EGR 265-6D, Fall 2012, Final Exam 1

EGR 265-6D, Math Tools for Engineering Problem Solving

December 14, 2012, 1:30pm to 4:00pm

Name (Print last name ﬁrst): ..........................................

Student ID Number: ......... ...... ............

Final Exam

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Bonus Problem

Problem 9

Problem 10

Total

EGR 265-6D, Fall 2012, Final Exam 2

Problem 1 (8 points)

Find an explicit solution of the initial value problem

y′=ye2x, y(0) = 1.

EGR 265-6D, Fall 2012, Final Exam 3

Problem 2 (10 points)

Iron, which has a melting point of 2200◦F, is heated in a furnace to 2500◦F. After

extraction from the furnace it cools down according to Newton’s law of cooling in a

surrounding medium of temperature 100◦F. After two hours the Iron has cooled to

2300◦F.

(a) Write down the IVP governing the cooling process using an unknown cooling rate

k.

(b) Solve the IVP and determine kby using information provided in the problem.

(c) How long does it take the Iron to solidify?

Note: In parts (b) and (c) logarithms do not need to be evaluated.