Cornell University has long offered a Calculus for Life Sciences course. In this case study, we report on how a team of pure mathematicians has modernized both the content and teaching methods of this course. The content went from a standard calculus course with few genuine applications in the life sciences to a course focusing on dynamical systems and bifurcation theory with deep connections between two disciplines. We describe how we have determined the new content, created the teaching materials using active learning and implemented the course in the classroom. We show how bifurcation theory can provide a fruitful framework to study interesting applications of mathematics in the life sciences. Finally, we report on the challenges we have faced and what we have done to mitigate them.