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denverdoc
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Homework Statement
just looking for opinions regarding the best text for introductory calculus as in refresher--I used Taylor eons ago, which i recall as being pretty descent.
ZioX said:For those interested, Stewarts' defines the integral as riemann sums as the the mesh of the partitions (largest interval of the partition) goes to zero. The problem with this is if you look at the identity function on [0,1] of the rationals. You can always have the end points of your partitions be rationals, and then letting the mesh go to zero gives you 1. However, you can also always let the end points of your partitions be irrational, letting the mesh go to zero will yield 0.
ZioX said:For those interested, Stewarts' defines the integral as riemann sums as the the mesh of the partitions (largest interval of the partition) goes to zero. The problem with this is if you look at the identity function on [0,1] of the rationals. You can always have the end points of your partitions be rationals, and then letting the mesh go to zero gives you 1. However, you can also always let the end points of your partitions be irrational, letting the mesh go to zero will yield 0.
morphism said:I think ZioX meant to say the indicator -not identity- function (of the rationals), that is the function which is 1 on the rationals and 0 otherwise. Although I don't really follow his argument. It seems to me that in both cases you'd get 0.
The key features to look for in a textbook for an introductory calculus refresher include a clear and concise explanation of fundamental concepts, plenty of practice problems with solutions, and real-world examples to demonstrate the application of calculus. It should also have a user-friendly layout and organization, as well as access to online resources such as videos and interactive exercises.
There are several textbooks that are commonly recommended for an introductory calculus refresher, such as "Calculus: Early Transcendentals" by James Stewart, "Thomas' Calculus" by George B. Thomas Jr. and Maurice D. Weir, and "Calculus: A Complete Course" by Robert A. Adams and Christopher Essex. However, the best textbook for you may depend on your individual learning style and needs.
One way to determine if a textbook is suitable for your level of understanding is to look at the difficulty level of the problems and the level of detail in the explanations. Additionally, you can read reviews from other students or consult with your instructor for their recommendation. It's also helpful to preview the textbook before purchasing to see if the writing style and format align with your learning preference.
While it's always beneficial to have the most recent edition of a textbook, it's not always necessary for an introductory calculus refresher. Many of the fundamental concepts and principles remain the same in older editions, so as long as the textbook you choose covers the topics you need to review, it can still be a valuable resource. However, be sure to check with your instructor to see if they require a specific edition.
Yes, there are several online resources that can assist in finding the best textbook for an introductory calculus refresher. Some popular options include review websites such as Goodreads and Amazon, as well as education forums and blogs. It's also helpful to look for recommendations from other students or instructors who have taken a similar course.