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Calculus demystified
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Yavapai College Prescott - LIMBO - Items being donated to other libraries
QA303.2.K74 2003
1 available
QA303.2.K74 2003
1 available
Yavapai College Prescott - LIMBO - Items being donated to other libraries
QA303.2.K74 2011
1 available
QA303.2.K74 2011
1 available
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Contributors
Krantz, Steven G. Author
ISBN
9780071743631
9780071743648
9780071393089
9780071743648
9780071393089
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Table of Contents
From the Book - Regular Print
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 -- 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 -- 3. Applications of the derivative -- 3.1. Graphing of functions -- 3.2. Maximum/minimum problems -- 3.3. Related rates -- 3.4. Falling bodies -- 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 -- 5. Indeterminate forms -- 5.1. l'H^opital's rule -- 5.1.1. Introduction -- 5.1.2. l'H^opital's rule -- 5.2. Other indeterminate forms -- 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 --
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 loga x 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
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
8. Applications of the integral
8.1. Volumes by slicing
8.1.0. Introduction
8.1.1. The basic strategy
8.1.2. Examples
8.2. Volumes of solids and 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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