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I am going to deliver some lectures on curvature, envelopes and asypmtotes of curves in $\mathbb{R^2}$. Please recommend me some good books with geometric intuition in this area.

Arctic Char
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debabrata chakraborty
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    You have a differential geometry tag here. Curvature is a differential geometry concept (although it can be defined in single-variable calculus for curves in $\Bbb R^2$); asymptotes are a high school precalculus subject. Envelopes naturally require multivariable calculus. Can you be more specific about your background and that of your audience? (That said, I know no source that covers all three of these.) – Ted Shifrin Mar 11 '21 at 05:45
  • It's hard to find useful books on applications of those things, because the calculus level stuff is not sufficient to have applications yet. – Simplyorange Mar 11 '21 at 05:56
  • The course is intended for under graduate students. – debabrata chakraborty Mar 11 '21 at 06:01
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    There is a lot of differences between a course geared towards first-year undergrads and final-year undergrads. – user10354138 Mar 11 '21 at 06:04
  • @user10354138: I completely agree. If I'm going to spend 20-30 minutes flipping through several dozen book possibilities in my (extensive) library, I'd like to feel as if my time was well spent. Sometimes the OP's needs don't matter much to me because I feel the contribution would be useful to archive for future purposes, but in this case I'm less inclined to do this for that reason. So my possibly doing this will mostly depend on how desperate the OP's needs seem to be, and a question that appears to have taken 20-30 seconds to type and post doesn't provide much incentive in this way. – Dave L. Renfro Mar 11 '21 at 09:42
  • I am sorry for the matter that I have failed to clarify my needs properly. Actually my audience are first year UG students with basic high school knowledge on calculus. The syllabus is intended towards solving problems concerning curvature, envelopes and asypmtotes of some particular type of curves which is not at all intuitive. But I want to provide them the bigger picture . – debabrata chakraborty Mar 11 '21 at 10:09
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    Two books that might have useful things for you: Lines and Curves by Gutenmacher/Vasilyev (2004) and (selected chapters of) Uncommon Mathematical Excursions. Polynomia and Related Realms by Kalman (2009). – Dave L. Renfro Mar 11 '21 at 12:12
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    Also, don't overlook the many classic calculus texts from the late 1800s which often had a lot of material on these topics, such as Rice/Johnson (1877), Todhunter (1871), Edwards (1892), Byerly (1879), Smith (1898), and many others. – Dave L. Renfro Mar 11 '21 at 12:12

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