The Physics One Mechanics in a community college syllabus usually allocates more time to cover the topics in kinematics, dynamics, energy, momentum, and rotation; with relatively less time for the topics of fluid mechanics and heat diffusion in the creation of a knowledge gap for those students deciding on mechanical and chemical engineering education. The learning of fluid mechanics and diffusion process in student projects in a community college eliminates such knowledge gap that could discourage students' aspirations for mechanical and chemical engineering education programs in the senior colleges. Pedagogy borrowed from psychology counseling practice in terms of the creation of new memories and positive experiences with uncertainty reduction through self-affirmation has been applied. The new memories related to the differential equation solvers in Matlab have been found to be useful for skill development in student projects. The topics from the non-Newtonian flow with the Navier-Stokes equations to the Brusselator reaction-diffusion process with Turing pattern can be used to develop the differential equation solving skill, depending on each student's individual aspiration. Filling the knowledge gap and encouraging aspiration based on the engineering equation solving skills, knowledge of job market, and senior college academic perspective of industrial applications revealed in their publications, were found to foster self-affirmation in the participants. Assessment data on our community college pre-engineering students showed that the programing skill in solving coupled differential equations in terms of stability and deterministic chaos investigations are within their academic capability after taking Physics One Mechanics. The "differential equation solving skill" pedagogy provides a perspective of applied physics in the establishment of a practical connection with positive experience to the third and fourth years in the mechanical and chemical engineering related programs of the senior colleges. The transference to regular physics course pedagogy is also discussed. [For the complete proceedings, see ED672800.]