Schaum's outline of theory and problems of differential and integral calculus
/ Frank Ayres, Jr. and Elliott Mendelson
- 3rd ed.
- New York : McGraw-Hill, 1990
- 484 p. ill. ; 28 cm.
- Schaum's outline series .
Cover title: Theory and problems of differential and integral calculus. Spine title: Calculus. Includes index.
1. Linear coordinate systems 2. Absolute value 3. Inequalities 4. Rectangular coordinate systems 5. Lines 6. Circles 7. Equations and their graphs 8. Functions 9. Limits 10. Continuity 11. The derivative 12. Rules for differentiating functions 13. Implicit differentiation 14. Tangent and normal lines 15. Law of the mean 16. Increasing and decreasing functions 17. Maximum and minimum values 18. Curve sketching 19. Concavity 20. Symmetry 21. Review of trigonometry 22. Differentiation of trigonometric functions 23. Inverse trigonometric functions 24. Rectilinear and circular motion 25. Related rates 26. Differentials 27. Newton's method 28. Antiderivatives 29. The definite integral 30. Area under a curve 31. The fundamental theorem of calculus 32. The natural logarithm 33. Exponential and logarithmic functions 34. L'hopital's rule 35. Exponential growth and decay 36. Applications of integration i: area and arc length 37. Applications of integration ii: volume 38. Techniques of integration i: integration by parts 39. Techniques of integration ii: trigonometric integrands and trigonometric substitutions 40. Techniques of integration iii: integration by partial fractions 41. Miscellaneous substitutions 42. Improper integrals 43. Applications of integration ii: area of a surface of revolution 44. Parametric representation of curves 45. Curvature 46. Plane vectors 47. Curvilinear motion 48. Polar coordinates 49. Infinite sequences 50. Infinite series 51. Series with positive terms 52. The integral test 53. Comparison tests 54. Alternating series 55. Absolute and conditional convergence 56. The ratio test 57. Power series 58. Taylor and maclaurin series 59. Taylor's formual with remainder 60. Partial derivatives 61. Total differential 62. Differentiability 63. Chain rules 64. Space vectors 65. Surface and curves in space 66. Directional derivatives 67. Maximum and minimum values 68. Vector differentiation and integration 69. Double and iterated integrals 70. Centroids and moments of inertia of plane areas 71. Double integration applied to volume under a surface and the area of a curved surface 72. Triple integrals 73. Masses of variable density 74. Differential equations of first and second order