Math 365-002
Introduction to Computational Mathematics
Fall 2017

Basic Information

Instructor:  Dr. Grady Wright, MB 140, 426-4674, Email:
Time and Place:  TuTh 9:00-10:15am, MB 136
  • Office Hours:  Wednesday, 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

    Day Topics
    22-Aug
    Lecture
    Syllabus
    Find a homework partner
    Introduction to computational math: slides
    Overview of Matlab
    24-Aug
    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
    29-Aug
    Lecture
    Arithmetic on arrays
    Scripts
    Plotting using linspace
    Lab
    Writing MATLAB scripts
    Arithmetic expressions involving arrays
    31-Aug
    Lecture
    For loops
    Functions
    Homework 1 discussion
    Publish
    Lab
    The for loop
    Formatting output
    05-Sep
    Lecture
    Questions about the homework
    Root finding (Chapter 4): Bisection
    07-Sep
    Lecture
    Root finding (Chapter 4): Newton and secant methods
    12-Sep
    Lecture
    Root finding (Chapter 4): secant method, fzero, fixed point iteration
    Lab
    Root finding
    14-Sep
    Lecture
    Minimization (Chapter 4): fminbnd
    Linear algebra review
    19-Sep
    Lecture
    Linear algebra review
    Solving linear systems of equations using Gaussian elimination (slides).
    Lab
    Two dimensional arrays and matrices
    Introduction to matrices and matrix algebra
    21-Sep
    Lecture
    Matrix-vector operations
    Solving linear systems in MATLAB
    26-Sep
    Lecture
    Solving linear systems in MATLAB
    Ex.
    Countercurrent exchanger
    Lab
    Direct methods for linear systems of equations
    28-Sep
    Lecture
    Solving tridiagonal linear systems and other sparse matrices
    Lab
    Sparse matrices
    3-Oct
    Lecture
    Google PageRank: slides
    5-Oct
    Quiz covering homework 1 and 2
    Lecture
    Interpolation with polynomials
    10-Oct
    Lecture
    Barycentric forms of the interpolating polynomial (baryinterp.m)
    12-Oct
    Lecture
    Runge phenomenon
    Interpolation at Chebyshev points
    Piecewise polynomial interpolation
    17-Oct
    Piecewise cubic Hermite interpolation
    Lab
    Piecewise polynomial interpolation
    19-Oct
    Lecture
    Splines
    24-Oct
    Lecture
    Parametric interpolation: Dot-to-Dot, Bitmap font, Postscript font.
    Interpolation in two and higher dimensions (RBF slides)
    26-Oct
    Lecture
    Vector norms (basic concepts in linear algebra)
    Linear regression (linear least squares) (slides)
    More general regression (slides).
    31-Oct
    Lecture
    Least squares solutions to overdetermine linear systems (Chapter 5)
    Separable least squares (expfitdata.mat)
    2-Nov
    Lecture
    Numerical integration: Trapezoidal, midpoint, and Simpson's rules
    7-Nov
    Lecture
    Programming Trapezoidal rule.
    Error estimates for Trapezoidal and midpoint
    Adaptive numerical integration
    9-Nov
    Lecture
    Integration in higher dimensions.
    Quiz covering homework 3 and 4
    14-Nov
    Lecture
    Quasi-Monte Carlo integration
    Initial value problems (IVPs)
    16-Nov
    Lecture
    Runge-Kutta methods for (IVPs)
    Matlab's IVP solvers
    Predator-prey models (chapter 7)
    28-Nov
    Lecture
    Matlab's IVP solvers
    Predator-prey models (chapter 7)
    Event detection
    30-Nov
    Lecture
    Matlab's IVP solvers
    Event detection
    5-Dec
    Lecture
    Second-order equations: Double pendulum : driverPend.m, dblPend.m, dblPendPlot.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
    7-Sep-2017 Homework 1 hmwk1_template.m, heights.dat homework_tips.pdf (m-file),
    22-Sep-2017 Homework 2
    06-Oct-2017 Homework 3 bsusurfer.m, pagerank.m, tridisolve.m
    20-OCT-2017 Homework 4 shark.mat
    03-NOV-2017 Homework 5 roller_coaster.dat, rbffit.m, rbfval.m, topodata.mat,
    17-NOV-2017 Homework 6
    01-DEC-2017 Homework 7
    12-DEC-2017 Homework 8 bsubronco.png

    Matlab tutorials and labs

    Miscellaneous


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