Math 365
Introduction to Computational Mathematics
Spring 2018

Basic Information

Instructor:  Dr. Grady Wright, MB 140, 426-4674, Email:
  • Office Hours:  Friday, 1:00pm-3:00pm, or by appointment (please e-mail to set it up).

  • Text Books

    Required

    Supplementary:

    Software: MATLAB

    MATLAB is available in most computing labs around the university, including the mathematics computing lab. A student version can be purchased at a big discount from the bookstore. Alternatively, students can obtain a free copy from OIT.

    Lectures

    PiecewisePolynomialInterpolation.pdf
    Day Topics
    10-Jan
    Lecture
    Syllabus
    Find a homework partner
    Introduction to computational math: slides
    Overview of Matlab
    12-Jan
    Lecture
    Overview of MATLAB
    Lab
    MATLAB as a graphing scientific calculator (part I)
    MATLAB as a graphing scientific calculator (part II)
    MATLAB as a graphing scientific calculator (part III)
    One dimensional arrays
    17-Jan
    Lecture
    Arithmetic on arrays
    Scripts
    Plotting using linspace
    Lab
    Writing MATLAB scripts
    Arithmetic expressions involving arrays
    19-Jan
    No lecture
    Assignment
    Complete the MATLAB Onramp (see instructions below)
    24-Jan
    Lecture
    More on plotting
    For loops
    Functions
    Homework 1 discussion
    Publish
    Lab
    The for loop
    Formatting output
    26-Jan
    Lecture
    Functions
    Tables
    Homework 1 discussion
    Publish
    31-Jan
    Lecture
    Questions about the homework
    More on publish (Example homework, Solution)
    Root finding (Chapter 4): Bisection
    Lab
    Conditional statements
    02-Feb
    Lecture
    Implementing bisection
    Newton's method
    07-Feb
    Lecture
    Newton's method
    Secant method
    09-Feb
    Lecture
    Secant method
    fzero (Chapter 4)
    Minimization: fminbnd
    Lab
    Root finding
    14-Feb
    Lecture
    Minimization (Chapter 4): fminbnd
    Linear algebra review
    16-Feb
    Lecture
    Linear algebra review
    Lab
    Two dimensional arrays and matrices
    Introduction to matrices and matrix algebra
    21-Feb
    Lecture
    Solving linear systems of equations using Gaussian elimination (slides).
    23-Feb
    Lecture
    Solving linear systems in MATLAB
    Ex.
    Countercurrent exchanger
    Lab
    Direct methods for linear systems of equations
    28-Feb
    Tridiagonal linear systems
    Sparse and banded matrices
    2-Mar
    Quiz
    Lecture
    Sparse and banded matrices
    Lab
    Sparse matrices
    7-Mar
    Lecture
    Sparse and banded matrices
    Google PageRank: slides
    9-Mar
    Lecture
    Vector and matrix norms (slides)
    Linear regression (linear least squares) (slides, mathrules.mat)
    More general regression (slides).
    Reference
    Least squares solutions to overdetermine linear systems (Chapter 5)
    14-Mar
    Lecture
    More general regression (slides).
    Interpolation with polynomials
    16-Mar
    Lecture
    Interpolation with polynomials: Lagrange interpolation
    Barycentric forms of the interpolating polynomial (baryinterp.m)
    21-Mar
    Lecture
    Interpolation with polynomials (baryinterp.m)
    Runge phenomenon (slides, animation)
    Interpolation at Chebyshev points
    23-Mar
    Lecture
    Piecewise polynomial interpolation(slides)
    4-Apr
    Quiz
    Lecture
    PCHIP - shape preserving piecewise cubic polynomial interpolation (slides)
    Lab
    Piecewise polynomial interpolation
    6-Apr
    Lecture
    Cubic splines (slides)
    11-Apr
    Lecture
    Parametric interpolation: Dot-to-Dot, Bitmap font, Postscript font.
    Interpolation in two and higher dimensions (RBF slides)
    13-Apr
    Lecture
    Numerical integration: Trapezoidal rule (slides)
    18-Apr
    Lecture
    Numerical integration: Simpson rule (slides)
    20-Apr
    Lecture
    The rank of a matrix
    Singular value decomposition (SVD)
    25-Apr
    Lecture
    Singular value decomposition: image compression (bsubronco.bmp)
    Singular value decomposition: principal component analysis (mathrules.mat)
    27-Apr
    Lecture
    Classification with the SVD: MNIST digits (mnist_training_data.mat, mnist_test_data.mat, mnist_classification_ex.m, mnist_svd.m)

    Homework problem sets

    Homework assignments will involve a mix of programming and analytical work.

    Format

    One PDF file should be submitted electronically for each team through the dropbox folder that I set up for you. The name of the file should be HWx_LastNames, where x is the homework number and LastNames is the alphabetical listing of the last names of the group members.

    The completed homework assignments should answer all questions from the homework problems. Include in the document any code asked for in the problem, or any code you feel necessary to include that helped you solve your problem. All plots and tables should be labeled and also included in document. Codes, plots, and tables should put in the document at the location of the problem they correspond to, not as appendices in the back.

    You will use "publish" in MATLAB to produce your homework. This will allow you to embed equations with code, plots, and tables in one easy to follow document. See the Matlab help pages on publish for more details. Please read these homework tips for producing an acceptable assignment. You can download the MATLAB source code for this file here and publish it yourself.

    All MATLAB code should also be submitted as an m-file in your dropbox folder. I should be able to run this code to reproduce your results. It is important that you document your code to describe what it does.

    Assignments

    Due date Problem set Notes
    2-Feb Homework 1 hmwk1_template.m, heights.dat homework_tips.pdf (m-file),
    16-Feb Homework 2
    02-Mar Homework 3 tridisolve.m
    16-Mar Homework 4 bsusurfer.m, pagerank.m
    6-Apr Homework 5 baryinterp.m
    20-Apr Homework 6 shark.mat rbffit.m, rbfval.m, topodata.mat,
    03-May Homework 7 bsubronco.png

    Online assignments

    Due date Instructions
    19-JAN Complete the MATLAB Onramp course. Save the certificate showing you completed the course and put it in the shared dropbox folder.
    26-JAN Assignment 1 - Some basics of MATLAB (Cody)
    21-FEB Assignment 2 - Vectorization and functions (Cody)

    Miscellaneous


    Please e-mail me regarding any problems with the links on this page.