Description of this Site

On this site, I will be placing my homework solutions for the Spring 2013 teaching of Math 563 at Duke university. Many of the files are .m's that require you to use MATLAB to run, and a few non-programming exercises are scans of handwritten work. I have the contents of each .m file available as a .txt if you would like to take a peek inside of them.

Homework Solutions

Homework 1

• .m file of the solution
• .m file for generating Lagrange polynomials from a set of x and y values
• txt file of the .m file
• .txt file of the .m file for generating Lagrange polynomials from a set of x and y values
• Images associated with HW1

Homework 2

• .m file of the solution
• .m file for generating Lagrange polynomials from a set of x and y values
• txt file of the .m file of my solution
• .txt file of the .m file for generating Lagrange polynomials from a set of x and y values
• Images associated with HW2

Homework 3

• .pdf scan of my solution to HW3

Homework 4

• .m file of a script for my solution
• .txt file of the .m file
• Pictures of various S's drawn as combination of two C's

Homework 5

• Not homework 5, but a problem that was listed as 10.7.2

Homework 6

• Description of a class for a highpass/lowpass filter bank

Homework 7
Coming Soon
Homework 8

• .m file of the solution
• .txt file of the solution
• Pictures of the errors in the second derivative as a function of step size h.

Homework 9

• .m file of the solution
• .txt file of the solution
• Picture of the error in approximation as a function of number of points used

Homework 10

• Approximation of the Gamma function using Laguerre Polynomials

Homework 11

• .m file of the solution
• .txt file of the solution
• .m Function for finding the value of the legendre Polynomials at a point
• .txt of Function for finding the value of the legendre Polynomials at a point

Homework 12

• Using a Pade approximation for the Exponential

Homework for March 5

• Exploration of stability regions

Homework for March 7

• Script for performing the refinement with both Adams-Bashforth and Euler
• .txt of that script

Homework for March 21

• Setup for the pendulum problem
• MATLAB program for the refinement studies of both forced and unforced pendulum
• .txt of the above MATLAB program
• Matlab images generated from the refinement study

Homework for March 26

• A non-working attempt at deferred correction algorithm using improved Euler's Method
• .txt of the above script
• Function that returns the value of a Legendre Polynomial of degree "degree" at point x.
• .txt of the above function
• Function that returns the value of the derivative of a Legendre Polynomial of degree n at point x.
• .txt of the above function
• Function that returns the Lagrange Polynomial from a list of times and values
• .txt of the above function
• Function to find Gauss-Lobatto quadrature points and weights, and perform the quadrature rule
• .txt of the above function
• Function to perform Gauss-Lobatto quadrature that takes in the location of points but finds the weights
• .txt of the above function

Homework for March 28

• Page 1 of finding fixed points
• Page 2 of finding fixed points

Homework for April 2

• MATLAB program for the solving of the Bratu problem using shooting
• .txt of the above MATLAB program
• Matlab images generated from the refinement study

Homework for April 4

• Script to perform a refinement study with finite difference method on the problem
• .txt of the above script
• Images associated with this refinement study

Homework for April 9

• Script for the finite element method of this problem
• .txt of the above script
• Images associated with the refinement study
• .pdf of the analytical work (parts a,b,e) on the problem

Homework for April 11

• .pdf of my solution to the problem

Homework for April 16

• .pdf of my solution to the problem
• script to use the finite element method to solve the problem and perform a refinement study
• .txt of the above script
• Images associated with this refinement

Homework for April 18

• .pdf of my solution to the problem