![]() These two courses, from the OCW Scholar series, provide the complete teaching materials comprising MIT’s undergraduate calculus requirement. You’ll find complete courses, online textbooks, videos, many sample problems with solutions, and more. OCW has a wealth of inspiring calculus teaching materials, all free and licensed for you to re-use and remix in your classroom. ![]() (Again, see Steven Strogatz’s engaging explanation.)Īs Professor Bush says, calculus “is a language that’s valuable in virtually all disciplines, from physics to biology, from finance to engineering.” Motivate deeper student engagement by demonstrating how beautiful it can be to describe their ever-changing world with the poetics of mathematics. Archimedes’ Principle is a great way to experience the concept and importance of volume, and also the way integrals work.(See this explanation of route-finding by mathematician and writer Steven Strogatz.) But calculus can show that it’s fundamentally an optimization problem of light following the fastest route just like how a smartphone GPS map calculates your fastest route home through tangled streets and busy traffic. Introductory physics students will have learned Snell’s law as an equation about the angles of light paths through different media.Sharks hunt with calculus! They intuitively “follow the gradient” of scent, or the direction that gives the highest rate of increase, to take them toward their prey.We hope you can motivate students by demonstrating how to revel in the beauty of the language, and all the things it can do, before diving into the nitty-gritty grammar of deltas and epsilons. Professor Bush suggests: MIT’s John Bush, professor of applied mathematics (and a fabulous photographer of fluid phenomena), offers some great calculus teaching tips in the above video. It’s a beautiful and powerful expression of this universal phenomenon, and a great way to tackle a wide range of real-world problems. More than a math subject, calculus is fundamentally the language of change. As teachers know, it’s a rich opportunity for student growth and insight, and also scary as they’re getting started. ![]() The same could be said of the millions of students who take calculus classes every year. Yet change can also be an opportunity for growth, for progress, for new insights. And change can be scary, especially when you don’t understand what’s happening. So many ways to look at change, to talk about change. Move…accelerate…reach the peak…bottom out…transform… ![]()
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