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Alignment: Schaum’s Outlines • Calculus • Sixth Edition

Use Nagwa in conjunction with your preferred textbook. The recommended lessons from Nagwa for each section of this textbook are provided below. This alignment is not affiliated with, sponsored by, or endorsed by the publisher of the referenced textbook. Nagwa is a registered trademark of Nagwa Limited. All other trademarks and registered trademarks are the property of their respective owners.

Table of 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⁻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^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 0⁰, ∞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 Trigonometric Formulas
  • Appendix B Geometric Formulas
  • Index