Practice Prelim

# Practice Prelim - Math 321 practice problems for first...

• Notes
• 1
• 100% (1) 1 out of 1 people found this document helpful

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 321 practice problems for first prelim Fall 2006 There are more problems here than many of you can do in fifty minutes, but they are representative of the type of problems you might expect on the exam. On the exam you may use a one-sided letter-size crib sheet, but no books, notes, or calculators. From notes: 2.7, 2.8, 2.13(i). (These problems will also be on the next homework assignment.) (Use the fundamental theorem of calculus, the chain rule and differentiate under the integral sign.) 4. Thermodynamicists like to use rules such as Explain the rule and show that it is correct. (Assume that the variables are subject to a relation defining functions , , , and differentiate implicitly.) Naively cancelling numerators against denominators gives the wrong answer! stants. Deduce from the chain rule that j for all x. Here is a positive constant and s jr 2 4 ! kl m l 32 4 RRC 4 l l 4 C C s h gdtRRB" 8dIG%B i f "C C C e "s 6. Suppose that q y q q y (a) (b) (c) , , , ; ; . R R is a smooth function satisfying x , , , are arbitrary real conx. x x v s 3DwDDD r x DIDw3DDwD 5ry 3DwDuY DtGrVq s x v Y x v s x v s 5. Let , forms on R . Calculate and \$" i &%#!p a `hg\$ 0) f " " \$ a a CT\$U 2 \$" &%` Q HF 32 RP IGE S Y W " #!X88#!I#! C ' b 32 a 2 32 a \$ 2 \$ 2 2 \$ \$" VUT%! d " \$" eA 0%`Gc a Q HF RP IGE S D 3. Let R R and R R be smooth functions. Show that " \$ 10) ' \$" (&%#! C 4 " 7 [email protected] 32 \$ ' 7" 4 2 (#9865 32 2 2. Let R R be a smooth function and assume 1. Let R -form . R be a smooth function and define x sin x x . Find the . Show that be ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern