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

1. SECTION

   PAGE

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 $\scriptstyle {n{\text{th}}}$ 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.  

36. INDEX ................................................................................................................................................................................................................................................................................................................................................................................................

    461