Calculus Demystified 2nd Edition by Steven Krantz 0071743642 9780071743648

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ISBN 10: 0071743642 

ISBN 13: 9780071743648

Author: Steven G. Krantz

Calculate this: learning CALCULUS just got a whole lot easier! Stumped trying to understand calculus? Calculus Demystified, Second Edition, will help you master this essential mathematical subject. Written in a step-by-step format, this practical guide begins by covering the basics–number systems, coordinates, sets, and functions. You’ll move on to limits, derivatives, integrals, and indeterminate forms. Transcendental functions, methods of integration, and applications of the integral are also covered. Clear examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key concepts. It’s a no-brainer! You’ll get: Applications of the derivative and the integral Rules of integration Coverage of improper integrals An explanation of calculus with logarithmic and exponential functions Details on calculation of work, averages, arc length, and surface area Simple enough for a beginner, but challenging enough for an advanced student, Calculus Demystified, Second Edition, is one book you won’t want to function without!

Table of contents:

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 The Slope of a Line in the Plane
1.5 The 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 The Inverse of a Function
1.9 A 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 The Derivative
2.5 Rules for Calculating Derivatives
 2.5.1 The Derivative of an Inverse
2.6 The 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: The Integral
4.0 Introduction
4.1 Antiderivatives and Indefinite Integrals
 4.1.1 The Concept of Antiderivative
 4.1.2 The Indefinite Integral
4.2 Area
4.3 Signed Area
4.4 The 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‘Hôpital‘s Rule
 5.1.1 Introduction
 5.1.2 I‘Hôpital‘s Rule
5.2.1 Introduction
5.2.2 Writing a Product as a Quotient
5.2.3 The 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 An Application to Area
5.4 More on Improper Integrals
 5.4.1 Introduction
 5.4.2 The 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 A New Approach to Logarithms
 6.1.2 The 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 The 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 logₐx and aˣ
 6.4.2 Graphing of Logarithmic and Exponential Functions
 6.4.3 Logarithmic Differentiation
6.5 Exponential Growth and Decay
 6.5.1 A 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 The Inverse Tangent Function
 6.6.4 Integrals in Which Inverse Trigonometric Functions Arise
 6.6.5 Other Inverse Trigonometric Functions
 6.6.6 An 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 The Basic Strategy
8.2 Volumes of Solids of Revolution
 8.2.0 Introduction
 8.2.1 The Method of Washers
 8.2.2 The 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 The Trapezoid Rule
 8.7.2 Simpson’s Rule

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