ROB 201 Calculus for the Modern Engineer

The second option is ROB 201: Calculus for the Modern Engineer, a streamlined 4-credit course completed in a single semester. Designed for students in robotics, mechanical engineering, electrical engineering, aerospace engineering, computer science, physics, and naval architecture, ROB 201 focuses on the most critical aspects of calculus while emphasizing practical applications. You’ll not only learn what calculus is but also why it matters and how to use it in solving real-world problems.

Students who take ROB 201 emerge better prepared for upper-level courses in their disciplines, with a stronger foundation in applied math. Taught by a professor with extensive experience in engineering and applied mathematics, this course ensures a meaningful, efficient, and practical calculus education.

The choice is clear: ROB 201 offers a modern, application-focused approach to calculus that’s perfect for today’s engineers and scientists.

Rather than following the traditional calculus sequence, I deconstructed the subject and rebuilt it from the ground up, rearranging topics to improve conceptual flow. Instead of starting with derivatives, I introduced students to numerical integration first, leveraging their intuitive understanding of summation (I thank Prof. Chad Jenkins for this idea). Antiderivative rules were separated into a distinct chapter, reducing the frustration of manual symbolic integration. This restructuring allowed calculus to unfold in a way that aligned with how students naturally think about and use mathematics in engineering applications.

To make the subject more engaging and relevant, I shifted the emphasis from manual computation to computational problem-solving. By integrating software tools, students could visualize mathematical concepts and experiment with them interactively. Jupyter notebooks played a crucial role in this transformation, allowing homework assignments to combine explanatory text with executable code. This approach harnessed students' intrinsic motivation—when their code produces meaningful results, they are more willing to engage with the underlying mathematical theory.

I also identified natural synergies across topics. For example, numerically evaluating an integral and solving an ODE share the same computational framework. By introducing numerical integration early, I prepared students for ODEs without them realizing it. Similarly, my second project, which uses constrained gradient descent to model a 3-meter platform diver’s motion, is actually an ODE problem in disguise. Students are solving for trajectories without explicitly confronting the underlying differential equations, making the eventual transition to ODEs much smoother. This deliberate layering of concepts ensured that students were ready for ODEs by the time they formally encountered them.

By prioritizing real-world applications, computational exploration, and a logical restructuring of topics, I created a course that not only condenses three traditional courses into one but also makes calculus more intuitive, engaging, and effective for engineering students.