What is the meaning of transcendentals for calc books?

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SUMMARY

The discussion clarifies the distinction between 'early transcendentals' and 'late transcendentals' in calculus textbooks, specifically highlighting that early transcendentals introduce functions like e^x sooner than late transcendentals. Participants recommend using Lang or Spivak's calculus texts over Larson's, which is currently used in the forum member's course. The conversation also touches on the order of presenting calculus concepts, noting that older texts often introduce integrals before derivatives, while modern texts typically follow a limit-derivative-integral sequence.

PREREQUISITES
  • Understanding of calculus concepts such as limits, derivatives, and integrals.
  • Familiarity with different calculus textbooks, specifically Lang and Spivak.
  • Knowledge of the terminology used in calculus education, including 'transcendentals'.
  • Awareness of the historical context of calculus teaching methods.
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  • Research the differences between early and late transcendentals in calculus textbooks.
  • Explore Lang's and Spivak's calculus texts for supplemental learning.
  • Investigate the pedagogical reasoning behind the order of calculus concepts in textbooks.
  • Examine the impact of different calculus teaching methods on student understanding and performance.
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Students currently enrolled in calculus courses, educators seeking to enhance their teaching materials, and anyone interested in the pedagogical approaches to teaching calculus concepts.

mindheavy
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I see these calculus books, some titled 'early transcendentals' some 'late transcendentals'. What does this mean? What is the difference?
 
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It means that book is bad. Just get a copy of Lang or Spivak's calculus.

Seriously (or not): it means that functions such as e^x are introduced later or earlier in the book.
 
wow. I've seen this book by Lang recommended before. I'm in Calculus I currently, and my school is using Larson's Calculus for Calc I,II, and III, which I will be taking all of. Would you recommend either of Lang or Spivak as supplemental reading or that I just stick to the prescribed course book? I do enjoy having multiple sources of literature to gain more perspective on sometimes. Thoughts?
 
Confusing and plain bad terminology, indeed. There's only one type of transcendentals = numerical values in the images of transcendental functions, such as sin x.
 
Another thing that interests me is, most 'older' texts seem to present the integral before the derivative, while some books present the limit->derivative->integrals, is there any reasoning behind the order of presentation, or are they completely interchangeable and authors preference?
 
Last edited:
micromass said:
It means that book is bad. Just get a copy of Lang or Spivak's calculus.

Ahahaha and I was thinking of a clever way to answer this question! :D

Well said! :D

SolsticeFire
 

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