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8 of 8 people found the following review helpful

ByA customeron June 3, 1999

As a college student, I used this text for Calculus I and found it amazing! After being turned off from math by years of dry, repetitive exercises and abstract concepts which I failed to see as useful, here is a math book that has intriguing, fun problems, helpful visualizations, and encourages THINKING.

This textbook introduces calculus as a language and tool for exploration and understanding in the life and social sciences. Through CONTEXT (e.g. problems involving epidemiology, population dynamics, physics etc.)one gets an in-depth knowledge of mathematical concepts and procedures. Emphasis is given to differential equations, approximation and successive approximations, geometric visualization and mathematical models, and technology (coaching students through programing and utilizing calculators and computers). For those who miss having the formulas spoon-fed to them ahead of time, there are lengthy appendices which include: graphing calculator programs for 5 different calculators, formulas from geometry, algebra, and trig, differential equations, derivatives of functions and inverses, integrals, Taylor polynomials, Taylor's Theorem, antiderivatives, and answers to selected problems.

_Calculus in Context_ challenges readers to figure out problems for themselves; use our OWN brains to come up not only with solutions, but to figure out the MEANS by which to get these solutions. *** NOT spoon-fed and NOT dry or boring!!! ***

This textbook introduces calculus as a language and tool for exploration and understanding in the life and social sciences. Through CONTEXT (e.g. problems involving epidemiology, population dynamics, physics etc.)one gets an in-depth knowledge of mathematical concepts and procedures. Emphasis is given to differential equations, approximation and successive approximations, geometric visualization and mathematical models, and technology (coaching students through programing and utilizing calculators and computers). For those who miss having the formulas spoon-fed to them ahead of time, there are lengthy appendices which include: graphing calculator programs for 5 different calculators, formulas from geometry, algebra, and trig, differential equations, derivatives of functions and inverses, integrals, Taylor polynomials, Taylor's Theorem, antiderivatives, and answers to selected problems.

_Calculus in Context_ challenges readers to figure out problems for themselves; use our OWN brains to come up not only with solutions, but to figure out the MEANS by which to get these solutions. *** NOT spoon-fed and NOT dry or boring!!! ***

12 of 18 people found the following review helpful

ByA customeron April 20, 1999

I've actually used this as a textbook for a class taught by one of the book's writers, and although the instructor himself is brilliant--one of the best teachers I've ever had--the text is absolutely horrendous. The professors who put the text together are opposed to the idea that a book should be based entirely on formulas. Furthermore, they detest the fact that most books give a few example problems in the text upon which EVERY PROBLEM that a student encounters in the excercises will be based. Thus, the teachers decided to write a book wherein hardly any procedural (as opposed to conceptual) examples are given, and which is composed mostly of text. In this way, the teachers hoped to create a MENTAL CONCEPT of the mathematical ideas that are presented. As an added bonus to this tactic, the book is able to introduce a variety of subjects that are normally addressed in a traditional calculus course, since the text focuses primarily on concept rather than implementation. I wholeheartedly agree with the intentions of this book; the execution of these intentions, however, is tremendously disappointing.

In trying to create a mental concept of the mathematics WITHOUT basing that concept on formulas that a student can blindly apply, the writers have intentionally neglected to give the formulas for many important calculus operations. They describe the CONCEPTS behind the equations and the operations only, hoping that the students will be able to figure out what the formulas are themselves; only at later points in the text do they give the actual formulas (sometimes the way they present the formulas are so confusing that you'd wish they hadn't given them; a supreme example of this is their discussion of the formula for integration by parts). Paradoxically, therefore, by trying to form a concept of calculus that does not rely on formulas, the writers have neglected to COMPLETE the concept that they attempt to present, for without discussion of the formulas, the concepts are incomplete, in my opinion.

While I do not necessarily disagree with the idea of having the students figure out the formulas for themselves (after all, it makes them think very seriously about the subject matter) the student is simply not given enough information in the book to be able to do so. Half of the students dropped the class I'm taking now, and of those I talked to, most dropped the class because they were not able to solve the problems with the information they were given in the text (of course, they perceived their incapability as arising from their own failures, which is probably not the case).

Moreover, while I also support the idea of having a book that does not rely on examples as the primary teaching tool, the fact that procedural examples are almost completely omitted is detrimental to the book's efficacy. Examples are helpful in that they show the student how to think mathematically in order to solve certain problems. Thus, without examples, the student often does not know how to approach a problem encountered in the excercises, making it very difficult to tackle them.

Finally, the problems themselves: the amazing majority of the problems have more than one step; there will be a 1.a, 1.b, 1.c, etc. However, each of these sub-problems will consist of at least four computational steps of considerable complexity, so the problems are INCREDIBLY complex, long and tedious (at least I, and the other people I work with, think so). These multi-stepped problems are also very difficult because they require the student to incorporate methods that were not adequately explained, so it takes even longer to solve them. Then, as if this weren't enough, the problems are VERY poorly worded. It is very difficult to figure out what the problem is asking the student to do; sometimes my professor, who had a hand in writing the book, will not know what a problem is asking for (hopefully he did not write the ones he does not himself understand). All in all, therefore, the problems are also seriously defective.

Were these professors to seriously revise this book, it is likely that it could become one of the best textbooks on calculus available. In its present form, though--despite the fact that the intentions of the book are good--the book is completely inadequate for its task.

In trying to create a mental concept of the mathematics WITHOUT basing that concept on formulas that a student can blindly apply, the writers have intentionally neglected to give the formulas for many important calculus operations. They describe the CONCEPTS behind the equations and the operations only, hoping that the students will be able to figure out what the formulas are themselves; only at later points in the text do they give the actual formulas (sometimes the way they present the formulas are so confusing that you'd wish they hadn't given them; a supreme example of this is their discussion of the formula for integration by parts). Paradoxically, therefore, by trying to form a concept of calculus that does not rely on formulas, the writers have neglected to COMPLETE the concept that they attempt to present, for without discussion of the formulas, the concepts are incomplete, in my opinion.

While I do not necessarily disagree with the idea of having the students figure out the formulas for themselves (after all, it makes them think very seriously about the subject matter) the student is simply not given enough information in the book to be able to do so. Half of the students dropped the class I'm taking now, and of those I talked to, most dropped the class because they were not able to solve the problems with the information they were given in the text (of course, they perceived their incapability as arising from their own failures, which is probably not the case).

Moreover, while I also support the idea of having a book that does not rely on examples as the primary teaching tool, the fact that procedural examples are almost completely omitted is detrimental to the book's efficacy. Examples are helpful in that they show the student how to think mathematically in order to solve certain problems. Thus, without examples, the student often does not know how to approach a problem encountered in the excercises, making it very difficult to tackle them.

Finally, the problems themselves: the amazing majority of the problems have more than one step; there will be a 1.a, 1.b, 1.c, etc. However, each of these sub-problems will consist of at least four computational steps of considerable complexity, so the problems are INCREDIBLY complex, long and tedious (at least I, and the other people I work with, think so). These multi-stepped problems are also very difficult because they require the student to incorporate methods that were not adequately explained, so it takes even longer to solve them. Then, as if this weren't enough, the problems are VERY poorly worded. It is very difficult to figure out what the problem is asking the student to do; sometimes my professor, who had a hand in writing the book, will not know what a problem is asking for (hopefully he did not write the ones he does not himself understand). All in all, therefore, the problems are also seriously defective.

Were these professors to seriously revise this book, it is likely that it could become one of the best textbooks on calculus available. In its present form, though--despite the fact that the intentions of the book are good--the book is completely inadequate for its task.

8 of 8 people found the following review helpful

ByA customeron June 3, 1999

As a college student, I used this text for Calculus I and found it amazing! After being turned off from math by years of dry, repetitive exercises and abstract concepts which I failed to see as useful, here is a math book that has intriguing, fun problems, helpful visualizations, and encourages THINKING.

This textbook introduces calculus as a language and tool for exploration and understanding in the life and social sciences. Through CONTEXT (e.g. problems involving epidemiology, population dynamics, physics etc.)one gets an in-depth knowledge of mathematical concepts and procedures. Emphasis is given to differential equations, approximation and successive approximations, geometric visualization and mathematical models, and technology (coaching students through programing and utilizing calculators and computers). For those who miss having the formulas spoon-fed to them ahead of time, there are lengthy appendices which include: graphing calculator programs for 5 different calculators, formulas from geometry, algebra, and trig, differential equations, derivatives of functions and inverses, integrals, Taylor polynomials, Taylor's Theorem, antiderivatives, and answers to selected problems.

_Calculus in Context_ challenges readers to figure out problems for themselves; use our OWN brains to come up not only with solutions, but to figure out the MEANS by which to get these solutions. *** NOT spoon-fed and NOT dry or boring!!! ***

This textbook introduces calculus as a language and tool for exploration and understanding in the life and social sciences. Through CONTEXT (e.g. problems involving epidemiology, population dynamics, physics etc.)one gets an in-depth knowledge of mathematical concepts and procedures. Emphasis is given to differential equations, approximation and successive approximations, geometric visualization and mathematical models, and technology (coaching students through programing and utilizing calculators and computers). For those who miss having the formulas spoon-fed to them ahead of time, there are lengthy appendices which include: graphing calculator programs for 5 different calculators, formulas from geometry, algebra, and trig, differential equations, derivatives of functions and inverses, integrals, Taylor polynomials, Taylor's Theorem, antiderivatives, and answers to selected problems.

_Calculus in Context_ challenges readers to figure out problems for themselves; use our OWN brains to come up not only with solutions, but to figure out the MEANS by which to get these solutions. *** NOT spoon-fed and NOT dry or boring!!! ***

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7 of 8 people found the following review helpful

ByTim Essingtonon November 24, 1999

This text is astounding. As someone who frequently needs to brush up on my math, I find this to be the most well organized, well written, and well-thought out text that I've encountered. Of particular interest is the acknowledgment of computer-based numerical methods, which helps alleviate that 'black-box' feeling that one often gets when your favorite analytic program spits an answer out.

I normally wouldn't bother to write a review, but I felt compelled to write one after reading through the critical review below. This reviewer was clearly frustrated by the text, but the reasons for his frustration are actually the texts strengths. Namely, this is not a 'recipe book'. To do the problems, one must learn the underlying theory and concepts, (which are laid out very well in the text). Ultimately, this is a much more powerful teaching method, to which nearly ANY educational professional will attest.

This is text to keep on your shelf!

I normally wouldn't bother to write a review, but I felt compelled to write one after reading through the critical review below. This reviewer was clearly frustrated by the text, but the reasons for his frustration are actually the texts strengths. Namely, this is not a 'recipe book'. To do the problems, one must learn the underlying theory and concepts, (which are laid out very well in the text). Ultimately, this is a much more powerful teaching method, to which nearly ANY educational professional will attest.

This is text to keep on your shelf!

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1 of 1 people found the following review helpful

ByReini2150on October 14, 2013

This book has nothing to do with all the standard (read boring) books used in all kind of calculus courses. This standard books are not bad and you will most likely need them to get a good report mark at the end of your calculus course. But if you are really interested in understanding the concepts and ideas behind calculus than you should buy this one. Really great stuff!!

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12 of 18 people found the following review helpful

ByA customeron April 20, 1999

I've actually used this as a textbook for a class taught by one of the book's writers, and although the instructor himself is brilliant--one of the best teachers I've ever had--the text is absolutely horrendous. The professors who put the text together are opposed to the idea that a book should be based entirely on formulas. Furthermore, they detest the fact that most books give a few example problems in the text upon which EVERY PROBLEM that a student encounters in the excercises will be based. Thus, the teachers decided to write a book wherein hardly any procedural (as opposed to conceptual) examples are given, and which is composed mostly of text. In this way, the teachers hoped to create a MENTAL CONCEPT of the mathematical ideas that are presented. As an added bonus to this tactic, the book is able to introduce a variety of subjects that are normally addressed in a traditional calculus course, since the text focuses primarily on concept rather than implementation. I wholeheartedly agree with the intentions of this book; the execution of these intentions, however, is tremendously disappointing.

In trying to create a mental concept of the mathematics WITHOUT basing that concept on formulas that a student can blindly apply, the writers have intentionally neglected to give the formulas for many important calculus operations. They describe the CONCEPTS behind the equations and the operations only, hoping that the students will be able to figure out what the formulas are themselves; only at later points in the text do they give the actual formulas (sometimes the way they present the formulas are so confusing that you'd wish they hadn't given them; a supreme example of this is their discussion of the formula for integration by parts). Paradoxically, therefore, by trying to form a concept of calculus that does not rely on formulas, the writers have neglected to COMPLETE the concept that they attempt to present, for without discussion of the formulas, the concepts are incomplete, in my opinion.

While I do not necessarily disagree with the idea of having the students figure out the formulas for themselves (after all, it makes them think very seriously about the subject matter) the student is simply not given enough information in the book to be able to do so. Half of the students dropped the class I'm taking now, and of those I talked to, most dropped the class because they were not able to solve the problems with the information they were given in the text (of course, they perceived their incapability as arising from their own failures, which is probably not the case).

Moreover, while I also support the idea of having a book that does not rely on examples as the primary teaching tool, the fact that procedural examples are almost completely omitted is detrimental to the book's efficacy. Examples are helpful in that they show the student how to think mathematically in order to solve certain problems. Thus, without examples, the student often does not know how to approach a problem encountered in the excercises, making it very difficult to tackle them.

Finally, the problems themselves: the amazing majority of the problems have more than one step; there will be a 1.a, 1.b, 1.c, etc. However, each of these sub-problems will consist of at least four computational steps of considerable complexity, so the problems are INCREDIBLY complex, long and tedious (at least I, and the other people I work with, think so). These multi-stepped problems are also very difficult because they require the student to incorporate methods that were not adequately explained, so it takes even longer to solve them. Then, as if this weren't enough, the problems are VERY poorly worded. It is very difficult to figure out what the problem is asking the student to do; sometimes my professor, who had a hand in writing the book, will not know what a problem is asking for (hopefully he did not write the ones he does not himself understand). All in all, therefore, the problems are also seriously defective.

Were these professors to seriously revise this book, it is likely that it could become one of the best textbooks on calculus available. In its present form, though--despite the fact that the intentions of the book are good--the book is completely inadequate for its task.

In trying to create a mental concept of the mathematics WITHOUT basing that concept on formulas that a student can blindly apply, the writers have intentionally neglected to give the formulas for many important calculus operations. They describe the CONCEPTS behind the equations and the operations only, hoping that the students will be able to figure out what the formulas are themselves; only at later points in the text do they give the actual formulas (sometimes the way they present the formulas are so confusing that you'd wish they hadn't given them; a supreme example of this is their discussion of the formula for integration by parts). Paradoxically, therefore, by trying to form a concept of calculus that does not rely on formulas, the writers have neglected to COMPLETE the concept that they attempt to present, for without discussion of the formulas, the concepts are incomplete, in my opinion.

While I do not necessarily disagree with the idea of having the students figure out the formulas for themselves (after all, it makes them think very seriously about the subject matter) the student is simply not given enough information in the book to be able to do so. Half of the students dropped the class I'm taking now, and of those I talked to, most dropped the class because they were not able to solve the problems with the information they were given in the text (of course, they perceived their incapability as arising from their own failures, which is probably not the case).

Moreover, while I also support the idea of having a book that does not rely on examples as the primary teaching tool, the fact that procedural examples are almost completely omitted is detrimental to the book's efficacy. Examples are helpful in that they show the student how to think mathematically in order to solve certain problems. Thus, without examples, the student often does not know how to approach a problem encountered in the excercises, making it very difficult to tackle them.

Finally, the problems themselves: the amazing majority of the problems have more than one step; there will be a 1.a, 1.b, 1.c, etc. However, each of these sub-problems will consist of at least four computational steps of considerable complexity, so the problems are INCREDIBLY complex, long and tedious (at least I, and the other people I work with, think so). These multi-stepped problems are also very difficult because they require the student to incorporate methods that were not adequately explained, so it takes even longer to solve them. Then, as if this weren't enough, the problems are VERY poorly worded. It is very difficult to figure out what the problem is asking the student to do; sometimes my professor, who had a hand in writing the book, will not know what a problem is asking for (hopefully he did not write the ones he does not himself understand). All in all, therefore, the problems are also seriously defective.

Were these professors to seriously revise this book, it is likely that it could become one of the best textbooks on calculus available. In its present form, though--despite the fact that the intentions of the book are good--the book is completely inadequate for its task.

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ByChris Aldrichon February 19, 2015

A wonderful calculus text written by some of the leading thinkers in the modern pedagogy of mathematics. One should note that the authors have released an updated 2008 edition of this text for free online.

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2 of 6 people found the following review helpful

ByA customeron January 26, 2000

If you can deduce, by my "star" rating of this text, that I disagree with the Amherst, MA reader, then you have enough scruples to learn quite a lot from this text, and have fun doing it!

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