What is the meaning of transcendentals for calc books?

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In summary, there are two types of calculus books: early transcendentals and late transcendentals. The difference between the two is when they introduce functions such as e^x. The books by Lang and Spivak are recommended over other calculus books. The order of presentation in calculus books can vary, with some presenting the integral before the derivative and others presenting the limit, derivative, and integral. In general, the order is up to the author's preference.
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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 [itex]e^x[/itex] are introduced later or earlier in the book.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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?
 
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  • #6
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
 

1. What are the transcendentals in calculus books?

The transcendentals in calculus books refer to the three basic mathematical functions: sine, cosine, and tangent. These functions are used to describe the relationship between the sides and angles of a right triangle.

2. Why are the transcendentals important in calculus?

The transcendentals are important in calculus because they are fundamental to understanding and solving various mathematical problems related to geometry, physics, and engineering. These functions are also used to model real-world phenomena and make predictions.

3. How are the transcendentals different from other mathematical functions?

The transcendentals are different from other mathematical functions because they are not algebraic functions and cannot be expressed as a finite combination of algebraic operations. They are also continuous and have infinite values.

4. Can the transcendentals be used in other branches of mathematics?

Yes, the transcendentals can be used in other branches of mathematics, such as trigonometry, complex analysis, and differential equations. They are also used in fields like physics, engineering, and computer science.

5. Are there other transcendentals besides sine, cosine, and tangent?

Yes, there are other transcendentals besides sine, cosine, and tangent, such as secant, cosecant, and cotangent. These functions are derived from the basic three and are used in more advanced mathematical concepts and applications.

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