Unformatted text preview: k is a constant for each k = 1 , 2 ,...,n and n X k =1 a 2 k = 1. Let z = e u ( x 1 , x 2 ,..., x n ) and verify that n X k =1 ∂ 2 z ∂x 2 k = z . 7. Let z = x 2 + xy + y 2 , x = s + t, and y = st . Find ∂z ∂s and ∂z ∂t two ways: (a) By ﬁrst substituting x and y as functions of s and t and diﬀerentiating directly. (b) By the chain rule. 8. Repeat problem 7 for the functions z = x y , x = se t , and y = 1 + se-t NOTES: 1. The FINAL EXAMINATION is on Tuesday, April 22, 9am-12noon in the GYM. A Review Sheet for the Exam will be posted at the Website in due course. 2. Friday, March 21 is a holiday and thus there are no MATA33 lectures on that day. That missed lecture will essentially be made-up on Tuesday, April 7 in accordance with the UTSC Calendar....
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- Spring '11
- Math, 1978, relevant text readings