In the ever-evolving landscape of engineering education, calculus stands as a foundational pillar, yet its teaching methods have remained largely unchanged for decades. This textbook is born out of a deep-seated need for reform. Traditional calculus courses struggle to incorporate relevant, real-world examples. The disconnect between mathematical theory and its real-world uses hinders the learning process and fails to fully engage students in the practical applications of calculus. A second core issue lies not in the examples used but in the selection of material and the overemphasis on lengthy, manual calculations that lack meaningful context. This book represents a radical departure from conventional approaches, inspired by Prof. Grizzle’s experience developing and teaching the first-semester course ROB 101 Computational Linear Algebra. Its goal is to breathe life into mathematics through programming and realistic examples. It begins by placing integration at the beginning of the learning process, starting with sums and progressing to integration, which is not only more intuitive but also lends itself well to programming applications, such as calculating the change in position of mobile robots from velocity curves. Following integration, the book delves into differentiation (both single-variable and multivariable) and its myriad applications. Traditional methods of computing integrals, such as antiderivatives and substitution methods, are then introduced and framed within the context of both manual calculations and modern symbolic tools. The journey continues through improper integrals, ordinary differential equations (ODEs), Laplace Transforms, and Feedback Control, encompassing a breadth of topics rarely seen in a single calculus course.  

Jessy W. Grizzle is the Elmer Gilbert Distinguished University Professor and Jerry and Carol Levin Professor of Engineering at the University of Michigan, where he is a Professor of Robotics. A Fellow of IEEE and IFAC, he holds seventeen US patents. His pioneering contributions have earned him many of control theory’s top honors, including the IEEE Vehicular Technology Society Paper of the Year Award (1993), the George S. Axelby Award (2002), the Control Systems Technology Award (2003), the Bode Prize (2012), the IEEE Transactions on Control Systems Technology Outstanding Paper Award (2014), the IEEE Transactions on Automation Science Best New Application Paper Award (2019), and the ASME Journal of Dynamic Systems, Measurement, and Control’s Kalman Award for Outstanding Paper (2023).

Grizzle is internationally recognized for his groundbreaking research on bipedal locomotion, which has been featured in plenary lectures and profiled by CNN, ESPN, Discovery Channel, The Economist, Wired, Discover, Scientific American, and Popular Mechanics. As founding director of the University of Michigan Robotics Institute, he co-led its transformation into the first standalone Robotics Department at an R1 public university. His current passion is mathematics education for today’s engineering students.