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.