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Calculus is one of mathematics’ most important branches, and it provides the mathematical theories needed to support a wide range of modern applications, from physics to computing to the proverbial “rocket science.” The field is derived from algebra and geometry, and it was developed at the end of the 17th century by Sir Isaac Newton and Gottfried Wilhelm Liebniz, both of whom discovered the fundamental theorem of calculus at about the same time. In brief, they discovered that differential and integral functions are inverse functions. (Don’t worry…learning what this means is what calculus is all about!) As a result of this discovery, calculus developed its own body of theory and became its own branch of mathematics, finally achieving coherence and rigor in the 19th century with the work of Augustin Louis Cauchy.
Today, calculus informs nearly everything that makes use of modern mathematics. When you use your calculator to find the square root of 3, your calculator gives you a number determined by calculus. When you look at the speedometer of your car, you’re looking at a calculus function in action, since it calculates speed based on velocity and acceleration. It is also heavily involved in a number of fields you might not expect, like biology, economics, and medicine. All of these make use of calculus’ broad power to crunch numbers and better understand topics in these fields. More specifically, you can expect to encounter calculus if you want to be an astronomer, biologist; computer programmer, aerospace, air quality, chemical, electronic, mechanical, or microwave engineer, or research physicist.
Students taking calculus today do a lot more than simply enter numbers into complex formulae for their own sake as so many earlier generations did. Today’s calculus teachers often use a problem-solving approach to demonstrate the utility of calculus in real-world applications. A recent textbook by Ellen Kamishke includes a number of activities specifically designed for that purpose; students explore topographical maps, watch a mug of hot coffee cool, and they calculate the volume of a lake to figure out how quickly they can eliminate a pollutant [1]. By showing the value of calculus in action, this new generation of teachers has made studying calculus more fun and relevant than ever.
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[1] Ellen Kamishke, A Watched Cup Never Cools: Lab Activities for Calculus and Precalculus (Key College Publishing, 1999).
