Home Work One Solutions
1. (a)
i. Norm of the vector (1 2 1) is 1 + 4 + 1= 6.
ii. Norm of the vector (1 1 1) is 1 + 1 + 1= 3.
iii. Norm of the vector (2 3 0) is 4 + 9 + 0= 13.
(b) The cosine of the angle between any two vectors a and b is given as follows
1
ESE501: First Midterm Exam
There are 20 multiple choice questions. Please circle one appropriate answer. Total time of the exam is
90 minutes after which you must stop working. The exam is open notes and books but calculators and
computers are strictly
ESE501 Solutions to the Midterm II
1. In this problem we are considering a rst order ordinary dierential equation given by
y (t) + 3 y (t) = 5 u(t),
where
y (0) = 2,
and where
u(t) = e7t , t 0.
Calculate y(t) manually by showing all the steps.
Solution:
U
ESE501 Midterm II
There are four questions of equal weightage. The exam is open book and notes. Calculators
and computers are not allowed. Total time allotted is 90 minutes.
1. In this problem we are considering a rst order ordinary dierential equation gi