Rutherford Aris was at the forefront of the movement to utilize mathematical rigor to understand the foundations of chemical engineering practice. The impact of Aris, his Minnesota colleagues, and their students is felt throughout the chemical engineering curriculum. One place that impact has not been felt, however, is in the introductory course in chemical engineering. This course should develop a framework that enables students to move effortlessly from basic science and mathematics courses into the engineering science and technology courses that form the core of a professional education, as well as to provide them with a comprehensive overview of the scope and practice of the profession, but it rarely accomplishes this goal. The introductory course comes at a critical point in the academic life of the student, yet it is widely considered to be the weakest element in the curriculum. The introductory course can be made meaningful by utilizing and reinforcing the students' understanding of differential and integral calculus and elementary chemistry to explore pertinent chemical engineering design problems, including feedback level control, membrane separation and hemodialysis, optimal design of a process with chemical reaction and separation, and avoidance of washout in a bioreactor.