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(* Content-type: application/mathematica *
CreatedBy='Mathematica 5.0'
Mathematica-Compatible Notebook
This notebook can be used with any Mathematica-compatible
application, such as Mathematica, MathReader or Publicon. The data
for the notebook starts wit
MA530. Midterm exam.
Students have two choices, they can do this exam in class on Oct 25 or takehome In class: to get A one should solve any 3 problems Takehome (due Nov. 1): to get A one should solve all problems to solve means to present a correct detai
ME 641 Eigenvalues and Eigenvectors
Learning Objectives
The student will be able to:
Calculate eigenvalues and eigenfunctions of various
linear operators
Find characteristic polynomial for matrices
Solve matrix eigenvalue problems analytically using
c
ME641 Engineering Analysis I
Homework Assignment 2
ME641 Homework Assignment 2
Problem 1
Consider the square matrix A given below.
8
0 4
0
A = 1 0
1 3 7
a) Using Laplace expansion, calculate det(A).
b) Using LU decomposition, calculate det(A). Hint: Pe
ME641 Engineering Analysis I
Homework Assignment 1
ME641 Homework Assignment 1
Problem 1
Show that if x is a nonzero vector,
is a unit vector.
Problem 2
Show that the oblique rank 2 projection of vector x along vector a onto a planar surface with
normal b
ME641 Engineering Analysis I
Homework Assignment 3
ME641 Homework Assignment 3
Problem 1
t 2t
Consider the matrix A =
that depends on the parameter t. Find the eigenvalues.
2 t t
Problem 2
2 1 1
Calculate the eigenvalues and eigenvectors of the matr
ME 641 Linear Differential Equations
Prerequisites
The student is able to:
State definition of term differential equation
Classify ODEs
Type
Order
Linearity
Homogeneity
Write DEs in general form and normal form (if
applicable)
State definition of ter
ME641 Engineering Analysis I
Homework Assignment 4
ME641 Homework Assignment 4
Problem 1
Classify the following differential equations by type, order and linearity. Determine the
independent and dependent variables.
a) y + 5 y = x 2 , y = y(x )
2 dy
b) (x