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The 7th edition of Stewart's Calculus is the official book for the course, and the syllabus and homework will be written from that book. The 6th edition is similar. You may choose to use it instead of the 7th, but you have to be aware of which sections of the 6th edition correspond to the relevant sections of the 7th. Also, some graded homework problems will be taken from the book (7th edition), so to complete those problems you will have to either look in a friend's book or in a copy of the 7th edition in the library.
In short, you can get by with the 6th edition, but you have to be aware that it is your responsibility (and only yours), to note the differences and complete the assigned work.
The table below gives the correspondence between sections in the 6th and 7th editions. Notice that section 15.6 in the 7th edition (which is not on our syllabus) does not exist in the 6th edition.
| 7th Edition | 6th Edition |
|---|---|
| 12.1-12.5 | 13.1-13.5 |
| 13.1-13.3 | 14.1-14.3 |
| 14.1-14.8 | 15.1-15.8 |
| 15.1-15.5 | 16.1-16.5 |
| 15.7 | 16.6 |
| 15.8 | 16.7 |
| 15.9 | 16.8 |
| 16.1-16.9 | 17.1-17.9 |