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The Calculus Lifesaver: All the Tools You Need to Excel at Calculus [Princeton L
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- Compralo SubitoThe Calculus Lifesaver: All the Tools You Need to Excel at Calculus [Princeton L
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Oggetto che si trova a: Albany, Georgia, Stati Uniti
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Numero oggetto eBay:145728752378
Specifiche dell'oggetto
- Condizione
- ISBN
- 9780691131535
Informazioni su questo prodotto
Product Identifiers
Publisher
Princeton University Press
ISBN-10
0691131538
ISBN-13
9780691131535
eBay Product ID (ePID)
59012694
Product Key Features
Number of Pages
728 Pages
Language
English
Publication Name
Calculus Lifesaver : All the Tools You Need to Excel at Calculus
Subject
Calculus
Publication Year
2007
Type
Textbook
Subject Area
Mathematics
Series
Princeton Lifesaver Study Guides
Format
Hardcover
Dimensions
Item Height
1.9 in
Item Weight
49.1 Oz
Item Length
10 in
Item Width
7 in
Additional Product Features
Intended Audience
College Audience
LCCN
2006-939343
Reviews
"Banner's style is informal, engaging and distinctly non-intimidating, and he takes pains to not skip any steps in discussing a problem. Because of its unique approach, The Calculus Lifesaver is a welcome addition to the arsenal of calculus teaching aids."-- MAA Online, "Banner's style is informal, engaging and distinctly non-intimidating, and he takes pains to not skip any steps in discussing a problem. Because of its unique approach, The Calculus Lifesaver is a welcome addition to the arsenal of calculus teaching aids." -- MAA Online, Students who are having difficulty in calculus could use it as a resource in addition to their professor and teaching assistant., "This rather lengthy book serves as an excellent resource as well as a text for a refresher course in single-variable calculus, and as a study guide for anyone who needs or is required to know basic calculus concepts....Readers will find this book written for them, as calculus is presented in a very casual conversational tone; certainly, students who are not mathematics majors will benefit greatly." ---J.T. Zerger, Choice, Banner's style is informal, engaging and distinctly non-intimidating, and he takes pains to not skip any steps in discussing a problem. Because of its unique approach,The Calculus Lifesaveris a welcome addition to the arsenal of calculus teaching aids., "Banner's book is a chatty, user-friendly guide to calculus that will be a useful addition to the resources available to students. Banner does an exceptionally thorough job while maintaining an engaging style." --Gerald B. Folland, author of Advanced Calculus, This rather lengthy book serves as an excellent resource as well as a text for a refresher course in single-variable calculus, and as a study guide for anyone who needs or is required to know basic calculus concepts....Readers will find this book written for them, as calculus is presented in a very casual conversational tone; certainly, students who are not mathematics majors will benefit greatly. ---J.T. Zerger, Choice, "This rather lengthy book serves as an excellent resource as well as a text for a refresher course in single-variable calculus, and as a study guide for anyone who needs or is required to know basic calculus concepts....Readers will find this book written for them, as calculus is presented in a very casual conversational tone; certainly, students who are not mathematics majors will benefit greatly."-- J.T. Zerger, Choice, "I used Adrian Banner's The Calculus Lifesaver as the sole textbook for an intensive, three-week summer Calculus I course for high-school students. I chose this book for several reasons, among them its conversational expository style, its wealth of worked-out examples, and its price. This book is designed to supplement any standard calculus textbook, thus my students will be able to use it again when they take later calculus courses. The students in my class came from diverse backgrounds, ranging from those who had already seen much of the material to others who were struggling with basic algebra. They all uniformly praised the book for being one of the clearest mathematics texts they have ever read, and because it reviews the required prerequisite material. The numerous worked-out examples are an ideal supplement to the lectures. The only difficulty in using this book as a primary text is the lack of additional exercises in the text. However, there are so many sites and sources for calculus problems that this was not a problem. I would definitely use this book again." --Steven J. Miller, Brown University, Banner's style is informal, engaging and distinctly non-intimidating, and he takes pains to not skip any steps in discussing a problem. Because of its unique approach, "The Calculus Lifesaver" is a welcome addition to the arsenal of calculus teaching aids., "This is an engaging read. Each page engenders at least one smile, often a chuckle, occasionally a belly laugh." --Charles R. MacCluer, author of Honors Calculus, "Students who are having difficulty in calculus could use it as a resource in addition to their professor and teaching assistant."-- Mathematics Teacher, "This rather lengthy book serves as an excellent resource as well as a text for a refresher course in single-variable calculus, and as a study guide for anyone who needs or is required to know basic calculus concepts....Readers will find this book written for them, as calculus is presented in a very casual conversational tone; certainly, students who are not mathematics majors will benefit greatly." --J.T. Zerger, Choice, "Students who are having difficulty in calculus could use it as a resource in addition to their professor and teaching assistant." -- Mathematics Teacher, "This book is significant. The author's attempt to give an 'inner monologue' into the thought process that is needed to solve calculus problems rather than just providing worked examples is novel and is in line with his purpose of helping the reader get a deeper understanding of calculus. The book is well written and the author's examples are clear and complete." --Thomas Seidenberg, Phillips Exeter Academy, "Banner's book is a chatty, user-friendly guide to calculus that will be a useful addition to the resources available to students. Banner does an exceptionally thorough job while maintaining an engaging style." -- Gerald B. Folland, Banner's style is informal, engaging and distinctly non-intimidating, and he takes pains to not skip any steps in discussing a problem. Because of its unique approach, The Calculus Lifesaver is a welcome addition to the arsenal of calculus teaching aids.
Dewey Edition
22
TitleLeading
The
Illustrated
Yes
Dewey Decimal
515
Table Of Content
Welcome xviii How to Use This Book to Study for an Exam xix Two all-purpose study tips xx Key sections for exam review (by topic) xx Acknowledgments xxiii Chapter 1: Functions, Graphs, and Lines 1 1.1 Functions 1 1.1.1 Interval notation 3 1.1.2 Finding the domain 4 1.1.3 Finding the range using the graph 5 1.1.4 The vertical line test 6 1.2 Inverse Functions 7 1.2.1 The horizontal line test 8 1.2.2 Finding the inverse 9 1.2.3 Restricting the domain 9 1.2.4 Inverses of inverse functions 11 1.3 Composition of Functions 11 1.4 Odd and Even Functions 14 1.5 Graphs of Linear Functions 17 1.6 Common Functions and Graphs 19 Chapter 2: Review of Trigonometry 25 2.1 The Basics 25 2.2 Extending the Domain of Trig Functions 28 2.2.1 The ASTC method 31 2.2.2 Trig functions outside [0; 2pi;] 33 2.3 The Graphs of Trig Functions 35 2.4 Trig Identities 39 Chapter 3: Introduction to Limits 41 3.1 Limits: The Basic Idea 41 3.2 Left-Hand and Right-Hand Limits 43 3.3 When the Limit Does Not Exist 45 3.4 Limits at 1 and -infin; 47 3.4.1 Large numbers and small numbers 48 3.5 Two Common Misconceptions about Asymptotes 50 3.6 The Sandwich Principle 51 3.7 Summary of Basic Types of Limits 54 Chapter 4: How to Solve Limit Problems Involving Polynomials 57 4.1 Limits Involving Rational Functions as chi; rarr; alpha;a 57 4.2 Limits Involving Square Roots as chi; rarr; alpha; 61 4.3 Limits Involving Rational Functions as chi; rarr; infin; 61 4.3.1 Method and examples 64 4.4 Limits Involving Poly-type Functions as chi; rarr; infin; 66 4.5 Limits Involving Rational Functions as chi; rarr; -infin; 70 4.6 Limits Involving Absolute Values 72 Chapter 5: Continuity and Differentiability 75 5.1 Continuity 75 5.1.1 Continuity at a point 76 5.1.2 Continuity on an interval 77 5.1.3 Examples of continuous functions 77 5.1.4 The Intermediate Value Theorem 80 5.1.5 A harder IVT example 82 5.1.6 Maxima and minima of continuous functions 82 5.2 Differentiability 84 5.2.1 Average speed 84 5.2.2 Displacement and velocity 85 5.2.3 Instantaneous velocity 86 5.2.4 The graphical interpretation of velocity 87 5.2.5 Tangent lines 88 5.2.6 The derivative function 90 5.2.7 The derivative as a limiting ratio 91 5.2.8 The derivative of linear functions 93 5.2.9 Second and higher-order derivatives 94 5.2.10 When the derivative does not exist 94 5.2.11 Differentiability and continuity 96 Chapter 6: How to Solve Differentiation Problems 99 6.1 Finding Derivatives Using the Difinition 99 6.2 Finding Derivatives (the Nice Way) 102 6.2.1 Constant multiples of functions 103 6.2.2 Sums and Differences of functions 103 6.2.3 Products of functions via the product rule 104 6.2.4 Quotients of functions via the quotient rule 105 6.2.5 Composition of functions via the chain rule 107 6.2.6 A nasty example 109 6.2.7 Justification of the product rule and the chain rule 111 6.3 Finding the Equation of a Tangent Line 114 6.4 Velocity and Acceleration 114 6.4.1 Constant negative acceleration 115 6.5 Limits Which Are Derivatives in Disguise 117 6.6 Derivatives of Piecewise-Difined Functions 119 6.7 Sketching Derivative Graphs Directly 123 Chapter 7: Trig Limits and Derivatives 127 7.1 Limits Involving Trig Functions 127 7.1.1 The small case 128 7.1.2 Solving problems the small case 129 7.1.3 The large case 134 7.1.4 The "other" case 137 7.1.5 Proof of an important limit 137 7.2 Derivatives Involving Trig Functions 141 7.2.1 Examples of Differentiating trig functions 143 7.2.2 Simple harmonic motion 145 7.2.3 A curious function 146 Chapter 8: Implicit Differentiation and Related Rates 149 8.1 Implicit Differentiation 149 8.1.1 Techniques and exam
Synopsis
For many students, calculus can be the most mystifying and frustrating course they will ever take. "The Calculus Lifesaver" provides students with the essential tools they need not only to learn calculus, but to excel at it.All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory."The Calculus Lifesaver" combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.Serves as a companion to any single-variable calculus textbook Informal, entertaining, and not intimidating Informative videos that follow the book--a full forty-eight hours ofBanner's Princeton calculus-review course--will be available through the book's Web site at www.calclifesaver.comMore than 475 examples (ranging from easy to hard) provide step-by-step reasoning Theorems and methods justified and connections made to actual practice Difficult topics such as improper integrals and infinite series covered in detail Tried and tested by students taking freshman calculus, For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it. All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory. The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus. Serves as a companion to any single-variable calculus textbook Informal, entertaining, and not intimidating Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures More than 475 examples (ranging from easy to hard) provide step-by-step reasoning Theorems and methods justified and connections made to actual practice Difficult topics such as improper integrals and infinite series covered in detail Tried and tested by students taking freshman calculus
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