SCHAUM'S outlines Calculus

Cover
Title Page
Copyright Page
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
		Notation
	Higher Derivatives
		Notation
	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
		Case {+, -}
		Case {-, +}
		Cases {+, +} and {-, -}
	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
		Definition
	The General Exponential Function
		Definition
	General Logarithmic Functions
		Definition
	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
		Case I
		Case II
		Case III
		Case IV
	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
		(37.1) First Derivative
		(37.2) Second Derivative
	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 ã 1)
	Chain Rule (2 ã 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
		Triple Vector 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