## 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

#### Supplementary:

• T. A. Driscoll, Learning MATLAB, SIAM 2009. Available as an e-book from the library (click the link).

### 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 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)

### 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, shark.mat

### 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)