TOBB EKONOMİ VE TEKNOLOJİ ÜNİVERSİTESİ MAK 501

TOBB EKONOMİ VE TEKNOLOJİ ÜNİVERSİTESİ
MAK 501 ENGINEERING MATHEMATICS
FALL 2014
Due Date: 23.09.2014- Tuesday*
HOMEWORK 1
In question 1 and 2 derive the general solution of the given equation by using an appropriate change
of variables.
𝟏. 2
𝟐.
𝜕𝑢
𝜕𝑢
+3
=0
𝜕𝑡
𝜕𝑥
𝜕𝑢
𝜕𝑢
−2
=2
𝜕𝑡
𝜕𝑥
3. (a) Use the change of variables α = x + ct, β = x − ct to transform the wave equation (1) into
∂2 u
∂2 u
= 0. (You should assume that ∂α ∂β =
∂α ∂β
𝜕2 𝑢
𝜕𝑡 2
∂2 u
)
∂β ∂α
𝜕2 𝑢
= 𝑐 2 𝜕𝑥 2
(1)
𝜕𝑢
(b) Integrate the equation with respect to α to obtain 𝜕𝛽 = 𝑔(𝛽), where g is an arbitrary function.
(c) Integrate with respect to 𝛽 to arrive 𝑢 = 𝐹(𝛼) + 𝐺(𝛽) where F is an arbitrary function and G
is an antiderivative of g.
In question 4 and 5 you are asked to solve the wave equation (1), subject to the boundary conditions
(3), (4) and the initial conditions (5), (6) for the given data [equations are given in Asmar section
1.2].
1
4. 𝑓(𝑥) = 0, 𝑔(𝑥) = 2 𝑠𝑖𝑛
5. 𝑓(𝑥) = 0, 𝑔(𝑥) =
5𝜋𝑥
𝐿
1
− 10 𝑠𝑖𝑛
8𝜋𝑥
𝐿
3𝜋𝑥
𝐿
*Ödevin geç getirildiği gün başına 15 puan kesilecektir.
*Ödevleri Teknoloji Merkezi/Su Türbini Test Merkezi/ ZA-06 nolu ofis’e Ece Aylı’ya teslim
ediniz.

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