### MATH 10B  --  Midterm Review Topics

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