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||| = Chapter Four Engineering Analysis Partial differential equations Home Works of Partial Differential Equations H.W1: solve the following boundary value problem using method of separation of variables: u4uxxi Where: u(0,t) = 0; u(5,t) = 0; u(x, 0) = f(x) = x(1-x) H.W2: solve the following boundary value problem using method of separation of variables: u4uxxi Where: u(0,t) = 0; u(5,t) = 0; u(x, 0) = f(x) = 3 sin 5x-8 sin 20πx H.W3: solve the following boundary value problem using method of separation of variables: (60 0 0. H.W7: Solve the following Laplace Equation for the given boundary conditions: J² ²u + =0 ax²ay² u(0, y) = 0; u(10, y) = 0; u(x, 0) = 0; u(x, 20) = sin 7 ηπ MUSTA IYAH UNIVERSITY ناك العديدة COLLEGE OF E ENGINEER

||| = Chapter Four Engineering Analysis Partial differential equations Home Works of Partial Differential Equations H.W1: solve the following boundary value problem using method of separation of variables: u4uxxi Where: u(0,t) = 0; u(5,t) = 0; u(x, 0) = f(x) = x(1-x) H.W2: solve the following boundary value problem using method of separation of variables: u4uxxi Where: u(0,t) = 0; u(5,t) = 0; u(x, 0) = f(x) = 3 sin 5x-8 sin 20πx H.W3: solve the following boundary value problem using method of separation of variables: (60 0 0. H.W7: Solve the following Laplace Equation for the given boundary conditions: J² ²u + =0 ax²ay² u(0, y) = 0; u(10, y) = 0; u(x, 0) = 0; u(x, 20) = sin 7 ηπ MUSTA IYAH UNIVERSITY ناك العديدة COLLEGE OF E ENGINEER

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
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||| = Chapter Four Engineering Analysis Partial differential equations Home Works of Partial Differential Equations H.W1: solve the following boundary value problem using method of separation of variables: u4uxxi Where: u(0,t) = 0; u(5,t) = 0; u(x, 0) = f(x) = x(1-x) H.W2: solve the following boundary value problem using method of separation of variables: u4uxxi Where: u(0,t) = 0; u(5,t) = 0; u(x, 0) = f(x) = 3 sin 5x-8 sin 20πx H.W3: solve the following boundary value problem using method of separation of variables: (60 0<x<50 u =0.16uxx; Where: u(0,t) = 0; u(100, t) = 0; u(x, 0) 140 50 < x < 100 H.W4: Find the temperature u(x, t) in a bar of length , which is perfectly insulated everywhere including the ends x = 0 and x = . This leads to the conditions u,(0, t) = 0; u,(,t) = 0. The initial temperature is given by the function f(x) = 3 cos x + 7 cos 2x H.W5: solve the following boundary value problem using method of separation of variables: = 4 ax² u(0,t) = 0; u(10,t) = 0; u(x, 0) = x + 2; u(x, 0) = g(x) = {x- 0<x<5 :-10 5<x<10 H.W6: Vibration of an elastic is governed by the partial differential equation ut ur. The length of string is π and the ends are fixed. The initial deflection is zero and the initial velocity is u(x, 0) = 6 sin 2x + 7 sin 5x-4 sin 10x. Find the deflection of the vibration string fort > 0. H.W7: Solve the following Laplace Equation for the given boundary conditions: J² ²u + =0 ax²ay² u(0, y) = 0; u(10, y) = 0; u(x, 0) = 0; u(x, 20) = sin 7 ηπ MUSTA IYAH UNIVERSITY ناك العديدة COLLEGE OF E ENGINEER
Transcribed Image Text:||| = Chapter Four Engineering Analysis Partial differential equations Home Works of Partial Differential Equations H.W1: solve the following boundary value problem using method of separation of variables: u4uxxi Where: u(0,t) = 0; u(5,t) = 0; u(x, 0) = f(x) = x(1-x) H.W2: solve the following boundary value problem using method of separation of variables: u4uxxi Where: u(0,t) = 0; u(5,t) = 0; u(x, 0) = f(x) = 3 sin 5x-8 sin 20πx H.W3: solve the following boundary value problem using method of separation of variables: (60 0<x<50 u =0.16uxx; Where: u(0,t) = 0; u(100, t) = 0; u(x, 0) 140 50 < x < 100 H.W4: Find the temperature u(x, t) in a bar of length , which is perfectly insulated everywhere including the ends x = 0 and x = . This leads to the conditions u,(0, t) = 0; u,(,t) = 0. The initial temperature is given by the function f(x) = 3 cos x + 7 cos 2x H.W5: solve the following boundary value problem using method of separation of variables: = 4 ax² u(0,t) = 0; u(10,t) = 0; u(x, 0) = x + 2; u(x, 0) = g(x) = {x- 0<x<5 :-10 5<x<10 H.W6: Vibration of an elastic is governed by the partial differential equation ut ur. The length of string is π and the ends are fixed. The initial deflection is zero and the initial velocity is u(x, 0) = 6 sin 2x + 7 sin 5x-4 sin 10x. Find the deflection of the vibration string fort > 0. H.W7: Solve the following Laplace Equation for the given boundary conditions: J² ²u + =0 ax²ay² u(0, y) = 0; u(10, y) = 0; u(x, 0) = 0; u(x, 20) = sin 7 ηπ MUSTA IYAH UNIVERSITY ناك العديدة COLLEGE OF E ENGINEER
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