Calculus Ii Textbook Pdf

[Chanelle Kirksey]

Thetime it takes to complete a Calculus textbook can vary depending on the individual's learning pace and level of understanding. However, on average, it can take anywhere from 1 to 2 semesters to complete a Calculus textbook.

Yes, the time to complete a Calculus textbook can be shortened by studying consistently and efficiently. It is also helpful to seek additional resources, such as online tutorials or study groups, to supplement the textbook material.

The time to complete a Calculus textbook can be affected by various factors such as the individual's prior knowledge and understanding of math concepts, the difficulty level of the textbook, and the amount of time dedicated to studying and practicing problems.

The time spent on each problem in a Calculus textbook can also vary depending on the individual's understanding and the difficulty level of the problem. However, it is recommended to spend an average of 5-10 minutes on each problem to fully understand and solve it.

Yes, the time to complete a Calculus textbook can vary for different individuals based on their learning pace, prior knowledge and understanding of math concepts, and dedication to studying. It is important to work at your own pace and focus on understanding the material rather than comparing your progress to others.

Perhaps I could write this book someday, but it'd be a lot easier for me if my students and I could just buy and/or download a book that takesthis approach without neglecting to provide a cornucopia of exercises, examples, and applications similar to what's available in today's most popular calculus textbooks.

There is a marvelous old book (19th Century if I recall correctly) where I learned Calculus the first time, called "Calculus Made Easy" by Silvanus P. Thompson, and subtitled "What one fool can do another can". He explains that dx means a "little bit of x" and shows a square with sides x and x + dx and you can see why you can "ignore dx^2". Of course it isn't rigorous in any sense, but it uses differentials to get all the essential ideas of both differential and integral Calculus across quickly and smoothly. Needless to say, once I had absorbed all these essential ideas I went on to read more rigorous books where limits were introduced and used to make precise what I already understood well from this intuitive introduction. If I recall correctly Calculus Made Easy was republished some years back (Dover?) and was quite popular. I would suggest that you recommend it to your students, with appropriate caveats.

(Added later) I checked online and indeed there is a recent reprinting (available from Amazon and the other usual places). Moreover it has three new chapters written by the late great Martin Gardner aimed at the modern reader. I'm going to buy myself a copy!

I have written a textbook called Intuitive Infinitesimal Calculus, which teaches infinitesimal calculus the classical, informal way, informed by my Ph.D. research on the history of the Leibnizian calculus.

This approach is suggested by Tevian Dray and Corinne Manogue in their program of Bridging the Vector Calculus Gap. They focus on multivariable calculus and differential forms, but they discuss single-variable calculus (pdf) once. Unfortunately, they don't seem to have a textbook for that.

Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide.

MIT Professor Gilbert Strang has created a series of videos to show ways in which calculus is important in our lives. The videos, which include real-life examples to illustrate the concepts, are ideal for high school students, college students, and anyone interested in learning the basics of calculus.

In some of our calculus classes, we have used Python-based Jupyter notebooks as tutorial assignments. These are now available as a Jupyter book, along with some supporting documentation on the basics of using Python (and the SymPy and NumPy libraries) for Calculus.

For users at the University of Lethbridge, the Jupyter notebook pages can be launched in an interactive environment, using our Syzygy Jupyter hub. (U of L login required.) Look for the rocket ship icon at the top of the page to launch the interactive notebook.

APEX Calculus is a free, open calculus textbook created by Greg Hartman of the Virginia Military Institute. University of Lethbridge has used APEX Calculus since 2015. Traditionally we used PDF textbooks edited by Sean Fitzpatrick to align with the U of L calculus courses.

The PDF books look great, and they're a good choice if you want to print a coursepack. But the PDF does not meet basic accessibility requirements, and it does not scale well for students wanting to access the book on a phone.

Since 2019, Sean Fitzpatrick has been working with Greg Hartman and a team of editors to convert the book to a new format, called PreTeXt. PreTeXt allows us to output to both PDF and HTML, and the HTML supports a lot of nice features, like optimization for small screens, embedded videos, and interactive exercises.

The next version is divided into parts to reflect the standard four-semester calculus sequence at U of L. This version also contains embedded videos recorded by Sean Fitzpatrick to match the content of the book. Videos are currently available for all chapters except for the chapters on vectors, and vector-valued functions. The PDF version has exactly the same content as the HTML. Videos are replaced by a thumbnail and a QR code the reader can use to access the video on a mobile device.

There are several PDF versions of these textbooks available. For each course, we provide both the original and PreTeXt-based versions of the book, in both colour and print formats. For details, see our home page.

There are many other excellent calculus resources. We have chosen to link to books written in PreTeXt, since these are available in HTML, and they often have useful features for self-study, such as interactive exercises.

Finney, et al., Calculus: Graphical, Numerical, Algebraic (2003). This is clearly a standard high school textbook, which seems to provide the most basic of AP Calculus BC training. While the limit is defined in epsilon-delta form, it doesn't seem to be used except for some exercises in an appendix, and I didn't find any proofs in the book. The material, including definitions, does seem carefully presented, but it's a very elementary text, and there are quite a few exercises rather than challenging problems. There is a very, very heavy use of graphing calculators to give a graphical view of functions, limits, etc. -- not necessarily bad, but I'm trying to give an idea of the type of text. While the text has a strong school text feel, it isn't plagued by excessive, distracting sidebars, at least in the edition I reviewed. The text is too basic for us, but I could see the text's usefulness to explain concepts which are not grasped via the primary text you're using. The order of most of the texts seems pretty standard, except for some including transcendental functions earlier vs. some later, so some cross-use of texts isn't out of the question.

Strang also has a calculus text available for free download on the MIT Open Courseware site. I have not had a chance to review it yet, but his Linear Algebra and Its Applications text was my favorite math text as an undergraduate. My prof. (admittedly) was a terrible teacher, but I had no problem learning the material from the text, and I've heard that his calculus text is clear and direct too. At the same MIT OCW site, Dr. Strang has a series of videos "to show ways calculus is important in our lives."

ETA: some of the links and the Finney text review. Some later notes shown in green and will be discussed in a later post. The review of Thomas' Calculus below was added in response to a question by Mike:

Thomas' Calculus: Early Transcendentals 12th edition (2010) based on the original work by George Thomas as revised by Weir and Hass. There are many editions of Thomas' Calculus and this one is intended as a college course either for those with high school calculus or without. (For example, the text University Calculus by the same authors is a streamlined version meant for those who took calculus in high school, so it's outside the scope of this review. The next text to be reviewed is an older, explicitly high school text by George Thomas.) Thomas' Calculus seems to be at about the same level as Anton; there's perhaps more theory in Thomas' text but there's a good amount of rigor in Anton, and probably more than Thomas, if you select it, and Anton seems to have a significantly greater depth of practical problems. Thomas' Calculus 12 ed. appears rigorous, although it does not prove every result -- none of the texts except perhaps Spivak and Apostol do, but that's not what we or most high school students want anyhow. Thomas' has a lot of exercises, both simple and medium in difficulty. Thomas' seems like a good book, although I like Anton better for deeper applied problems and seemingly more flexibility with the theory. The most important thing, however, is how well the text explains concepts to the new learner, and, unfortunately, I can't say for sure. I'll just say it's worth considering.

Thomas Elements of Calculus and Analytic Geometry 2nd edition (1976) is an adaptation of George Thomas' calculus for high school students, by George Thomas himself. It looks like a 1970s high school textbook. Transcendental functions are covered late in the book, which I'm not a fan of since it leaves less time for working with transcendental functions during the course -- this is hotly debated, which is why most textbooks nowadays have versions with late transcendentals and early transcendentals. The presentation in this relatively simple, short book does strike me as straightforward and probably fairly easy to follow. There are a few simple theorems proved. Most of the problems are simple exercises with little sense for the range of applications of calculus and not many challenging problems. In summary, I don't think this is the best choice as the core text, but it seems to have value in having around as a way of describing a problematic topic if a student is struggling.

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