Dear Readers,
Once upon a time during my doctoral studies, I met my match: the product integral. My syllabus consisted of dense chapters from the definitive book Product Integration: Its History and Applications, written by none other than Antonín Slavík—who also served as my examiner and thesis consultant.
To say the concept of the product integral was challenging would be an understatement—it took me six months of studying just to wrap my head around it. As my study notes grew increasingly massive and detailed, my esteemed consultant jokingly remarked that I might as well write a sequel called Product Integral for Dummies.
Challenge accepted! This project is my attempt to make this concept accessible to fellow students and enthusiasts.
While the core mathematical text belongs to the author of the book, I have expanded upon it with fresh sections, practical commentaries, examples, and illustrations to guide you through the maze.
A massive thank you goes to Antonín Slavík for his expert consultation, his humor, and the creative spark that made this website possible. Happy learning!
Explore the intuitive roots of multiplicative calculus through Euler's method and the fish population example.
In standard calculus, constants disappear when you add them. In multiplicative calculus, they disappear when you multiply them. Want to see why?
What happens when calculus stops adding and starts multiplying? Welcome to the counterintuitive world of the product integral.
How exactly do you calculate the product integral? What about the constant and scalar cases?
How do you model biological populations that transition into each other when the rates change abruptly? Witness the exact breaking point of the classical integral—and how the product integral comes to the rescue.
Next chapters: Formal Definitions, Rules of Multiplicative Calculus, and Historical Context are being prepared.