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Schaums Outlines Calculus Fifth Edition by Frank Ayres, Jr. and Elliott Mendelson

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Schaumes Outlines Calculus Fifth Edition written by Frank Ayres, Jr., PhD. , Formerly Professor and Head of the Department of Mathematics, Dickinson College and Elliott Mendelson, PhD. , Professor of Mathematics, Queens College.

Schaumes Outlines Calculus Fifth Edition written by Frank Ayres, Jr., PhD. and Elliott Mendelson, PhD. cover the following topics.

  • 1. Linear Coordinate Systems. Absolute Value. Inequalities
    Linear Coordinate System, Finite Intervals, Infinite Intervals, Inequalities

  • 2. Rectangular Coordinate Systems
    Coordinate Axes, Coordinates, Quadrants, The Distance Formula, Midpoint Formulas, Proofs of Geometric Theorems

  • 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

  • 4. Circles
    Equations of Circles, The Standard Equation of a Circle

  • 5. Equations and Their Graphs
    The Graph of an Equation, Parabolas, Ellipses, Hyperbolas, Conic Sections

  • 6. Functions

  • 7. Limits
    Limit of a Function Right and Left Limits Theorems on Limits Infinity

  • 8. Continuity
    Continuous Function

  • 9. The Derivative
    Delta Notation, The Derivative, Notation for Derivatives, Differentiability

  • 10. Rules for Differentiating Functions
    Differentiation, Composite Functions, The Chain Rule, Alternative Formulation of the Chain Rule, Inverse Functions, Higher Derivatives

  • 11. Implicit Differentiation
    Implicit Functions, Derivatives of Higher Order

  • 12. Tanglmt and Normal Lines
    The Angles of Intersection

  • 13. Law Ilf the Mean. Increasing and Decreasing Functions
    Relative Maximum and Minimum, Increasing and Decreasing Functions

  • 14. Maximum and Minimum Values
    Critical Number,s Second Derivative Test for Relative Extrema, First Derivative, Test Absolute Maximum and Minimum, Tabular Method for Finding the Absolute Maximum and Minimum

  • 15. Curve Sketching. Concavity, Symmetry
    Concavity, Points of Inflection, Vertical Asymptotes, Symmetry, Inverse Functions and Symmetry, Even and Odd Functions, Hints for Sketching the Graph of y = f (x)

  • 16. Review of Trigonometry Angle Measure, Directed Angles, Sine and Cosine Functions

  • 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

  • 18. Invelse Trigonometric Functions
    The Derivative of sin^-I x, The Inverse Cosine Function, The Inverse Tangent Function

  • 19. Rectilinear and Circular Motion
    Rectilinear Motion, Motion Under the Influence of Gravity, Circular Motion

  • 20. Related Rates

  • 21. Diffe!rentials. Newton's Method
    The Differential Newtons Method

  • 22. Antiderivatives
    Laws for Antiderivatives

  • 23. The Definite Integral. Area Under a Curve
    Sigma Notation, Area Under a Curve, Properties of the Definite Integral

  • 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

  • 25. The Natural Logarithm
    The Natural Logarithm, Properties of the Natural Logarithm

  • 26. Exponential and Logarithmic Functions
    Properties of e^x, The General Exponential Function, General Logarithmic Functions

  • 27. L'Hopital's Rule
    L'Hopital's Rule, Indeterminate Type 0 to Infintiy, Indeterminate Type Infinity to -Infinity, Indeterminate Type 0^0, Infinity^0 and 1^Infinity

  • 28. Exponential Growth and Decay

  • 29. Applications of Integration I: Area and Arc Length
    Area Between a Curve and the y Axis, Areas Between Curves Arc Length

  • 30. Applications of Integration II: Volume Disk Formula, Washer Method, Cylindrical Shell Method, Difference of Shells Formula, Cross-Section Formula (Slicing Formula)

  • 31. Techniques of Integration I: Integration by Parts

  • 32. Techniques of Integration II:Trigonometric Integrands and
    Trigonometric Substitutions, Trigonometric Integrands Trigonometric Substitutions

  • 33. Techniques of Integration III: Integration by Partial Fractions
    Method of Partial Fractions

  • 34. Techniques of Integration IV: Miscellaneous Substitutions

  • 35. Improper Integrals
    Infinite Limits of Integration, Discontinuities of the Integrand

  • 36. Applilcations of Integration III: Area of a Surface of Revolution

  • 37. Parametric Representation of Curves
    Parametric Equations Arc Length for a Parametric Curve

  • 38. Curvature Derivative of Arc Length, Curvature, The Radius of Curvature, The Circle of Curvature, The Center of Curvature, The Evolute

  • 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

  • 40. Curvilinear Motion
    Velocity in Curvilinear Motion, Acceleration in Curvilinear Motion, Tangential and Normal Components of Acceleration

  • 41. Polar Coordinates
    Polar and Rectangular Coordinates, Inclination Points of Intersection of the Arc Length Curvature

  • 42. Infinite Sequences
    Some Typical Polar Curves Angle of Angle of Intersection, The Derivative, Infinite Sequences, Limit of a Sequence, Monotonic Sequences

  • 43. Infinite Series
    Geometric Series

  • 44. Series with Positive Terms. The Integral Test. Comparison Tests
    Series of Positive Terms

  • 45. Altel'nating Series. Absolute and Conditional Convergence.
    The Ratio Test, Alternating Series

  • 46. Power Series
    Power Series, Uniform Convergence

  • 47. Taylor and Maclaurin Series. Taylor's Formula with Remainder
    Taylor and Maclaurin Series, Applications of Taylor's Fonnula with Remainder

  • 48. Partial Derivatives
    Functions of Several Variables, Limits, Continuity, Partial Derivatives, Partial Derivatives of Higher Order

  • 49. Total Differential.Differentiability.Chain Rules
    Total Differential, Differentiability, Chain Rules, Implicit Differentiation

  • 50. Space Vecturs
    Vectors in Space, Direction Cosines of a Vector, Detenninants Vector, Perpendicular to Two Vectors, Vector Product of Two Vectors, Triple Scalar Product, Triple Vector Product, The Straight Line The Plane

  • 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 Nonnal Plane to a Space Curve, Tangent Plane and Nonnal Line to a Surface, Surface of Revolution

  • 52. Directional Derivatives. Maximum and Minimum Values
    Directional Derivatives, Relative Maximum and Minimum Values, Absolute Maximum and Minimum Values

  • 53. Vector Differentiation and Integration
    Vector Differentiation, Divergence and Curl, Space Curves, Surfaces The Operation V, Integration, Line Integrals

  • 54. Double and Iterated Integrals The Double Inte~l The Iterated Integral

  • 55. Centroids and Moments of Iriertia of Plane Areas
    Plane Area by Double Integration, Centroids, Moments of Inertia

  • 56. Double Integration Applied to Volume Under a Surface and the Area of a Curved Surface

  • 57. Triple Integrals
    Cylindrical and Spherical Coordinates, The Triple Integral Evaluation of Triple Integrals, Centroids and Moments of Inertia

  • 58. Masses of Variable Density

  • 59. Differential Equations of First and Second Order
    Separable Differential Equations, Homogeneous Functions, Integrating Factors, Second Order Equations

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