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This review of standard college courses in calculus has been updated to reflect the latest course scope and sequences. The new edition includes Green's and Stokes' theorems, as well as explanations of tough topics such as delta-epsilon proofs and Reimann Integrals.
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Table of Contents
Schaum's Outline of Calculus, 5ed
1. Linear Coordinate Systems. Absolute Value. Inequalities.
2. Rectangular Coordinate Systems
5. Equations and their Graphs
9. The Derivative
10. Rules for Differentiating Functions
11. Implicit Differentiation
12. Tangent and Normal Lines
13. Law of the Mean. Increasing and Decreasing Functions
14. Maximum and Minimum Values
15. Curve Sketching. Concavity. Symmetry.
16. Review of Trigonometry
17. Differentiation of Trigonometric Functions
18. Inverse Trigonometric Functions
19. Rectilinear and Circular Motion
20. Related Rates
21. Differentials. Newton's Method
23. The Definite Integral. Area under a Curve
24. The Fundamental Theorem of Calculus
25. The Natural Logarithm
26. Exponential and Logarithmic Functions
27. L'Hopital's Rule
28. Exponential Growth and Decay
29. Applications of Integration I: Area and Arc Length
30. Applications of Integration II: Volume
31. Techniques of Integration I: Integration by Parts
32. Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions
33. Techniques of Integration III: Integration by Partial Fractions
34. Techniques of Integration IV: Miscellaneous Substitutions
35. Improper Integrals
36. Applications of Integration III: Area of a Surface of Revolution
37. Parametric Representation of Curves
39. Plane Vectors
40. Curvilinear Motion
41. Polar Coordinates
42. Infinite Sequences
43. Infinite Series
44. Series with Positive Terms. The Integral Test. Comparison Tests
45. Alternating Series. Absolute and Conditional Convergence. The Ratio Test
46. Power Series
47. Taylor and Maclaurin Series. Taylor's Formulas with Remainder
48. Partial Derivatives
49. Total Differential. Differentiability. Chain Rules
50. Space Vectors
51. Surfaces and Curves in Space
52. Directional Derivatives. Maximum and Minimum Values.
53. Vector Differentiation and Integration
54. Double and Iterated Integrals
55. Centroids and Moments of Inertia of Plane Areas
56. Double Integration Applied to Volume under a Surface and the Area of a Curved Surface
57. Triple Integrals
58. Masses of Variable Density
59. Differential Equations of First and Second Order