Machine epsilon – Question 5 of 5

In the previous blog posts, we answered

Here we answer the last question.

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Friday October 31, 2014, 11:59PM EDT, November 1, 2014 3:59AM GMT – Release Date for an Opencourseware in Introduction to Matrix Algebra

In a true Netflix style, on Halloween night, Friday October 31, 2014 at 11:59PM EST, we are releasing all resources simultaneously for an open courseware on Introduction to Matrix Algebra athttp://mathforcollege.com/ma/.  The courseware will include

  • 150 YouTube video lectures of total length of approximately 14 hours,
  • 10 textbook chapters,
  • 10 online multiple-choice quizzes with complete solutions,
  • 10 problem sets, and
  • PowerPoint presentations.

So set your calendar for October 31 for some matrix algebra binging rather than candy binging.  For more info and questions, contact Autar Kaw.

Chapter 1: Introduction 

Chapter 2: Vectors

Chapter 3: Binary Matrix Operations

Chapter 4: Unary Matrix Operations

Chapter 5: System of Equations

Chapter 6: Gaussian Elimination Method  

Chapter 7: LU Decomposition

Chapter 8: Gauss-Seidel Method

Chapter 9: Adequacy of Solutions

Chapter 10: Eigenvalues and Eigenvectors

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Repeated roots in ordinary differential equation – next independent solution – where does that come from?

When solving a fixed-constant linear ordinary differential equation where the characteristic equation has repeated roots, why do we get the next independent solution in the form of x^n*e^(m*x)?  Show this through an example.

See this pdf file for the answer.

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Machine Epsilon – Question 4 of 5

In the previous blog posts, we answered

Here we answer the next question.

Future post will answer this last question
Question 5 of 5: What is the proof that the absolute relative true error in representing a number on a machine is always less than the machine epsilon?
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Machine epsilon – Question 3 of 5

In the previous blog posts, we answered

Here we answer the next question.
Machine epsilon
Future posts will answer these questions
Question 4 of 5: What is the significance of machine epsilon for a student in an introductory course in numerical methods?
Question 5 of 5: What is the proof that the absolute relative true error in representing a number on a machine is always less than the machine epsilon?
________________________
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Machine epsilon – Question 2 of 5

In the previous blog post, we answered

Here we answer the next question.

Machine epsilon

Future posts will answer these questions
Question 3 of 5: How is machine epsilon related to the number of bits used to represent a floating point number?
Question 4 of 5: What is the significance of machine epsilon for a student in an introductory course in numerical methods?
Question 5 of 5: What is the proof that the absolute relative true error in representing a number on a machine is always less than the machine epsilon?
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Machine epsilon – Question 1 of 5

Future posts will answer these questions

Question  2 of 5: How do I find the machine epsilon using a MATLAB code?Question 3 of 5: How is machine epsilon related to the number of bits used to represent a floating point number?Question 4 of 5: What is the significance of machine epsilon for a student in an introductory course in numerical methods?Question 5 of 5: What is the proof that the absolute relative true error in representing a number on a machine is always less than the machine epsilon?________________________

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