Schaum's Outline of Calculus, Seventh Edition

by Elliott Mendelson

Overview

Study smarter and stay on top of your calculus course with the bestselling Schaum’s Outline—now with the NEW Schaum’s app and website!

Schaum’s Outline of Calculus, Seventh Edition is the go-to study guide for hundreds of thousands of high school and college students enrolled in calculus courses—including Calculus, Calculus II, Calculus III, AP Calculus and Precalculus. With an outline format that facilitates quick and easy review, Schaum’s Outline of Calculus, Seventh Edition helps you understand basic concepts and get the extra practice you need to excel in these courses.

Chapters include Linear Coordinate Systems, Functions, Limits, Rules for Differentiating Functions, Law of the Mean, Inverse Trigonometric Functions, The Definite Integral, Space Vectors, Directional Derivatives, and much, much more.

Features:

• NEW to this edition: the new Schaum’s app and website!
• 1,105 problems solved step by step
• 30 problem-solving videos online
• Outline format supplies a concise guide to the standard college course in calculus
• Clear, concise explanations covers all course fundamentals
• Hundreds of additional practice problems
• Supports the major leading textbooks in calculus
• Appropriate for the following courses: Calculus I, Calculus II, Calculus III, AP Calculus, Precalculus
  
  
  

Product Details

ISBN-13:	9781264258338
Publisher:	McGraw Hill LLC
Publication date:	10/22/2021
Edition description:	7th ed.
Pages:	592
Product dimensions:	8.10(w) x 10.80(h) x 1.10(d)

About the Author

Elliott Mendelson, Ph.D., is Professor of Mathematics at Queens College in New York City.

Table of Contents

Preface
Chapter 1 Linear Coordinate Systems. Absolute Value. Inequalities.
   Linear Coordinate System
   Finite Intervals
   Infinite Intervals
   Inequalities
   Solved Problems
   Supplementary Problems
Chapter 2 Rectangular Coordinate Systems
   Coordinate Axes
   Coordinates
   Quadrants
   The Distance Formula
   The Midpoint Formulas
   Proofs of Geometric Theorems
   Solved Problems
   Supplementary Problems
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
   Solved Problems
   Supplementary Problems
Chapter 4 Circles
   Equations of Circles
   The Standard Equation of a Circle
   Solved Problems
   Supplementary Problems
Chapter 5 Equations and Their Graphs
   The Graph of an Equation
   Parabolas
   Ellipses
   Hyperbolas
   Conic Sections
   Solved Problems
   Supplementary Problems
Chapter 6 Functions
   Solved Problems
   Supplementary Problems
Chapter 7 Limits
   Limit of a Function
   Right and Left Limits
   Theorems on Limits
   Infinity
   Solved Problems
   Supplementary Problems
Chapter 8 Continuity
   Continuous Function
   Solved Problems
   Supplementary Problems
Chapter 9 The Derivative
   Delta Notation
   The Derivative
   Notation for Derivatives
   Differentiability
   Solved Problems
   Supplementary Problems
Chapter 10 Rules for Differentiating Functions
   Differentiation
   Composite Functions. The Chain Rule.
   Chain Rule
   Alternative Formulation of the Chain Rule
   Inverse Functions
   Higher Derivatives
   Solved Problems
   Supplementary Problems
Chapter 11 Implicit Differentiation
   Implicit Functions
   Derivatives of Higher Order
   Solved Problems
   Supplementary Problems
Chapter 12 Tangent and Normal Lines
   The Angles of Intersection
   Solved Problems
   Supplementary Problems
Chapter 13 Law of the Mean. Increasing and Decreasing Functions.
   Relative Maximum and Minimum
   Increasing and Decreasing Functions
   Solved Problems
   Supplementary Problems
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
   Solved Problems
   Supplementary Problems
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 G of y = f (x)
   Solved Problems
   Supplementary Problems
Chapter 16 Review of Trigonometry
   Angle Measure
   Directed Angles
   Sine and Cosine Functions
   Solved Problems
   Supplementary Problems
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
   Solved Problems
   Supplementary Problems
Chapter 18 Inverse Trigonometric Functions
   The Derivative of sin−1 x
   The Inverse Cosine Function
   The Inverse Tangent Function
   Solved Problems
   Supplementary Problems
Chapter 19 Rectilinear and Circular Motion
   Rectilinear Motion
   Motion Under the Influence of Gravity
   Circular Motion
   Solved Problems
   Supplementary Problems
Chapter 20 Related Rates
   Solved Problems
   Supplementary Problems
Chapter 21 Differentials. Newton’s Method.
   The Differential
   Definition
   Newton’s Method
   Solved Problems
   Supplementary Problems
Chapter 22 Antiderivatives
   Laws for Antiderivatives
   Solved Problems
   Supplementary Problems
Chapter 23 The Definite Integral. Area Under a Curve.
   Sigma Notation
   Area Under a Curve
   Properties of the Definite Integral
   Solved Problems
   Supplementary Problems
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
   Solved Problems
   Supplementary Problems
Chapter 25 The Natural Logarithm
   The Natural Logarithm
   Definition
   Properties of the Natural Logarithm
   Solved Problems
   Supplementary Problems
Chapter 26 Exponential and Logarithmic Functions
   Definition
   Properties of ex
   The General Exponential Function
   General Logarithmic Functions
   Solved Problems
   Supplementary Problems
Chapter 27 L’Hôpital’s Rule
   L’Hôpital’s Rule
   Indeterminate Type 0 · ∞
   Indeterminate Type ∞ − ∞
   Indeterminate Types 00, ∞0, and 1∞
   Solved Problems
   Supplementary Problems
Chapter 28 Exponential Growth and Decay
   Half-Life
   Solved Problems
   Supplementary Problems
Chapter 29 Applications of Integration I: Area and Arc Length
   Area Between a Curve and the Y-Axis
   Areas Between Curves
   Arc Length
   Solved Problems
   Supplementary Problems
Chapter 30 Applications of Integration II: Volume
   Disk Formula
   Washer Method
   Cylindrical Shell Method
   Difference of Shells Formula
   Cross-Section Formula (Slicing Formula)
   Solved Problems
   Supplementary Problems
Chapter 31 Techniques of Integration I: Integration by Parts
   Solved Problems
   Supplementary Problems
Chapter 32 Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions
   Trigonometric Integrands
   Trigonometric Substitutions
   Solved Problems
   Supplementary Problems
Chapter 33 Techniques of Integration III: Integration by Partial Fractions
   Method of Partial Fractions
   Solved Problems
   Supplementary Problems
Chapter 34 Techniques of Integration IV: Miscellaneous Substitutions
   Solved Problems
   Supplementary Problems
Chapter 35 Improper Integrals
   Infinite Limits of Integration
   Discontinuities of the Integrand
   Solved Problems
   Supplementary Problems
Chapter 36 Applications of Integration III: Area of a Surface of Revolution
   Solved Problems
   Supplementary Problems
Chapter 37 Parametric Representation of Curves
   Parametric Equations
   Arc Length for a Parametric Curve
   Solved Problems
   Supplementary Problems
Chapter 38 Curvature
   Derivative of Arc Length
   Curvature
   The Radius of Curvature
   The Circle of Curvature
   The Center of Curvature
   The Evolute
   Solved Problems
   Supplementary Problems
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
   Solved Problems
   Supplementary Problems
Chapter 40 Curvilinear Motion
   Velocity in Curvilinear Motion
   Acceleration in Curvilinear Motion
   Tangential and Normal Components of Acceleration
   Solved Problems
   Supplementary Problems
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
   Solved Problems
   Supplementary Problems
Chapter 42 Infinite Sequences
   Infinite Sequences
   Limit of a Sequence
   Monotonic Sequences
   Solved Problems
   Supplementary Problems
Chapter 43 Infinite Series
   Geometric Series
   Solved Problems
   Supplementary Problems
Chapter 44 Series with Positive Terms. The Integral Test. Comparison Tests.
   Series of Positive Terms
   Solved Problems
   Supplementary Problems
Chapter 45 Alternating Series. Absolute and Conditional Convergence. The Ratio Test.
   Alternating Series
   Definition
   Solved Problems
   Supplementary Problems
Chapter 46 Power Series
   Power Series
   Uniform Convergence
   Solved Problems
   Supplementary Problems
Chapter 47 Taylor and Maclaurin Series. Taylor’s Formula with Remainder.
   Taylor and Maclaurin Series
   Applications of Taylor’s Formula with Remainder
   Solved Problems
   Supplementary Problems
Chapter 48 Partial Derivatives
   Functions of Several Variables
   Limits
   Continuity
   Partial Derivatives
   Partial Derivatives of Higher Order
   Solved Problems
   Supplementary Problems
Chapter 49 Total Differential. Differentiability. Chain Rules.
   Total Differential
   Differentiability
   Chain Rules
   Chain Rule (2 → 1)
   Chain Rule (2 → 2)
   Implicit Differentiation
   Solved Problems
   Supplementary Problems
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
   The Straight Line
   The Plane
   Solved Problems
   Supplementary Problems
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
   Solved Problems
   Supplementary Problems
Chapter 52 Directional Derivatives. Maximum and Minimum Values.
   Directional Derivatives
   Relative Maximum and Minimum Values
   Absolute Maximum and Minimum Values
   Solved Problems
   Supplementary Problems
Chapter 53 Vector Differentiation and Integration
   Vector Differentiation
   Space Curves
   Surfaces
   The Operation ∇
   Divergence and Curl
   Integration
   Line Integrals
   Solved Problems
   Supplementary Problems
Chapter 54 Double and Iterated Integrals
   The Double Integral
   The Iterated Integral
   Solved Problems
   Supplementary Problems
Chapter 55 Centroids and Moments of Inertia of Plane Areas
   Plane Area by Double Integration
   Centroids
   Moments of Inertia
   Solved Problems
   Supplementary Problems
Chapter 56 Double Integration Applied to Volume Under a Surface and the Area of a Curved Surface
   Solved Problems
   Supplementary Problems
Chapter 57 Triple Integrals
   Cylindrical and Spherical Coordinates
   The Triple Integral
   Evaluation of Triple Integrals
   Centroids and Moments of Inertia
   Solved Problems
   Supplementary Problems
Chapter 58 Masses of Variable Density
   Solved Problems
   Supplementary Problems
Chapter 59 Differential Equations of First and Second Order
   Separable Differential Equations
   Homogeneous Functions
   Integrating Factors
   Second-Order Equations
   Solved Problems
   Supplementary Problems
Appendix A Trigonometric Formulas
Appendix B Geometric Formulas
Index