The Space of Equation Sets
Reference Ayyub and McCuen Chapter 5
1
Types of Equations
There are three types of equation sets that can arise in engineering: Underdetermined Determined Overdetermined
2
Underdetermined
more unknowns than equations n<m Solut
MECH 342
Solutions to Homework Assignment #2
Problem 1: Generate a plot that compares the following two functions of time t:
x(t ) = 2sin( t / 2)
y (t ) = e
0.3 t
e i 2 t + ei 2 t
Plot the two functions for 0 t 5 using increment of 0.01, i.e., t = 0 : 0
MECH 342
Solution of Homework 7
1.
For the data pairs (xi, yi) given by:
x
y(x)
1.0
0.5
1.5
0.7
2.0
0.8
2.5
0.6
3.0
0.3
2
integrate the function y over x from x = 1 to x = 2, i.e., evaluate I = y ( x)dx , by
1
hand, first using the trapezoidal rule and th
Numerical Analysis for ME
Solution to Homework Assignment #3
1. For the nonlinear equation given by f ( x) = e x x 2 + 1 = 0
(a). Use the Newton-Raphson method and an initial guess of x0 = 3.5 to do two iterations for
the root BY HAND (i.e., find x1 and x
Numerical Analysis for ME
Solution to Homework Assignment #4
1. (a). Does the following linear equation set have a unique solution?
2 X 1 3 X 2 X 3 + 2 X 4 = 11.7
3 X 1 + X 2 + 2 X 3 X 4 = 11.5
X 1 2 X 2 + 3 X 3 + 5 X 4 = 0.4
3 X 1 + 3 X 2 X 3 + X 4 = 3.
Matrix Definitions and Basic Matrix Operations
Reference Ayyub & McCuen Chapter 2
1
Matrices
Definitions
2
Matrix
A rectangular array of numbers Notation:
Capital letter Enclosed by square brackets, [ A ]
Defined by the number of rows and number of col
Numerical Analysis for Mechanical Engineers (20-MECH-342)
Introduction Reference class syllabus
1
2
Professor Kumar Vemaganti
Office 629 Rhodes Hall
Office Hours MW 3:30-5:00 Other times by appointment (call/e-mail)
Phone - 556-2728 (time stamped voice
Numerical Differentiation and Integration
Reference Ayyub & McCuen Chapter 7
1
Numerical Differentiation
2
Why numerical?
Sometimes an analytical function is known but the derivative is not easily found. Sometimes an analytical function is not known, suc
Curve Fitting and Parameter Estimation
Finding Physical Parameters Working With Experimental Data Reference Ayyub & McCuen Chapter 10
2002 1
In the real world
A big part of engineering is being able to measure physical phenomena. This could be:
Temperat
Programming Concepts 1 Introduction
Computer programs use variables to hold information. Variables can be of several dierent types: integers, character strings, real numbers, etc., to name a few. We will mostly deal with scalars, vectors and matrices of i
LU Decomposition
The solution of linear equations How to find [L] and [U]
2002
1
The basic questions of: [A]cfw_x=cfw_b are: 1. Does a solution cfw_x exist (existence) 2. If a solution exists, is it unique (one solution or an infinity of solutions, unique
MECH 342
Solution of Homework 6
1. The population p of a small community has grown rapidly with time t (in years) during
the past 16-year period by
t
p
0
95
4
190
8
430
12
935
16
1950
As an engineer working for a utility company, you must forecast the pop