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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
Half-Life

• 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
Contents

• 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

• ##### Math Books of CALCULUS

Student Solutions Manual for Stewart Essential Calculus (2E)
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