Calculus Without Limits: Almost [Paperback]

John Sparks (Author)

Book Description

ISBN-10: 1418441244 | ISBN-13: 978-1418441241 | Publication Date: June 23, 2004 | Edition: 3rd Updated

Calculus without Limits is an original exposition of single-variable calculususing the classic differential approach. Written in an engaging, popular styleby an award-winning teacher, Calculus without Limits is thefirst completely new calculus book tohit the shelves in 95 years that deliberately minimizes the useof limits, one of the major stumbling blocks initially standing in the way ofcalculus students. Calculus without Limits presents its subject in nine chapters: 1) 'Introduction', 2) 'Barrow'sDiagram', 3) 'The Two Fundamental Problems of Calculus', 4) 'Foundations', 5)'Solving the First Problem', 6) 'Antiprocesses', 7) 'Solving the SecondProblem', 8) 'Sampling the Power of Differential Equations', and 9)'Conclusion: Magnificent Shoulders'. Approximately 85 diagrams and a plethoraof worked examples help facilitate student understanding in an exposition thatmeasures a mere 330 pages from cover to cover. Real-life applications examineproblems from a variety of disciplines ranging from physics to finance. Additionally,Calculus without Limits provides plenty of practice for the beginning calculusstudent via 200 exercises from routine to quite challenging-all answered in an'Answer to Problems' section in the back of the book. Five appendices summarizekey formulas from various mathematical disciplines, and a brief one-page bibliographycompletes the book. Calculus without Limits is suitable as a self-study text or as supplementarytext augmenting a regular multi-term college calculus sequence. It can alsoserve as the primary text for a one-term Business Calculus or Calculus forAppreciation Course. Advanced High School Students will find it ideal forquickly mastering calculus basics before engaging a more rigorous collegeoffering. Lastly, Calculus without Limits is meant for all those peoplewho really never learned the why behind calculus, and now, many yearslater-perhaps as a practicing professional-may want to reacquaint themselveswith an old academic friend for th

Editorial Reviews

About the Author

John C. Sparks is a career federal employee at Wright-Patterson Air Force Base (Dayton, Ohio) with over thirty years of engineering and management experience. Additionally, he is an award-winning-named the Ohio Association of Two Year Colleges' 2002-03 Adjunct Teacher of the Year-twenty-year veteran of Dayton's nationally recognized Sinclair Community College where he teaches mathematics on a part-time basis. Mr. Sparks is a native of Xenia, Ohio and is a graduate of Xenia High School (class of '65). He holds bachelor and master's degrees from Wright State University, and a master's degree from the Air Force Institute of Technology. John and his wife, Carolyn, have recently celebrated thirty-five years of marriage and have two married sons: Robert, living in Virginia, and Curtis, living in Nebraska.A writer at heart, Mr. Sparks has participated as a technical writer for eight curriculum-development activities sponsored by Sinclair's AIM - Advanced Integrated Manufacturing - Center. As early as 1985, he was 'writing across the curriculum' by requiring term papers in mathematics courses. Prior to coming to Author House, Mr. Sparks self-published two volumes of poetry in 1998 and 2000. Author House currently has three of his latest books in publication: Calculus without Limits (Mathematics, 2004); Gold, Hay and Stubble (Poetry, 2004); and The Student's Essential Formula Book (Mathematics/Reference, 2004).

Product Details

• Paperback: 392 pages
• Publisher: AuthorHouse; 3rd Updated edition (June 23, 2004)
• Language: English
• ISBN-10: 1418441244
• ISBN-13: 978-1418441241
• Product Dimensions: 9 x 6 x 0.9 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (10 customer reviews)
• Amazon Best Sellers Rank: #1,649,142 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

20 of 21 people found the following review helpful:

4.0 out of 5 stars An unusual approach, October 29, 2006

By 

Bruce R. Gilson (Wheaton, MD United States) - See all my reviews
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This review is from: Calculus Without Limits: Almost (Paperback)

This book is a very atypical introduction to calculus, which some people may like and others will hate. It clearly shows the orientation of its author, who is an engineer and not a mathematician.

Calculus can be presented in two approaches, one using infinitesimals (the way Leibniz thought of it) and one using limits (closer to Newton's picture, though he too would use infinitesimals when it suited him). Originally, either mode of thinking was applied intuitively, but mathematicians could not define the infinitesimal approach in a rigorous manner, and in the 19th century the subject was rigorously developed using limits. Eventually a rigorous approach was developed using infinitesimals by Robinson in the 20th century, but most mathematicians came to prefer the limit approach, because it was the first one developed with a degree of rigor to suit the mathematical community. But scientists and engineers developed an intuitive way of thinking about calculus, based primarily on the infinitesimal approach. So a typical scientist would come to calculus by means of a freshman course that presented the subject using limits, with only a slight reduction of the rigor to a level appropriate to college freshmen, and only in his physics and chemistry courses be presented with calculus as a problem-solving tool using a more intuitive approach based on infinitesimals. The author of this book seems to feel that it is better to present an intuitive approach to calculus, forgetting about rigor (he was once, he states, exposed to calculus in a course that was overly rigorous, even beyond the level usually met in freshman calculus classes!) and it is this which he does in this book.

The author starts off with an intuitive proof of the Pythagorean theorem, which works quite well. He does follow this with an equally intuitive proof of a geometric fallacy, which should clearly demonstrate the limits of intuitive thinking! But it seems that despite this, he intends to go on purely intuitively. The resulting book is one that mathematicians will find infuriating, but scientists and engineers will see as reflecting the way calculus is actually used in their disciplines. And so, I think, what you will think of this book will depend on your own orientation.

Before concluding I should say that one serious defect of this book, I would say, is the total absence of an index. In addition, I think that the title is somewhat misleading; the author uses the limit concept more than he implies. A better title would be "Calculus by an intuitive approach." It is the intuitive approach, even more than the fact that he uses infinitesimals rather than limits for many of his arguments, that defines the uniqueness of this book.

20 of 22 people found the following review helpful:

5.0 out of 5 stars Perspective from a Practicing Technologist, August 30, 2004

By 

E. Jennings Taylor - See all my reviews
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This review is from: Calculus Without Limits: Almost (Paperback)

I have a PhD in Materials Science and have been "practicing" scientific and engineering R&D for about 25 years. As a consequence, I'm fairly astute regarding calculus matters.

I was intrigued about this book because of its' approach to calculus with minimal emphasis on the limit theorem and because my son is entering high school mathematics.

I found the book to be very well laid out and the progression of subject matter to be very logical. Most importantly, the book provided real world examples for "using" the mathematical concepts introduced. One of my favorite was the example of transporting a ladder around a corner. While one would not use calculus in such a situation, these sort of examples, really analogies, provide an excellent perspective for the reader.

Finally, the book read almost like a novel. It was enjoyable and left one to anticipate the next chapter.

I think this book is an enjoyable read and suggest it for 1) someone like myself with the challenge of helping bring relevance to their young students, 2) a student currently being introduced to calculus and 3) a former student seeking a refresher.

18 of 20 people found the following review helpful:

5.0 out of 5 stars Review from the author of www.karlscalculus.org, March 13, 2005

By 

Karl D. Hahn (Florida) - See all my reviews
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This review is from: Calculus Without Limits: Almost (Paperback)

Only someone who has fallen in love with calculus can know its poetry. Just as any
musician can tell you how music is far deeper than mere spots on a score sheet,
John C. Sparks leads you to understand how calculus is far deeper than
mere cryptic symbols on a blackboard.

The sad truth is that too many calculus classes and texts teach students only
the rules by which you manipulate the cryptic symbols. But those cryptic symbols,
like all symbols, stand for something greater. Spots on a score sheet stand for
melodic sounds, and mathematical symbols stand for beautiful ideas. It is these
ideas that Calculus Without Limits teaches.

Without grasping the ideas and concepts of calculus, a student is left only with
the grind of applying pencil lead to paper in this or that prescribed manner and
has thoroughly missed the point. So it's hardly a surprise that so many calculus
students are frustrated. But for a student who reads John C. Sparks' explanations
of how the symbols assemble themselves into something meaningful, the symbology
becomes just a tool -- as it should have been all along. The real knowledge and
beauty behind the symbols glimmer through. And for a student who makes the special
effort (and all mathematics learning requires special effort, even from those who
love it) to follow that light where it leads -- that student too might very well
fall in love and know the poetry.