Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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h223Ex..018.pdf
[aj Use tne Caucny mtegrai rormuia to nna
D9.
zdz
(z + 1)(2:² + 3z – 2)
where r is the circle |z - il = 2.
[8]
(b) Evaluate the integral
(12 - 4)(r +
[12]
page 3 of 5
HIT 223
B10.
(a) Find the series of
valid in the domain 0 < |2| < 3.
[10]
22(z + 3)
(b) Use the method of residues to prove that
COS mr
dr =
(4e
-m/2 -e"),
4r4+ 5z? +1"
for m >0.
[10]
B11. (a) Find the solution to a root of r – 2 In z = 3 using at least four iterations. [6)
(b) Consider the initial value problem
dy
= yt,
y(0) = 1.
dt
Estimate y(0.2) using the Euler method with stepsize 0.1.
(6)
(c) Find an interpolation polynomial of degree four matching the following four points
01|2
|-1
f(T) 2
-4 |8
[8]
B12. (a) Find the values of a, b, c, d, e, f, g and h such that
ar",
S(r) = { b(x – 2)3 + c(x – 2)? + d(x – 2) + e, 2 <I<3
f(z – 3)* + g(x – 3) + h,
such that S(r) is a natural cubic spline.
[10]
(b) Use an iteration scheme to solve the following system of equations,
1.8r) + 3.1r2 +1.9r3 = 4.5
1.8r1 + 1.8r2 +2.5x3 = 12
0.99z, + 3.2r2 + 2.75r = 4.8
starting with initial solution x = [1,2, –1]7, and performing four iterations. [10]
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