Beginning Scientific Computing

Description and Objectives

Although the subject matter of Beginning Scientific Computing can be made rather difficult, I will attempt to present the course material in as simple a manner as possible. More theoretical aspects, such as proofs, will not be presented. Applications will be emphasized.

Textbook and Notes (.pdf)

Syllabus

(1) Review and Matlab Introduction: 3 lectures

• Lecture 1 (9/27): Introduction to MATLAB: Matrices and Vectors
• Lecture 2 (9/29): MATLAB Logic, Loops and Iterations (bisection.m)
• Lecture 3 (10/2): Plotting and Saving Data ( plotting.m)

(2) Linear Systems: 3 lectures

• Lecture 4 (10/4): Solving Linear Systems and LU Decomposition
• Lecture 5 (10/6): Iterative Methods for Linear Systems
• Lecture 6 (10/9): Eigenvalue Problems

(3) Curve Fitting, Interpolation, Splines: 3 lectures

• Lecture 7 (10/11): Least Square Fits
• Lecture 8 (10/13): Polynomial Fits and Splines
• Lecture 9 (10/16): Implementation of Curve Fits ( curvefitting.m, gafit.m, linefit.dat, gaussfit.dat)

(4) Numerical Differentiation and Integration: 3 lectures

• Lecture 10 (10/18): Numerical Differentiation
• Lecture 11 (10/20): Numerical Integration
• Lecture 12 (10/23): Implementation of Differentiation and Integration (diff_int.m)

(5) Differential Equations: 6 lectures

• Lecture 13 (10/30): Basic Time-Stepping Schemes
• Lecture 14 (11/1): Error Analysis for Time-Stepping ( sampleODE.m, rhs.m)
• Lecture 15 (11/3): Boundary Value Problems: Shooting Method
• Lecture 16 (11/6): Implementing Shooting ( shoot.m, shoot2.m)
• Lecture 17 (11/8): Boundary Value Problems: Direct Method
• Lecture 18 (11/13): Implementing the Direct Solve ( direct.m)

(6) Transforms and Spectral Analysis: 2 lectures

• Lecture 19 (11/15): The Fourier Transform
• Lecture 20 (11/17): Spectral Analysis and Applications of FFT

(7) Partial Differential Equations: 5 lectures

• Lecture 21 (11/20): Basic time- and space-stepping schemes
• Lecture 22 (11/22): Time stepping schemes: explicit and implicit schemes
• Lecture 23 (11/27): Implementing time- and space-stepping schemes
• Lecture 24 (11/29): Basic Methods using Spectral Methods
• Lecture 25 (12/1): Implementing Spectral Methods (spec_implement.m, rhs1.m, rhs2.m)

(8) Visualization: 2 lectures

• Lecture 26 (12/4): Advanced 2D Plotting (plotexample.m)
• Lecture 27 (12/6): Advanced 3D Plotting, Movies and Animation ( chimney.m, plot3d.m)

Schedule and Homework

Follow links in the table below to obtain a copy of the homework in 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 SUBMISSION

You can now submit homework at the following link: submit homework

Remember that the submission checks your answers and compares (anti-cheat) against the MATLAB codes of others in this class and those of last year.

Grading

You may view your homework and exam grades on-line.

Your course grade will be calculated by weighing the homework, the Midterm, and the Final in the proportions 60%, 20%, and 20%, respectively. Homework problem sets will be assigned roughly bi-weekly. Homework constitutes 60% of your final grade. There will also be a one-hour-long midterm and comprehensive final for 20% and 20% or your grade respectively.

The test schedule is as follows: