| Section | Page number (5th edition) |
Topic |
|---|---|---|
| 5.1 | 321 | The Slice Method -- Cavalieri's Principle |
| 327 | Exercises 10, 11 | |
| 5.2 | 334 | Fubini's Theorem |
| 339-340 | Exercises 1, 2, 5 | |
| 5.3 | 341 | Elementary regions |
| 348 | Exercises 5, 9, 10, 12, 14 | |
| 5.4 | 349 | Changing the order of integration |
| 353-354 | Exercises 2, 8, 11-13 | |
| 5.5 | 359-363 | Triple integrals over elementary regions |
| Examples 4-6 | ||
| 363-365 | Exercises 5-8, 15, 16, 22(b), 23-25 | |
| 367 | Exercise 33 | |
| 6.1 | 369 | Examples 1, 2 |
| 371 | Theorem 1 -- image of a linear transformation | |
| 372 | Definition of a one-to-one mapping | |
| 373 | Definition of an onto mapping | |
| 375 | Exercises 1, 4, 6, 7 | |
| 6.2 | 377 | Definition of the Jacobian determinant (in two variables) |
| Example 1 | ||
| 382 | Change of variables theorem (in two variables) | |
| 383 | Change of variables to polar coordinates | |
| 387 | Definition of the Jacobian determinant (in three variables) | |
| Change of variables theorem (in three variables) | ||
| 388 | Cylindrical coordinates | |
| Change of variables to cylindrical coordinates | ||
| 388-389 | Spherical coordinates | |
| Change of variables to spherical coordinates | ||
| 390-392 | Exercises 1, 2, 7, 19-28 | |
| 6.3 | 393 | Average values of functions |
| 396 | Center of mass of two-dimensional plates | |
| 397 | Center of mass of three-dimensional regions | |
| 400 | Moments of inertia about the coordinate axes | |
| 404-405 | Exercises 6, 8-10, 13 | |
| 6.4 | 409 | Improper integrals as limits of iterated integrals |
| 411-412 | Fubini's theorem for improper integrals | |
| Examples 2, 3 | ||
| 413-414 | Functions unbounded at isolated points | |
| Example 4 | ||
| 415-416 | Exercises 1, 3, 4, 5(a), 8 |