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Phy252-Thermal Physics: Assignment 1

Due: Friday, July 14

Question 1: [a: 4pt , b: 2pt, c: 8pt, d:1pt]

Letf and g be two realfunctions given by:

f (x, y)  =  x 2  + 3xy 2  + y 5 and g (x, y)  =  x  ln y

a. calculate thefirst partial derivatives offunctionsf and g.

b. write the total differentials df and dg.

c. calculate thefour second partial derivativesfor eachfunction.

d. are df and dg exact or inexact differentials?

Question 2: [a: 13pt, b: 1pt, c: 1pt]

a. Calculate the integral of the differential

6w = xy dx + xy dy along the red path (OBM), the green path (OAM) and the blue path (OM).

b. Evaluate the integral of 6w on the cycle (OBMAO)

c. Comment on the results.

Question 3 : [a: 13pt, b:1pt, c: 1pt]

a. Evaluate the integral of the differential df = (6xy2 − y3)dx + (6x'y − 3xy2)dy along the red path (ADB), the green path (ACB) and the blue path (AB).

b. Calculate the cyclic integral of df.

c. Comment on the results.