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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
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.
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.
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