simplified approach to understanding well-posed problems

DOI10.1080/0020739X.2017.1285062zbMath1397.97034OpenAlexW2587081548MaRDI QIDQ4689415

Christopher C. Tisdell

Publication date: 16 October 2018

Published in: International Journal of Mathematical Education in Science and Technology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/0020739x.2017.1285062

zbMATH Keywords

existence of solutionsordinary differential equationinitial value problemuniqueness of solutionswell-posed problemsuccessive approximationssecond-order problemhigher-order problem

Mathematics Subject Classification ID

Functional equations (educational aspects) (97I70)

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Establishing existence and uniqueness of solutions to the boundary value problem involving a generalized Emden equation, embracing Thomas-Fermi-like theories ⋮ Critical perspectives of pedagogical approaches to reversing the order of integration in double integrals ⋮ Sharper existence and uniqueness results for solutions to fourth-order boundary value problems and elastic beam analysis ⋮ The roles that shooting methods can play in the theory of discrete boundary value problems ⋮ Existence and uniqueness of solutions to third-order boundary value problems: analysis in closed and bounded sets ⋮ Pedogogical perspectives on the method of Wilmer III and Costa for solving second-order differential equations ⋮ On Picard's iteration method to solve differential equations and a pedagogical space for otherness ⋮ An accessible, justifiable and transferable pedagogical approach for the differential equations of simple harmonic motion ⋮ Existence and uniqueness of solutions to discrete,third-order three-point boundary value problems

Cites Work

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• An introduction to ordinary differential equations
• Alternative approach to second-order linear differential equations with constant coefficients
• A straightforward method to solve the linear differential equations with constant coefficients of ordern
• Alternate solution to generalized Bernoulli equations via an integrating factor: an exact differential equation approach
• Generalization of the Bernoulli ODE

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