Homework "LAPLACE TRANSFORM" 9. variant 1) Find the Laplace transform of the original a) f(t) =2cos6t-1-e²ªsin2t %3D b) f(t) = | ucoOs5udu 0. 2) Find the original of the Laplace transform eP a) F(p) = p+1' 1+ p p - 4 p+ 9 2- p (p+4)(p +1)’ b) F(p) = c) F(p) = 3) Solve the equation, and verify its solution. y' +8y + 52y= et У0) — 0, У(0)—4
Homework "LAPLACE TRANSFORM" 9. variant 1) Find the Laplace transform of the original a) f(t) =2cos6t-1-e²ªsin2t %3D b) f(t) = | ucoOs5udu 0. 2) Find the original of the Laplace transform eP a) F(p) = p+1' 1+ p p - 4 p+ 9 2- p (p+4)(p +1)’ b) F(p) = c) F(p) = 3) Solve the equation, and verify its solution. y' +8y + 52y= et У0) — 0, У(0)—4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Topic Video
Question
Please Do All the Questions in these 2 Papers. Thanks.
![Homework "LAPLACE TRANSFORM"
9. variant
1) Find the Laplace transform of the original
a) f(t) =2cos6t-1-e²'sin2t
b) f(t) = [ ucos5udu
2) Find the original of the Laplace transform
a) F(p) =
P+1'
1+ p
p - 4p+9
2-p
(p+4)(p +1)’
b) F(p) =
c) F(p) =
3) Solve the equation, and verify its solution.
y'+8y+ 52y= e
У О) %3 0, у(0) - 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff096764-66ce-4681-80b1-5d0e9e4b014a%2Fc68b5bab-df11-45f5-8476-a2131b76e262%2F66gra38_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Homework "LAPLACE TRANSFORM"
9. variant
1) Find the Laplace transform of the original
a) f(t) =2cos6t-1-e²'sin2t
b) f(t) = [ ucos5udu
2) Find the original of the Laplace transform
a) F(p) =
P+1'
1+ p
p - 4p+9
2-p
(p+4)(p +1)’
b) F(p) =
c) F(p) =
3) Solve the equation, and verify its solution.
y'+8y+ 52y= e
У О) %3 0, у(0) - 4
![Homework 1: "COMPLEX VARIABLES"
Variant 9.
1
1. Given two complex numbers z =-
i
and
Z =-27i.
a) Represent the numbers z and z, graphically in the complex plane;
b) Find the principle value of the argument and modulus of
and
c) Express the numbers z and z, intrigommetric and exponential fom;
18
d) Calculate z and
e) Calculate all values of the root /z, , and represent these values in the complex plane;
f) Represent geometrically points of the complex plane which satisfy the following inequalities:
1) Rezs Rez,
3) |z-z |<2,
2) Imz2 Imz,
4) 1<|z-z |5 2,
5) s arg z<P2,
where
P = min{arg z, arg z}, = max{arg z, arg z}.
%3D
2. Calculate the value of the following complex functions:
b) In(v2-vZi),
e) con-3).
a) e
4
3. Check out if the Cauchy-Riemann equations are satisfied for the given function. Calculate f(z)
if it exists.
f(z) = iz+e
4. Evaluate the complex line integral [(zlmz+3z) dz, where L is a straight lie connecting
the points z = 0 and z, =1+3i. Draw the line and show the direction of integration.
cosh(iz) dz
5. Using the Cauchy's integral fomula, evaluate the contour integral z.47-3'
where
Cisa closed contourgiven by the equation | z-2. Graph the contour and singular points.
9.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff096764-66ce-4681-80b1-5d0e9e4b014a%2Fc68b5bab-df11-45f5-8476-a2131b76e262%2Ff70oiae_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Homework 1: "COMPLEX VARIABLES"
Variant 9.
1
1. Given two complex numbers z =-
i
and
Z =-27i.
a) Represent the numbers z and z, graphically in the complex plane;
b) Find the principle value of the argument and modulus of
and
c) Express the numbers z and z, intrigommetric and exponential fom;
18
d) Calculate z and
e) Calculate all values of the root /z, , and represent these values in the complex plane;
f) Represent geometrically points of the complex plane which satisfy the following inequalities:
1) Rezs Rez,
3) |z-z |<2,
2) Imz2 Imz,
4) 1<|z-z |5 2,
5) s arg z<P2,
where
P = min{arg z, arg z}, = max{arg z, arg z}.
%3D
2. Calculate the value of the following complex functions:
b) In(v2-vZi),
e) con-3).
a) e
4
3. Check out if the Cauchy-Riemann equations are satisfied for the given function. Calculate f(z)
if it exists.
f(z) = iz+e
4. Evaluate the complex line integral [(zlmz+3z) dz, where L is a straight lie connecting
the points z = 0 and z, =1+3i. Draw the line and show the direction of integration.
cosh(iz) dz
5. Using the Cauchy's integral fomula, evaluate the contour integral z.47-3'
where
Cisa closed contourgiven by the equation | z-2. Graph the contour and singular points.
9.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)