Improved pedagogy for linear differential equations by reconsidering how we measure the size of solutions

DOI10.1080/0020739X.2017.1298856zbMath1397.97035MaRDI QIDQ4689424

Christopher C. Tisdell

Publication date: 16 October 2018

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

zbMATH Keywords

ordinary differential equationslinear differential equationsinitial value problemssecond-order differential equationsuniqueness of solutionshigher-order differential equations\textit{a priori} boundspedagogyManhattan distancetaxicab geometryuber metric

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Differential inequalities involving functions of a single real variable (34A40) Functional equations (educational aspects) (97I70)

Related Items (5)

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 ⋮ The taxicab locus of Apollonius: promoting exploratory routes to the punchline using rich undergraduate tasks ⋮ Existence and uniqueness of solutions to discrete,third-order three-point boundary value problems

Cites Work

• 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
• Why teach existence and uniqueness theorems in the first course in ordinary differential equations?
• Alternate solution to generalized Bernoulli equations via an integrating factor: an exact differential equation approach
• Generalization of the Bernoulli ODE
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