Work in Progress: Effects of Computational Aspects of Differential Equations (DE) Course Delivery on Students’ Computing Experience in Engineering Instruction

Recent literature and Industry 4.0 discussions have highlighted the need for engineering graduates to gain computational facility in all stages of ill-posed, industry-relevant problem solving, from problem framing to understanding of and confidence in algorithm output. Chemical and mechanical engineering students grapple with both ordinary and partial differential equations (DE) in their engineering coursework using computational methods that they may not have been prepared for in their basic DE courses in academically siloed mathematics departments. Research question: How do mathematical-computational aspects of delivery in DE courses effect engineering students' recognition and use of relevant differential equations methods and knowledge in computational engineering course settings? Mathematical-computational aspects of course delivery include instructor choices of analytic and numerical methods, instructor incorporation of programming or software packages in lectures and/or assignments, and instructor use of disciplinary examples. Data are gathered from western U.S. universities housing ABET-accredited engineering programs, and include examination of course artifacts from both DE and engineering courses, lecture observations, and interviews with mathematics faculty, engineering faculty, and engineering students. Initial summary of a subset of interviews revealed engineering students may not recognize when numerical/computational approaches to DE problems are warranted. Ongoing findings are anticipated to inform both mathematics and engineering faculty as (1) many math programs are experiencing the need to evolve DE course delivery into an increasingly computational endeavor and (2) many engineering programs may find support for students' increased computational problem-solving through collaboration with math educators on DE course design.