Beginning Scientific Computing (AMATH 301)

AMATH 301: Beginning Scientific Computing

SLN 10054, MWThF 2:30-3:20, Sieg Hall 225

(Prerequisites: MATH 126 or MATH 136: recommended: CSE 142)

Instructor:

Lisa Bishop
Guggenheim 407
Tel: (206) 685-9395
Fax: (206) 685-1440
lbishop@amath.washington.edu
Office hours: at AS Lab Mon 4-5, Wed 4-5

Lab TA:

Peizhe Shi
Guggenheim 407
Tel: (206) 685-9395
Fax: (206) 685-1440
ship@u.washington.edu
Office hours:at AS Lab Tues 2-4, Thurs 10-12

Course description

Textbook

Syllabus

Schedule

Homework

Grades

Course Description

Introduction to use of computers to solve scientific and engineering problems. Application of mathematical judgment in selecting tools to solve problems and to communicate results. MATLAB, MATHEMATICA/MAPLE, and NETLIB software used for numerical computation and symbolic manipulation.

Textbook and Notes

There is no text required for this course. Professor Kutz's notes are available on-line here and there are a variety of MATLAB help books available in the library.

Syllabus

Introduction to Matlab: How to create and manipulate vectors and matrices, create loops and logic statements, and output data in plots and data files.
Review of Applied Linear Algebra: Basis, range, rank vector norms, matrix norms. Special matrices: symmetric, orthogonal, lower and upper triangular, tridiagonal.
Direct Methods for Solving Dense Systems of Linear Equations: Gaussian elimination with partial pivoting. Solution of triangular systems, multiple right hand sides. Tridiagonal systems.
Solution of a Single Nonlinear Equation: Bisection method. Newton's method. Convergence to a root.
Interpolation: Polynomial interpolation by Lagrange polynomials. Cubic splines.
Numerical Quadrature: Trapezoid and Simpson quadrature. Richardson extrapolation. Infinite limits of integration.
Ordinary Differential Equations - Initial Value Problems: Euler's method. Accuracy and stability. Trapezoid method. Runge-Kutta method.
Partial Differential Equations: Basic time and space stepping techniques, both implicit and explicit.

Schedule

Week 1 - Introduction to Matlab Programming
- Lecture 1 (6/23): MATLAB intro: Matrices and Vectors
- Lecture 2 (6/25): MATLAB intro: Logic, Loops and Iterations (bisection.m)
- MATLAB Lab 1 (6/26): MATLAB worksheet in AS Lab Rm B027
- Lecture 3 (6/27): MATLAB intro: Plotting, importing and exporting data (plotting.m),(plotSURF.m)
Week 2 - Solving Linear Systems
- Lecture 4 (6/30): Solving Linear Systems-Direct Methods
- Lecture 5 (7/2): Solving Linear Systems-Iterative Methods (jacobi_example.m),(jacobi_example2.m),(GS_example.m)
- MATLAB Lab 2 (7/3): (class7_3.m),(SDD.m)
Week 3 - Solving Linear Systems
- Lecture 6 (6/7): Eigenvalues and Eigenvectors
- Lecture 7 (7/9): Least-Squares Fitting Methods
- MATLAB Lab 3 (7/10): (class7_10.m),(E2function.m), (linefit.dat)
- Lecture 8 (7/11): Polynomial Fits and Splines: (polyfitEX.m),(curvefitting.m), (linefit.dat),(gaussfit.dat),(gafit.m)
Week 4 - Numerical Differentiation and Integration
- Lecture 9 (7/14): Numerical Differentiation
- Lecture 10 (7/16): Roundoff Error and Optimal Step Size/Numerical Integration
- MATLAB Lab 4 (7/17): (class7_17.m)
- Lecture 11 (7/18): Numerical Integration
Week 5 - Time Stepping/Midterm
- Lecture 12 (7/21): Numerical Integration/Introduction to IVPs:(DiffEx.m), (Suns.dat), (IntEX.m), (intfun.m), (adapquadEX.m), (adapquad.m), (myfeval.m)
- Lecture 13 (7/23): IVPs continued: (EulerEX.m)
- MATLAB Lab 5 (7/24): Midterm Review (class7_24.m)
- MIDTERM (7/25)
Week 6 - IVPs
- Lecture 14 (7/28): Adams Methods for IVPs
- Lecture 15 (7/30): Adams Methods, Accuracy
- MATLAB Lab 6 (7/31): (class7_31.m), (odefun.m), (odefun2.m), (rabbitfox.m), (chem.m)
- Lecture 16 (8/1): Accuracy and Stability of Time Stepping Methods: (RKMethods.m), (AdamsMethods.m), (odefun.m)
Week 7 - BVPs
- Lecture 17 (8/4): Shooting Method for BVPs: (EXmakeplotS.m), (plotS.m), (shoot_demo.m), (shoot2), (class8_4.m), (oscil.m)
- Lecture 18 (8/6): Direct Methods for BVPs: (bvp_shoot_bisection.m), (bvp_shooting_error.m), (bvp_shooting_rhs.m), (bvp_direct_example.m)
- MATLAB Lab 7 (8/7): (class8_7.m), (oscil.m)
- Lecture 19 (8/8): Direct Method/Intro to Fourier Transforms: (class8_8.m)
Week 8 - FFT
- Lecture 20 (8/11): Fast Fourier Transform: (fft_gaussian.m),
- Lecture 21 (8/13): FFT cont: (fft_modes.m), (PoissonFFTEX.m)
- MATLAB Lab 7 (8/14): (class8_7.m), (fft_ode_hat.m), (heat2D_fft.m), (heat2D_fft_rhs.m), (nls_fft.m), (nls_rhs.m)
- Lecture 19 (8/15): Overview Solving PDE's

Homework Schedule

Follow links in the table below to obtain a copy of the homework in PostScript (.ps) or

Adobe Acrobat (.pdf) format. You may also obtain here solutions to some of the homework and exam problems. An item shown below in plain text is not yet available. For additional information regarding viewing and printing the homework and solution sets, click here.

Homework and Exams	Homework Due Date	Homework Problem Sets	Homework Solutions
First day of classes	Monday, June 23
Homework#1	due Tuesday, July 8	Homework #1	hw1.m
Independence Day	Friday, July 4	No class
Homework#2	due Thursday, July 17	Homework #2	hw2.m, fit_func.m
Midterm	Friday, July 25	Review,Review Solution	Midterm Solution
Homework#3	due Thursday, July 31	Homework #3,velocity.dat	hw3.m, fit_error.m
Homework#4	due Thursday, August 14	Homework #4	hw4.m, lorentz_rhs.m, bvp_rhs.m, p2_rhs.m
Final Exam Part I	Thursday, August 21	milkadj.dat	Review, Review Solution
Final Exam Part II	Friday, August 22

Homework Submission

Submit homework at the following link:

Grading

Your course grade will be calculated as the following:

	Homework Midterm Final	50% 20% 30%

Matlab Resources

In this course we will make extensive use of Matlab, a technical computing environment for numerical computions and visualization produced by The MathWorks, Inc. A Matlab manual is available in the ICL Lab. If you are working in the Windows environment, be sure to check out the Matlab notebook feature that integrates Matlab with Microsoft Word.

Here is a list of possible useful internet resources as well:

Matlab Hypertext Reference, Portland State University

<lbishop@amath.washington.edu>

Thu Jun 12 15:56:47 PDT 2008