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
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