Ordinary Differential
Equations
Reference
Chapter 22, Section 23.1.1, and
Chapter 24
2015
1
What Is a Differential Equation (DE)?
An equation that involves a function and its
derivatives
1st order DE: function + 1st derivative
y xy 2 x 3
2nd order DE:
Curve Fitting
by Least-Squares
Regression
Reference
Textbook: Chapters 14 & 15
2015
1
Objective
Given a set of data
( x1 , y1 ), ( x2 , y2 ), K
, ( xn , y n ) ,
find an analytic expression, i.e., an explicit
function y = f (x), to represent the overall
re
Matrix Definitions and
Basic Matrix Operations
Reference
Textbook: Sections 8.1 & 9.1.2
2015
1
Matrix Definition
A rectangular array of numbers
Notation:
Capital letter enclosed by square brackets, [A]
Or bold capital letter, A
Defined by the number
Introduction to the
Linear Equation Sets
Reference
Textbook: Sections 8.1.3, 9.1.1, 9.1.2
2015
1
General Set of n Linear Equations
A lot of problems ultimately result in a series of coupled
linear equations:
a11 x1 a12 x2 L a1n xn b1
a21 x1 a22 x2 L a2 n
Roots of a Single Nonlinear Equation
Reference
Textbook: Chapters 5 6
2015
1
Nonlinear Equations
Many engineering and scientific problems involve
solving a non-linear equation.
Example: Van der Waals equation of state which is
used when the ideal gas law
Numerical Integration
Reference
Chapter 19
Chapter 20: 20.2.1, 20.4.2
2015
1
What is integration?
The integral of a
function f (x) from
x = a to b, i.e.,
b
I f ( x)dx
a
is equivalent to the
area under the
curve.
2015
2
Why numerical?
Sometimes a function
One-dimensional
Optimization
Reference
Textbook: Chapter 7
2015
1
What is Optimization?
In general terms, optimization can be defined as a
method for determining the best way to do
something.
Example 1: Schedule construction in the most efficient
manner,
Polynomial Interpolation
Reference
Chapter 17: 17.1, 17.2, 17.4, 17.5
Chapter 18: 18.5.2, 18.6
2015
1
Overview
Table lookup is quite common in engineering:
When no explicit expression is available for a
function f (x), its values obtained by either
comp
MATLAB Programming
Reference
Textbook: Chapters 2 & 3
2015
1
MATLAB Overview
MATLAB provides a convenient tool for
numerical computation, graphical display,
and many other special tasks.
The command window is your primary way
to interface with MATLAB al
Numerical
Differentiation
Reference
Textbook: Chapter 21
2015
1
What is differentiation?
For a given function y = f (x), derivative dy /dx (or
y just the slop of its tangent.
) is
Mathematically, slop represents the ratio of change
in function y to chan
Numerical Techniques
20-MECH-3042
Class Syllabus and Policies
2015
1
Instructor
Dr. Bingjing Su, Associate Professor of Nuclear
Engineering
Office 622 Rhodes Hall
Office Hours: TR 12:20 - 1:00 pm
Other times by appointment (call/e-mail)
Phone 556-2960
E
Introduction to
Eigen-values and Eigenvectors of a Matrix
Reference
Textbook: Chapter 13
2015
1
Eigen-values and Eigen-vectors
Representing the characteristics of a system, like
vibration of a structure
Definition:
A*x = x
where is eigen-value, and non-
Homework Two Intelligent Systems Theory Due, Monday, October 26, 2015
You may work on this individually or as a project team of two or three people to do this homework.
Show all your work. There is partial credit. Turn this in via email at [email protected]
Intelligent Systems Test Two Solution December 3, 2015
Each question is worth 11 points. You get one point if you submit the completed test certification
page. Dont spend too much time on any one question. You have eighty minutes for the test.
1.) We live
Homework Four Intelligent Systems Theory Due 8:00 PM Monday, November 16, 2015
You may work on this individually or in groups of two or three students. If you are submitting as a
group, just submit one solution with all the names on it. Submit it via emai
Intelligent Systems Test One Solution November 4, 2015
Each question is worth 11 points. Dont spend too much time on any one question. You have
the full class period for the test.
1-)
2-)
4.)
The ID3, C4.5, and C50 algorithms are very good at what applica
Intelligent Systems
Homework Five
Solution
You may work on this individually or in groups of two or three students. If you are submitting as a group,
just submit one solution with all the names on it.
1.)
Define what is meant by the terms plastic and stab
Intelligent Systems Theory
Homework One Solutions
You may work on this individually or in groups of two or three. If you are a group, just turn in one
assignment with all the names on it. Email the completed assignment to [email protected] as either
a .d
Homework Three
Intelligent Systems Theory
Each problem is worth 15% except for problem one which is worth 25%.
You may work on this individually or in groups of two or three students. If you are submitting as a group,
just submit one solution with all the
MECH 3042
Homework Assignment 8
Name: _
I. Given the following 1st order ordinary differential equation
2
e x / 2
y ( x ) 2 x ;
y
y ( x0 0) 1
1. Use Eulers method and step size x = 0.1 to calculate y(0.1) and y(0.2) by hand.
2. Use Heuns method and step s
MECH 3042
Homework Assignment 7
Name: _
1.
For the data pairs (xi, yi) given by:
x
y(x)
1.0
3.0
1.5
2.8
2.0
3.0
2.5
3.8
3.0
5.0
integrate the function y over x from x = 1 to x = 3, i.e., evaluate
3
, by
I y ( x )dx
1
hand, first using the (composite) trap
MECH 3042
111Equation Chapter 1 Section 1Homework Assignment 6
Name: _
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 uti
Name -
Dr. Kazmierczak Heat Transfer
Autumn 2008 QUIZ #6 20-MECH-413
(1 1/13/08)
Re-Re-Revisit Problem 1.71 (i.e. 4th time) - CE? = 47 0c
14>
kwire = 25 W/m K; Ac = 1 mm x 0.25 mm; L: 4mm
Focus on single wire lead and here, since air ows all around
TABLE 3.4. Temperature distribution and" heat loss for [ins of uniform crass section
W
, Tip Conttion Temperature ' , Fin Heat
Case (x = L) Distribution 0/0, Transfer- Rate 4;
A Convection hear cash m(. - x] + cfw_ix/mic) sinh mu: - x) ' , summL "r (Mmlc)
Qn
Summer 2010 Exam#2 - ' ' "Name-
Problem 4 10 ptsz
Carefully sketch, the anticipated temperature distribution along the length of the wire, i.e. T(X)
versus X, of the two cases analyzed in Problem #3, both superimposed on the same figure below.
L=