Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/21

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CONTENTS
xv
  1. SECTIONPAGE
  2. 212.
    Volumes of solids of revolution
    ................................................................................................................................................................................................................................................................................................................................................................................................
    377
  3. 213.
    Areas of surfaces of revolution
    ................................................................................................................................................................................................................................................................................................................................................................................................
    381
  4. 214.
    Miscellaneous applications
    ................................................................................................................................................................................................................................................................................................................................................................................................
    385
  5. CHAPTER XXIX
    SUCCESSIVE AND PARTIAL INTEGRATION

  6. 215.
    Successive integration
    ................................................................................................................................................................................................................................................................................................................................................................................................
    393
  7. 216.
    Partial integration
    ................................................................................................................................................................................................................................................................................................................................................................................................
    395
  8. 217.
    Definite double integral. Geometric interpretation
    ................................................................................................................................................................................................................................................................................................................................................................................................
    396
  9. 218.
    Value of a definite double integral over a region
    ................................................................................................................................................................................................................................................................................................................................................................................................
    400
  10. 219.
    Plane area as a definite double integral. Rectangular coördinates
    ................................................................................................................................................................................................................................................................................................................................................................................................
    402
  11. 220.
    Plane area as a definite double integral. Polar coördinates
    ................................................................................................................................................................................................................................................................................................................................................................................................
    406
  12. 221.
    Moment of area
    ................................................................................................................................................................................................................................................................................................................................................................................................
    408
  13. 222.
    Center of area
    ................................................................................................................................................................................................................................................................................................................................................................................................
    408
  14. 223.
    Moment of inertia. Plane areas
    ................................................................................................................................................................................................................................................................................................................................................................................................
    410
  15. 224.
    Polar moment of inertia. Rectangular coördinates
    ................................................................................................................................................................................................................................................................................................................................................................................................
    410
  16. 225.
    Polar moment of inertia. Polar coördinates
    ................................................................................................................................................................................................................................................................................................................................................................................................
    411
  17. 226.
    General method for finding the areas of surfaces
    ................................................................................................................................................................................................................................................................................................................................................................................................
    413
  18. 227.
    Volumes found by triple integration
    ................................................................................................................................................................................................................................................................................................................................................................................................
    417
  19. CHAPTER XXX
    ORDINARY DIFFERENTIAL EQUATIONS

  20. 228.
    Differential equations. Order and degree
    ................................................................................................................................................................................................................................................................................................................................................................................................
    421
  21. 229.
    Solutions of differential equations
    ................................................................................................................................................................................................................................................................................................................................................................................................
    422
  22. 230.
    Verifications of solutions
    ................................................................................................................................................................................................................................................................................................................................................................................................
    423
  23. 231.
    Differential equations of the first order and of the first degree
    ................................................................................................................................................................................................................................................................................................................................................................................................
    424
  24. 232.
    Differential equations of the order and of the first degree
    ................................................................................................................................................................................................................................................................................................................................................................................................
    432
  25. CHAPTER XXXI
    INTEGRAPH. APPROXIMATE INTEGRATION. TABLE OF INTEGRALS

  26. 233.
    Mechanical integration
    ................................................................................................................................................................................................................................................................................................................................................................................................
    443
  27. 234.
    Integral curves
    ................................................................................................................................................................................................................................................................................................................................................................................................
    443
  28. 235.
    The integraph
    ................................................................................................................................................................................................................................................................................................................................................................................................
    445
  29. 236.
    Polar planimeter
    ................................................................................................................................................................................................................................................................................................................................................................................................
    446
  30. 237.
    Area swept over by a line
    ................................................................................................................................................................................................................................................................................................................................................................................................
    446
  31. 238.
    Approximate integration
    ................................................................................................................................................................................................................................................................................................................................................................................................
    448
  32. 239.
    Trapezoidal rule
    ................................................................................................................................................................................................................................................................................................................................................................................................
    448
  33. 240.
    Simpson's rule (parabolic rule)
    ................................................................................................................................................................................................................................................................................................................................................................................................
    449
  34. 241.
    Integrals for reference
    ................................................................................................................................................................................................................................................................................................................................................................................................
    451
  35. ................................................................................................................................................................................................................................................................................................................................................................................................
    461