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CITATION

Ayres, Frank and Mendelson, Elliott. Schaum's Outline of Calculus, 6th Edition. US: McGraw-Hill, 2012.

Schaum's Outline of Calculus, 6th Edition

Authors: Frank Ayres and Elliott Mendelson

Published:  November 2012

eISBN: 9780071795548 0071795545 | ISBN: 9780071795531
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  • Cover
  • Title Page
  • Copyright Page
  • Contents
  • Chapter 1 Linear Coordinate Systems. Absolute Value. Inequalities
  • Linear Coordinate System
  • Finite Intervals
  • Infinite Intervals
  • Inequalities
  • Chapter 2 Rectangular Coordinate Systems
  • Coordinate Axes
  • Coordinates
  • Quadrants
  • The Distance Formula
  • The Midpoint Formulas
  • Proofs of Geometric Theorems
  • Chapter 3 Lines
  • The Steepness of a Line
  • The Sign of the Slope
  • Slope and Steepness
  • Equations of Lines
  • A Point–Slope Equation
  • Slope–Intercept Equation
  • Parallel Lines
  • Perpendicular Lines
  • Chapter 4 Circles
  • Equations of Circles
  • The Standard Equation of a Circle
  • Chapter 5 Equations and Their Graphs
  • The Graph of an Equation
  • Parabolas
  • Ellipses
  • Hyperbolas
  • Conic Sections
  • Chapter 6 Functions
  • Chapter 7 Limits
  • Limit of a Function
  • Right and Left Limits
  • Theorems on Limits
  • Infinity
  • Chapter 8 Continuity
  • Continuous Function
  • Chapter 9 The Derivative
  • Delta Notation
  • The Derivative
  • Notation for Derivatives
  • Differentiability
  • Chapter 10 Rules for Differentiating Functions
  • Differentiation
  • Composite Functions. The Chain Rule
  • Alternative Formulation of the Chain Rule
  • Inverse Functions
  • Higher Derivatives
  • Chapter 11 Implicit Differentiation
  • Implicit Functions
  • Derivatives of Higher Order
  • Chapter 12 Tangent and Normal Lines
  • The Angles of Intersection
  • Chapter 13 Law of the Mean. Increasing and Decreasing Functions
  • Relative Maximum and Minimum
  • Increasing and Decreasing Functions
  • Chapter 14 Maximum and Minimum Values
  • Critical Numbers
  • Second Derivative Test for Relative Extrema
  • First Derivative Test
  • Absolute Maximum and Minimum
  • Tabular Method for Finding the Absolute Maximum and Minimum
  • Chapter 15 Curve Sketching. Concavity. Symmetry
  • Concavity
  • Points of Inflection
  • Vertical Asymptotes
  • Horizontal Asymptotes
  • Symmetry
  • Inverse Functions and Symmetry
  • Even and Odd Functions
  • Hints for Sketching the Graph of y = f (x)
  • Chapter 16 Review of Trigonometry
  • Angle Measure
  • Directed Angles
  • Sine and Cosine Functions
  • Chapter 17 Differentiation of Trigonometric Functions
  • Continuity of cos x and sin x
  • Graph of sin x
  • Graph of cos x
  • Other Trigonometric Functions
  • Derivatives
  • Other Relationships
  • Graph of y = tan x
  • Graph of y = sec x
  • Angles Between Curves
  • Chapter 18 Inverse Trigonometric Functions
  • The Derivative of sin[sup(-1)] x
  • The Inverse Cosine Function
  • The Inverse Tangent Function
  • Chapter 19 Rectilinear and Circular Motion
  • Rectilinear Motion
  • Motion Under the Influence of Gravity
  • Circular Motion
  • Chapter 20 Related Rates
  • Chapter 21 Differentials. Newton’s Method
  • The Differential
  • Newton’s Method
  • Chapter 22 Antiderivatives
  • Laws for Antiderivatives
  • Chapter 23 The Definite Integral. Area Under a Curve
  • Sigma Notation
  • Area Under a Curve
  • Properties of the Definite Integral
  • Chapter 24 The Fundamental Theorem of Calculus
  • Mean-Value Theorem for Integrals
  • Average Value of a Function on a Closed Interval
  • Fundamental Theorem of Calculus
  • Change of Variable in a Definite Integral
  • Chapter 25 The Natural Logarithm
  • The Natural Logarithm
  • Properties of the Natural Logarithm
  • Chapter 26 Exponential and Logarithmic Functions
  • Properties of e[sup(x)]
  • The General Exponential Function
  • General Logarithmic Functions
  • Chapter 27 L’Hôpital’s Rule
  • L’Hôpital’s Rule
  • Indeterminate Type 0 · ∞
  • Indeterminate Type ∞ - ∞
  • Indeterminate Types 0[sup(0)], ∞[sup(0)], and 1∞
  • Chapter 28 Exponential Growth and Decay
  • Half-Life
  • Chapter 29 Applications of Integration I: Area and Arc Length
  • Area Between a Curve and the y Axis
  • Areas Between Curves
  • Arc Length
  • Chapter 30 Applications of Integration II: Volume
  • Disk Formula
  • Washer Method
  • Cylindrical Shell Method
  • Difference of Shells Formula
  • Cross-Section Formula (Slicing Formula)
  • Chapter 31 Techniques of Integration I: Integration by Parts
  • Chapter 32 Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions
  • Trigonometric Integrands
  • Trigonometric Substitutions
  • Chapter 33 Techniques of Integration III: Integration by Partial Fractions
  • Method of Partial Fractions
  • Chapter 34 Techniques of Integration IV: Miscellaneous Substitutions
  • Chapter 35 Improper Integrals
  • Infinite Limits of Integration
  • Discontinuities of the Integrand
  • Chapter 36 Applications of Integration III: Area of a Surface of Revolution
  • Chapter 37 Parametric Representation of Curves
  • Parametric Equations
  • Arc Length for a Parametric Curve
  • Chapter 38 Curvature
  • Derivative of Arc Length
  • Curvature
  • The Radius of Curvature
  • The Circle of Curvature
  • The Center of Curvature
  • The Evolute
  • Chapter 39 Plane Vectors
  • Scalars and Vectors
  • Sum and Difference of Two Vectors
  • Components of a Vector
  • Scalar Product (or Dot Product)
  • Scalar and Vector Projections
  • Differentiation of Vector Functions
  • Chapter 40 Curvilinear Motion
  • Velocity in Curvilinear Motion
  • Acceleration in Curvilinear Motion
  • Tangential and Normal Components of Acceleration
  • Chapter 41 Polar Coordinates
  • Polar and Rectangular Coordinates
  • Some Typical Polar Curves
  • Angle of Inclination
  • Points of Intersection
  • Angle of Intersection
  • The Derivative of the Arc Length
  • Curvature
  • Chapter 42 Infinite Sequences
  • Infinite Sequences
  • Limit of a Sequence
  • Monotonic Sequences
  • Chapter 43 Infinite Series
  • Geometric Series
  • Chapter 44 Series with Positive Terms. The Integral Test. Comparison Tests
  • Series of Positive Terms
  • Chapter 45 Alternating Series. Absolute and Conditional Convergence. The Ratio Test
  • Alternating Series
  • Chapter 46 Power Series
  • Power Series
  • Uniform Convergence
  • Chapter 47 Taylor and Maclaurin Series. Taylor’s Formula with Remainder
  • Taylor and Maclaurin Series
  • Applications of Taylor’s Formula with Remainder
  • Chapter 48 Partial Derivatives
  • Functions of Several Variables
  • Limits
  • Continuity
  • Partial Derivatives
  • Partial Derivatives of Higher Order
  • Chapter 49 Total Differential.Differentiability.Chain Rules
  • Total Differential
  • Differentiability
  • Chain Rules
  • Implicit Differentiation
  • Chapter 50 Space Vectors
  • Vectors in Space
  • Direction Cosines of a Vector
  • Determinants
  • Vector Perpendicular to Two Vectors
  • Vector Product of Two Vectors
  • Triple Scalar Product
  • Triple Vector Product
  • The Straight Line
  • The Plane
  • Chapter 51 Surfaces and Curves in Space
  • Planes
  • Spheres
  • Cylindrical Surfaces
  • Ellipsoid
  • Elliptic Paraboloid
  • Elliptic Cone
  • Hyperbolic Paraboloid
  • Hyperboloid of One Sheet
  • Hyperboloid of Two Sheets
  • Tangent Line and Normal Plane to a Space Curve
  • Tangent Plane and Normal Line to a Surface
  • Surface of Revolution
  • Chapter 52 Directional Derivatives. Maximum and Minimum Values
  • Directional Derivatives
  • Relative Maximum and Minimum Values
  • Absolute Maximum and Minimum Values
  • Chapter 53 Vector Differentiation and Integration
  • Vector Differentiation
  • Space Curves
  • Surfaces
  • The Operation ∇
  • Divergence and Curl
  • Integration
  • Line Integrals
  • Chapter 54 Double and Iterated Integrals
  • The Double Integral
  • The Iterated Integral
  • Chapter 55 Centroids and Moments of Inertia of Plane Areas
  • Plane Area by Double Integration
  • Centroids
  • Moments of Inertia
  • Chapter 56 Double Integration Applied to Volume Under a Surface and the Area of a Curved Surface
  • Chapter 57 Triple Integrals
  • Cylindrical and Spherical Coordinates
  • The Triple Integral
  • Evaluation of Triple Integrals
  • Centroids and Moments of Inertia
  • Chapter 58 Masses of Variable Density
  • Chapter 59 Differential Equations of First and Second Order
  • Separable Differential Equations
  • Homogeneous Functions
  • Integrating Factors
  • Second-Order Equations
  • Appendix A
  • Appendix B
  • Index