As an undergraduate, I took five semesters of calculus. The last semester on partial differential equations supposedly gave me a head start for grad school in my chosen field of chemistry.
But, unlike my friends in engineering programs, I had little need for calculus except in a few physical-chemistry labs and classes. I can't remember using calculus in grad school, and since then I can't remember using it more than a few times to solve electronics problems. Instead of having to take all those calculus classes, two semesters would have provided sufficient knowledge. Classes in scientific data analysis, instrumentation techniques, and statistics would have made more sense, but at the time either the courses didn't exist, or no one suggested them.
I looked at the math requirements for an engineering school, and found the following requirements for a BS degree:
- Calculus I and II
- Ordinary Differential Equations
- Discrete Mathematics
That seems like a better series of course requirements (one semester each) for engineers than the "exposure" I got in college. My biggest impediment to learning calculus centered on the lack of a relation between it and practical problems. After the math professors got past a few simplistic examples, it was all x-this, y-that, and everything between plus and minus infinity. Practical examples of why nascent scientists and engineers might need a triple integral might have helped us understand calculus better. Or perhaps I'm just more of a practical than theoretical mind.
We now have many computer programs that can help analyze data, and that provide sophisticated mathematical tools. And using such tools takes the drudgery out of tedious mathematical analyses and equation evaluations. So, does it still make sense to load engineering and science students with more than an introduction to calculus? If so, what level of calculus should they reach? (Of course, math majors and students interested in calculus could still take more courses.)
During college, I had a dull-as-dirt calculus text I was glad to throw out. Since then, I discovered The Calculus Tutoring Book by Carol and Robert Ash. The IEEE Press published this book in the mid 1980s, and although now out of print, AbeBooks.com lists many copies at reasonable prices. I recommend this book highly to students who struggle with calculus. One summer I went through about half the book on my own, and worked many of the problems. Finally, I found calculus interesting and clear. It only took an extra 20 years to "get it."
What level of calculus should engineering students reach? Discuss in the comments section below.