2025 ASEE Annual Conference & Exposition

Work in Progress: Many engineering students enter college excited about mathematics, only to have their enthusiasm diminished by a rigid, outdated calculus curriculum. The Robotics Department at Michigan has piloted a new course, Calculus for the Modern Engineer, designed to restore the joy of learning advanced mathematics. This 4-credit course integrates Differential and Integral Calculus, vector derivatives, and Ordinary Differential Equations (ODEs) into a one-semester curriculum tailored specifically for robotics students. The pilot cohort included 24 students: one first-semester freshman with no college calculus credit, five students with credit for Calculus I, and 18 students who had completed both Calculus I and II. The recommended prerequisite is ROB 101: Computational Linear Algebra, which ensures familiarity with Julia programming.

Departing from the traditional calculus sequence codified in the 1950s, the course begins with definite integration---a concept students readily understand through sums---before progressing through limits, differentiation, antiderivatives, and ODEs. By leveraging modern computational tools such as Julia, Large Language Models (LLMs), and Wolfram Alpha Pro, the course shifts the focus from tedious hand calculations to conceptual mastery and real-world application. Three engineering projects reinforce this approach: (1) numerically integrating drone IMU data to estimate velocity and position while correcting acceleration bias, (2) optimizing motion through gradient descent and equality constraints in applications such as basketball trajectories and gymnast posture, and (3) modeling and designing controllers for a planar BallBot using state-variable models and feedback control.

Student evaluations indicate strong engagement: 85% of students reported an increased interest in calculus, and the course received an overall excellence rating of 4.8/5. Written feedback highlights the effectiveness of integrating programming and real-world applications, making calculus a more intuitive and empowering tool for engineering problem-solving. While direct comparisons with traditional calculus courses are not yet available, ROB 201 is designed to condense three semesters of calculus into a single semester, emphasizing practical applications that prepare students for elective coursework in Numerical Methods, Optimization, and Feedback Control.