ME 17 Spring 2007
Homework #1 Solutions
Problem 1 (10 pts) (a) [1pt] Verify that v(0) = 0. Start with the equations given:
v(t ) =
c g mg tanh d t , m cd
where tanh( x) =
e x - e- x e x + e- x
Substitute t = 0 into the expression for v(
Problem 1 Matlab Code %Let's define a square matrix A=[10 2 -1; -3 -6 2; 1 1 5] %Determinant of A detA = det(A) %Inverse of A invA = inv(A) %Let's see if invA is really the inverse of A I1 = A*inv(A) I2 = inv(A)*A
Output A= 10 2 -1 -3 -6 2 1 1 5
de
Problem 1:
The definition of the Jacobian is shown in the Matlab code. I also wrote a function to evaluate the values of the three functions at a given x, y and z values. After defining the Jacobian and the functions, a code was written for Newton it
ME17 Summer, 2008 Problem Set #2 Due Tuesday July 8th at class time Reading: Chap. 3, Section 3.1.2: Chap. 6, Sections 6.1-6.3: Chap. 8, all; Chap. 9, Sections 9.1-9.3; Chap 10, Sections 10.1, 10.2,; Handout on Matrix Algebra. Announcement: Midterm w
ME17, Summer, 2008 Problem Set #4 Due Thursday, July 24th at class time Reading: Sections 13.1, 13.2, 13.3, 14.1, 14.3, 14.5, 19.1, 19.2, 19.3, 17.1, 17.2, 17.3, 17.4 Problem 1. Here is one of the problems from a previous midterm: Consider the follow
ME17 Summer, 2008 Problem Set #1 Due Tuesday July 1st at classtime Reading: Chapter 1 (all): Chapter 2 (all): Chapter 3, 3.1-3.5: Chapter 4, 4.1-4.4: Chapter 5, 5.1-5.4 NOTE: All solutions must contain a copy of your MATLAB procedure as appropriate.
ME17, Summer, 2008 Problem Set #3 Due Tuesday July 15th at class time IMPORTANT - The Midterm is on Thursday July 17th Reading: 8.1, 8.2, 9.1, 9.2, 10.1, 10.2, 11.1, 15.1, 15.2, 15.3, 15.5, 13.1, 13.2, 13.3 Handout on linear algebra in MATLAB. Proble
ME17, Summer, 2008 SUMMARY SHEET
1. Numerical vs. Analytical solutions. Analytical solutions are given by mathematical formulae. Numerical solutions are a set of numbers produced by a computer. 2. Algorithms are the procedures by which numerical solu
ME17, Summer, 2008 Problem Set #5 Due Wednesday, July 30th at class time Reading: 13.1, 13.2, Various Handouts on Statistics, Chap 16, Chap 17, Chap 18 Problem 1. (Statistical analysis on a relatively large, real, data set) The first things students
Project 1: Monte Carlo Simulations
1. Introduction:
Whether one wants to accept it or not, probabilities are a huge part of business and
real life. Every day, retail stores use probabilities to find the likelihood that
customers will buy a certain type of
Poissons Equation:
1. Introduction
As defined in class, the Poisson Equation is the steady-state heat equation with a
source term. The steady state part of the equation can be defined as 2ux2 =f.
Using a numerical method, the Poisson Equation updates ui a
Advection Question:
1. Introduction
The term advection is used to describe the movement of something from one region
to another. The mathematics behind advection involves a partial differential
equation, which governs the motion of a conserved scalar fiel
Jordan Pine
Perm: 5654173
Project 3: Simulation of a Vibrating System
1. Introduction
When modeling real life systems, many times mathematical models are used. These
models may not always predict what will exactly happen, but they do predict what
will hap
Jordan Pine
Perm: 5654173
Project 2: Bouncing Ball, Solving Ordinary Differential Equations
1. Introduction
By definition, a simulation is the act of imitating the behavior of some situation or
some process by means of something suitably analogous 1. In m
ME 17, APPLIED NUMERICAL METHODS SOLUTION HOMEWORK 5 TA: GAURAV SONI
Problem1:
Part A:
The data set for this problem represents final scores of ME151C class from Spring 2008. The matlab code is attached for finding the mean, the median and the stand
ME 17, APPLIED NUMERICAL METHODS SOLUTION HOMEWORK 5 TA: GAURAV SONI
Problem1:
Part A:
The data set for this problem represents final scores of ME151C class from Spring 2008. The matlab code is attached for finding the mean, the median and the stand
Mathematics of Engineering - ME17 Spring 2007 Homework #2 - Solutions 1. (15 points total) (a) (10 pts) We need to write a Matlab program in which we take t = 0 : 0.1 : 3 and x(t) = v0x t + x0 , 1 2 y(t) = ay t + v0y t + y0 2 to find matrices with th
ME 17 Spring 2007
Homework #3 Solutions
Problem 1 (20 pts) (a) [15 pts] Write a Matlab program to determine (probabilistically i.e. Monte Carlo method) whether it's better to stick with Door 1 or switch to the other (unopened) door.
% Goatprob.m: U
Mathematics of Engineering - ME17 Spring 2007 Homework #4 - Solutions 1. (10 points total) (a) (3 pts) To compute the first three terms for the Taylor series of f (x) = sin(x) about the point x = /4, consider the general equation for a Taylor series
Mathematics of Engineering - ME17 Spring 2007
Homework #5 Solutions
Problem 1
[6pts] For matrices, prove that tr(AB) = tr(BA). Given the formula (for nxn matrices A and B with elements Aik and Bkj ):
n
tr(AB) =
i=1
(AB)ii
(1)
and the fact:
n
(AB
Mathematics of Engineering - ME17 Spring 2007
Homework #7 Solutions
Problem 1
[5pts] As for the last assignment, write a Matlab program to plot the five data points as circles, and the functions which pass through these points found using linear and
%problem 5 clear all; maxtotal = 5280; % maximum sum total = 0; for ii=1:99 total = total + ii^2; % sum of squares if(total> maxtotal) % sum is greater than max sum, exit the loop break; end end % display the number of n's and its sum disp(['Value of
Problem 1 Matlab Code %Let's define a square matrix A=[10 2 -1; -3 -6 2; 1 1 5] %Determinant of A detA = det(A) %Inverse of A invA = inv(A) %Let's see if invA is really the inverse of A I1 = A*inv(A) I2 = inv(A)*A Output A= 10 2 -3 -6 1 1 detA = -289
PROBLEM 5 There are two variations of the code which can be used for this problem. It is important to look at both for learning and having fun at the same time. CODE 1
sum=0; n=0; while (sum<5280) n=n+1; sum=sum+n^2; end disp(['The sum of series exce
ME 17 Summer 2008 Homework 2 Solution TA: Gaurav Soni PROBLEM 1
Part (1) and (2): In order to determine the critical mass of the jumper, the root of the following equation was found separately by two different iterative methods: Bisection method and
MATLAB Tutorial
ME17: Applied Numerical Methods
Your TA
Gaurav Soni
Email: [email protected] Class Webpage: www.engr.ucsb.edu/~gsoni/me17.html This tutorial is already posted on the webpage. Read chapter 2 and 3 of the book
MATLAB: A math tool
Diffusion in 2D:
1. Introduction:
In the world of science, diffusion is one of the transport phenomena that occur in nature. Simply put, diffusion is
the act of particles spreading out from one place to another. Unlike convection or advection, diffusion d