Cover image for Calculus demystified
Title:
Calculus demystified
Author:
Krantz, Steven G. (Steven George), 1951-
Publication Information:
New York : McGraw-Hill, [2003]

©2003
Physical Description:
xii, 343 pages : illustrations ; 23 cm
Language:
English
Subject Term:
ISBN:
9780071393089
Format :
Book

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Call Number
Material Type
Home Location
Status
Central Library QA303.2 .K74 2003 Adult Non-Fiction Non-Fiction Area
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Summary

Summary

LEARNING CALCULUS JUST GOT A LOT EASIER!

Here's an innovative shortcut to gaining a more intuitive understanding of both differential and integral calculus. In Calculus Demystified an experienced teacher and author of more than 30 books puts all the math background you need inside and uses practical examples, real data, and a totally different approach to mastering calculus.

With Calculus Demystified you ease into the subject one simple step at a time -- at your own speed. A user-friendly, accessible style incorporating frequent reviews, assessments, and the actual application of ideas helps you to understand and retain all the important concepts.

THIS ONE-OF-A-KIND SELF-TEACHING TEXT OFFERS:

Questions at the end of each chapter and section to reinforce learning and pinpoint weaknesses A 100-question final exam for self-assessment Detailed examples and solutions Numerous "Math Notes" and "You Try It" items to gauge progress and make learning more enjoyable An easy-to-absorb style -- perfect for those without a mathematics background

If you've been looking for a painless way to learn calculus, refresh your skills, or improve your classroom performance, your search ends here.


Table of Contents

Prefacep. xi
Chapter 1 Basicsp. 1
1.0 Introductory Remarksp. 1
1.1 Number Systemsp. 1
1.2 Coordinates in One Dimensionp. 3
1.3 Coordinates in Two Dimensionsp. 5
1.4 The Slope of a Line in the Planep. 8
1.5 The Equation of a Linep. 13
1.6 Loci in the Planep. 15
1.7 Trigonometryp. 19
1.8 Sets and Functionsp. 30
1.8.1 Examples of Functions of a Real Variablep. 31
1.8.2 Graphs of Functionsp. 33
1.8.3 Plotting the Graph of a Functionp. 35
1.8.4 Composition of Functionsp. 40
1.8.5 The Inverse of a Functionp. 42
1.9 A Few Words About Logarithms and Exponentialsp. 49
Chapter 2 Foundations of Calculusp. 57
2.1 Limitsp. 57
2.1.1 One-Sided Limitsp. 60
2.2 Properties of Limitsp. 61
2.3 Continuityp. 64
2.4 The Derivativep. 66
2.5 Rules for Calculating Derivativesp. 71
2.5.1 The Derivative of an Inversep. 76
2.6 The Derivative as a Rate of Changep. 76
Chapter 3 Applications of the Derivativep. 81
3.1 Graphing of Functionsp. 81
3.2 Maximum/Minimum Problemsp. 86
3.3 Related Ratesp. 91
3.4 Falling Bodiesp. 94
Chapter 4 The Integralp. 99
4.0 Introductionp. 99
4.1 Antiderivatives and Indefinite Integralsp. 99
4.1.1 The Concept of Antiderivativep. 99
4.1.2 The Indefinite Integralp. 100
4.2 Areap. 103
4.3 Signed Areap. 111
4.4 The Area Between Two Curvesp. 116
4.5 Rules of Integrationp. 120
4.5.1 Linear Propertiesp. 120
4.5.2 Additivityp. 120
Chapter 5 Indeterminate Formsp. 123
5.1 l'Hopital's Rulep. 123
5.1.1 Introductionp. 123
5.1.2 l'Hopital's Rulep. 124
5.2 Other Indeterminate Formsp. 128
5.2.1 Introductionp. 128
5.2.2 Writing a Product as a Quotientp. 128
5.2.3 The Use of the Logarithmp. 128
5.2.4 Putting Terms Over a Common Denominatorp. 130
5.2.5 Other Algebraic Manipulationsp. 131
5.3 Improper Integrals: A First Lookp. 132
5.3.1 Introductionp. 132
5.3.2 Integrals with Infinite Integrandsp. 133
5.3.3 An Application to Areap. 139
5.4 More on Improper Integralsp. 140
5.4.1 Introductionp. 140
5.4.2 The Integral on an Infinite Intervalp. 141
5.4.3 Some Applicationsp. 143
Chapter 6 Transcendental Functionsp. 147
6.0 Introductory Remarksp. 147
6.1 Logarithm Basicsp. 147
6.1.1 A New Approach to Logarithmsp. 148
6.1.2 The Logarithm Function and the Derivativep. 150
6.2 Exponential Basicsp. 154
6.2.1 Facts About the Exponential Functionp. 155
6.2.2 Calculus Properties of the Exponentialp. 156
6.2.3 The Number ep. 158
6.3 Exponentials with Arbitrary Basesp. 160
6.3.1 Arbitrary Powersp. 160
6.3.2 Logarithms with Arbitrary Basesp. 163
6.4 Calculus with Logs and Exponentials to Arbitrary Basesp. 166
6.4.1 Differentiation and Integration of log[subscript a] x and a[superscript x]p. 166
6.4.2 Graphing of Logarithmic and Exponential Functionsp. 168
6.4.3 Logarithmic Differentiationp. 170
6.5 Exponential Growth and Decayp. 172
6.5.1 A Differential Equationp. 173
6.5.2 Bacterial Growthp. 174
6.5.3 Radioactive Decayp. 176
6.5.4 Compound Interestp. 178
6.6 Inverse Trigonometric Functionsp. 180
6.6.1 Introductory Remarksp. 180
6.6.2 Inverse Sine and Cosinep. 180
6.6.3 The Inverse Tangent Functionp. 185
6.6.4 Integrals in Which Inverse Trigonometric Functions Arisep. 187
6.6.5 Other Inverse Trigonometric Functionsp. 189
6.6.6 An Example Involving Inverse Trigonometric Functionsp. 193
Chapter 7 Methods of Integrationp. 197
7.1 Integration by Partsp. 197
7.2 Partial Fractionsp. 202
7.2.1 Introductory Remarksp. 202
7.2.2 Products of Linear Factorsp. 203
7.2.3 Quadratic Factorsp. 206
7.3 Substitutionp. 207
7.4 Integrals of Trigonometric Expressionsp. 210
Chapter 8 Applications of the Integralp. 217
8.1 Volumes by Slicingp. 217
8.1.0 Introductionp. 217
8.1.1 The Basic Strategyp. 217
8.1.2 Examplesp. 219
8.2 Volumes of Solids of Revolutionp. 224
8.2.0 Introductionp. 224
8.2.1 The Method of Washersp. 225
8.2.2 The Method of Cylindrical Shellsp. 228
8.2.3 Different Axesp. 231
8.3 Workp. 233
8.4 Averagesp. 237
8.5 Arc Length and Surface Areap. 240
8.5.1 Arc Lengthp. 240
8.5.2 Surface Areap. 243
8.6 Hydrostatic Pressurep. 247
8.7 Numerical Methods of Integrationp. 252
8.7.1 The Trapezoid Rulep. 253
8.7.2 Simpson's Rulep. 256
Bibliographyp. 263
Solutions to Exercisesp. 265
Final Examp. 313
Indexp. 339

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