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## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
Steven G Krantz |

ISBN: | 9780071743631 0071743634 |

OCLC Number: | 692664068 |

Description: | xiv, 398 pages : illustrations ; 23 cm. |

Contents: | Preface -- How to use this book -- Chapter 1: Basics -- 1-0: Introductory remarks -- 1-1: Number systems -- 1-2: Coordinates in one dimension -- 1-3: Coordinates in two dimensions -- 1-4: Slope of a line in the plane -- 1-5: Equation of a line -- 1-6: Loci in the plane -- 1-7: Trigonometry -- 1-8: Sets and functions -- 1-8-1: Examples of functions of a real variable -- 1-8-2: Graphs of functions -- 1-8-3: Plotting the graph of a function -- 1-8-4: Composition of functions -- 1-8-5: Inverse of a function -- 1-9: Few words about logarithms and exponentials -- Quiz -- Chapter 2: Foundations Of Calculus -- 2-1: Limits -- 2-1-1: One-sided limits -- 2-2: Properties of limits -- 2-3: Continuity -- 2-4: Derivative -- 2-5: Rules for calculating derivatives -- 2-5-1: Derivative of an inverse -- 2-6: Derivative as a rate of change -- Quiz -- Chapter 3: Applications Of The Derivative -- 3-1: Graphing of functions -- 3-2: Maximum/minimum problems -- 3-3: Related rates -- 3-4: Falling bodies -- Quiz -- Chapter 4: Integral -- 4-0: Introduction -- 4-1: Antiderivatives and indefinite integrals -- 4-1-1: Concept of antiderivative -- 4-1-2: Indefinite integral -- 4-2: Area -- 4-3: Signed area -- 4-4: Area between two curves -- 4-5: Rules of integration -- 4-5-1: Linear properties -- 4-5-2: Additivity -- Quiz -- Chapter 5: Indeterminate Forms -- 5-1: I'Hopital's Rule -- 5-1-1: Introduction -- 5-1-2: I'Hopital's Rule -- 5-2: Other indeterminate forms -- 5-2-1: Introduction -- 5-2-2: Writing a product as a quotient -- 5-2-3: Use of the logarithm -- 5-2-4: Putting terms over a common denominator -- 5-2-5: Other algebraic manipulations -- 5-3: Improper integrals: a first look -- 5-3-1: Introduction -- 5-3-2: Integrals with infinite integrands -- 5-3-3: Application to area -- 5-4: More on improper integrals -- 5-4-1: Introduction -- 5-4-2: Integral on an infinite interval -- 5-4-3: Some applications -- Quiz. Chapter 6: Transcendental Functions -- 6-0: Introductory remarks -- 6-1: Logarithm basics -- 6-1-1: New approach to logarithms -- 6-1-2: Logarithm function and the derivative -- 6-2: Exponential basics -- 6-2-1: Facts about the exponential function -- 6-2-2: Calculus properties of the exponential -- 6-2-3: Number e -- 6-3: Exponentials with arbitrary bases -- 6-3-1: Arbitrary powers -- 6-3-2: Logarithms with arbitrary bases -- 6-4: Calculus with logs and exponentials to arbitrary bases -- 6-4-1: Differentiation and integration of log(a)x and a(x) -- 6-4-2: Graphing of logarithmic and exponential functions -- 6-4-3: Logarithmic differentiation -- 6-5: Exponential growth and decay -- 6-5-1: Differential equation -- 6-5-2: Bacterial growth -- 6-5-3: Radioactive decay -- 6-5-4: Compound interest -- 6-6: Inverse trigonometric functions -- 6-6-1: Introductory remarks -- 6-6-2: Inverse sine and cosine -- 6-6-3: Inverse tangent function -- 6-6-4: Integrals in which inverse trigonometric functions arise -- 6-6-5: Other inverse trigonometric functions -- 6-6-6: Example involving inverse trigonometric functions -- Quiz -- Chapter 7: Methods Of Integration -- 7-1: Integration by parts -- 7-2: Partial fractions -- 7-2-1: Introductory remarks -- 7-2-2: Products of linear factors -- 7-2-3: Quadratic factors -- 7-3: Substitution -- 7-4: Integrals of trigonometric expressions -- Quiz -- Chapter 8: Applications Of The Integral -- 8-1: Volumes by slicing -- 8-1-0: Introduction -- 8-1-1: Basic strategy -- 8-1-2: Examples -- 8-2: Volumes of solids of revolution -- 8-2-0: Introduction -- 8-2-1: Method of washers -- 8-2-2: Method of cylindrical shells -- 8-2-3: Different axes -- 8-3: Work -- 8-4: Averages -- 8-5: Arc length and surface area -- 8-5-1: Arc length -- 8-5-2: Surface area -- 8-6: Hydrostatic pressure -- 8-7: Numerical methods of integration -- 8-7-1: Trapezoid rule -- 8-7-2: Simpson's rule -- Quiz -- Final exam -- Answers to quizzes and final exam -- Bibliography -- Index. |

Series Title: | McGraw-Hill "Demystified" series. |

Responsibility: | Steven Krantz. |

### Abstract:

Hard stuff made easy! Your practical, self-paced guide to calculus.
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