Sharif University of Technology
Department of Mechanical Engineering
ME 28637
A. Bahrami
Aban 20, 1393
Due: Aban 26, 1393
Homework set # 4
You may use MATLAB for all problems of this set.
Consider the discrete data displayed in the following table. The co
Sharif University of Technology
Department of Mechanical Engineering
ME 28637
A. Bahrami
HW Set # 10
Azar 21, 1393
Due: Day 6, 1393
Problem 1. Consider the following firstorder equation
=
with y(0) = 1
Solve the equation from t = 0.0 to t = 1.0 with h =
Sharif University of Technology
Department of Mechanical Engineering
ME 28637
A. Bahrami
Superhomework # 1
Azar 6, 1393
Due: Day 30, 1393
Static behavior of an AFM microcantilever
Scanning probe microscopy (SPM) has been demonstrated as one of the most po
Sharif University of Technology
Department of Mechanical Engineering
ME 28637
A. Bahrami
Azar 22, 1393
Due: Day 30, 1393
SHW Set # 2
Vibrations of an EulerBernoulli beam
The partial differential equation (PDE) governing transverse vibrations of an Euler
In the Name of God
Numerical Methods
Sharif University of Technology
CE 40215/216
Homework 3
Due Wednesday,12 November, 2014
Reminders:
Typing the solutions has extra mark.
Collaboration is permitted, but you must write the solutions by yourself
without
In the Name of God
Numerical Methods
Sharif University of Technology
CE 40215/216
Homework 4
Due Wednesday 10, December, 2014
Reminders:
Typing the solutions has extra mark.
Collaboration is permitted, but you must write the solutions by yourself
withou
In the Name of God, the most powerful sound
Numerical Methods
Sharif University of Technology
CE 40215/216
Homework 2
Due Wednesday, October 29, 2014
Reminders:
Typing the solutions has extra mark.
Collaboration is permitted, but you must write the solu
In the Name of God
Numerical Methods
Sharif University of Technology
CE 40215/216
Introduction to MATLAB
Due Wednesday, 8 October 2014
Reminders:
Collaboration is permitted, but you must write the solutions by yourself
without assistance.
Getting soluti
Numerical Methods homework 3 solution
Problem 1.
in order to simplify the calculations, we could modify the table. Thus, the points we are
looking for are x = 8 and x = 40 :
x
y
0 5 10 15 20
11 10 9 8 5
1.
L0 (x) =
L1 (x) =
L2 (x) =
L3 (x) =
L4 (x) =
(x5)
In the Name of God, the most powerful sound
Numerical Methods
Sharif University of Technology
CE 40215/216
Problems And Solutions:
1. Solve the equation below for x in the interval (3, 4) using the following methods:
f (x) = ex (3.2sin(x) 0.5cos(x)
(a) Bi
In the Name of God
Numerical Methods
Sharif University of Technology
CE 40215/40216
Solution to Homework 6
Problems:
1. Calculate the determinant of the following matrix
1 2 4 2
1 6 3 1
9 2 1 4
1 2 5 0
L=
0
0
0
1
2 4
2
4 1 1
0 1
2
0 0 = 96
1 0
0
1
In the Name of God
Numerical Methods
Sharif University of Technology
CE 40215/216
Homework 5
Due Thursday, 12 December, 2013
Reminders:
Typing the solutions has extra mark.
Collaboration is permitted, but you must write the solutions by yourself
without
In the Name of God
Numerical Methods
Sharif University of Technology
CE 40215/216
Homework 1
Wednesday, 8 October 2014
Reminders:
Typing the solutions has extra mark.
Collaboration is permitted, but you must write the solutions by yourself
without assis
In the Name of God
Numerical Methods
Sharif University of Technology
CE 40215/216
Solutions to HW1:
1. (a) distance = 1000.512km = 0.1000512 104 km and door = 201.5cm = 0.2015 103 cm
Distance has 7 digit of mantissa and the door das 4 digit of mantissa.
(
% Mohammad Mahdi Seifi
% SHW1
clear
clc
close all
H = 2.96*10^(19);
E = 130;
l = 250;
I = 3.57*10^(23);
R = 10;
n = 5;
Z = 0;
P = 0;
W = P;
Es = 10.2;
a0 = 0.38;
for Z= 1:1:60
for i = 1:1:n
fx = W*Z^2W^32*W^2*Z*10^(9)(H*R*l^3/(18*E*I);
Fx = Z^23*W^
Note # 4
NewtonCotes formulas
A class of numerical integration formulas based on equally spaced increments, called
NewtonCotes formulas, was discussed in class last time. The trapezoid rule and Simpsons 1/3
and 3/8 rules are the first three NewtonCotes
GaussSeidel Iterative method
The final equation for the GaussSeidel iterative method is:
(
( )
)
=
=
( )
+
( )
(
)
( )
i = 1,2,3,n
Example. Consider the following system of linear equations (the same example as we did in class with
Jacobi iteration meth
Sharif University of Technology
Department of Mechanical Engineering
ME 28637
A. Bahrami
HW set # 8
Azar 9, 1393
Due: Azar 17, 1393
Problem 1. When a fluid flows over a surface, the shear stress (N/m2) at the surface is given by the expression
=

where i
Sharif University of Technology
Department of Mechanical Engineering
ME 28637
A. Bahrami
Problem 1. Evaluate the integral exp (
+
= 1. Use Cartesian coordinate.
Problem 2. Evaluate the integral
a. k = 2
b. k = 3
c. k = 4
Azar 19, 1393
Due: Azar 24, 1393
A man who sets out to justify his existence and his activities has to distinguish two different
questions. The first is whether the work which he does is worth doing; and the second is why he
does it, whatever its value may be. The first question is often
Sharif University of Technology
Department of Mechanical
Engineering
ME 28637
A. Bahrami
Mehr 14, 1393
Due: Mehr 28, 1393
Homework Set #1
Background: Taylor series provide a very useful and powerful tool in order to not only derive approximations
in discr
Sharif University of Technology
Department of Mechanical Engineering
ME 28637
A. Bahrami
Azar 26, 1393
Due: Azar 3, 1393
Homework set # 5
You may use MATLAB for all problems of this set.
Background. One advantage of using polynomials for least squares app
Sharif University of Technology
Department of Mechanical Engineering
ME 28637
A. Bahrami
Azar 3, 1393
Due: Azar 10, 1393
Homework set # 6
You may use MATLAB for all problems of this set.
( )=
2 2 =0
Problem 1. Consider the following equation:
a. Solve the
Where Newtons method fails to converge to the root
Newtons method (sometimes called the NewtonRhapson method) for solving nonlinear equations
is one of the most wellknown and powerful procedures in all of numerical analysis. It always
converges if the i
Sharif University of Technology
Department of Mechanical Engineering
ME 28637
A. Bahrami
Mehr 30, 1393
Due: Aban 5, 1393
Homework set # 2
Background. Many computational codes solving problems in mechanics will result in very large
systems of algebraic equ
Sharif University of Technology
Department of Mechanical Engineering
ME 28637
A. Bahrami
Azar 8, 1393
Due: Azar 17, 1393
KEEP SIX SIGNIFICANT DIGITS IN ALL YOUR CALCULATIONS.
+3 +2 =9
4 + 2 + 5 + = 27
3 3 + 2 + 4 = 19
+ 2 3 + 5 = 14
Problem 1. Consider t
Pivoting
1. Partial pivoting
The element on the major diagonal is called the pivot element. The Gauss elimination procedure
described in class so far fails immediately if the first pivot a11 element is zero. The procedure
also fails if any subsequent pivo
Sharif University of Technology
Department of Mechanical Engineering
ME 28637
A. Bahrami
Aban 8, 1393
Due: Aban 19, 1393
Homework set # 3
You may use MATLAB for all problems of this set.
25 + 3 + 5 + 2
3 + 17 + 7 + 5
5 + 7 + 23 + 8
2 + 5 + 8 + 29
=2
= 53
Sharif University of Technology
Department of Mechanical Engineering
ME 28637
A. Bahrami
Azar 21, 1393
Due: Day 22, 1393
HW Set # 11
Note: You can use MATLAB builtin ODE solvers for this set.
Problem 1. When an ideal gas flows in a variablearea passage
January 3, 2015
Numerical Methods (Assignment 4)
Answers
1
1.1
Rectangular Method
We devide the interval[a,b] into n subintervals with equal lengths and find the
integral by the summation of the rectangular area.(f(xi) is the length and h =
0.1 is the wid