Introduction to Scientific Computing

Revised: November, 2009 (Erin McNelis)

Course Description

This introduction to the field of scientific computing will focus on using mathematical software and programming as tools in mathematical problem solving. During the semester we will use :

• Non-traditional programming environments well-suited to mathematics: MATLAB and potentially NetLogo, and
• Mathematical software packages: MATLAB, Maple, Mathematica, and Vensim.

We will spend time learning the syntax, fundamentals, strengths and weaknesses of each type of soft- ware, keeping in mind that we are working in a fixed precision environment; we will review the fundamental of programming with regards to traditional and non-traditional programming environments; and we will use the LATEX typesetting system to document our progress with each tool and associated project.

Preq. Math 140 or Math 153 and some programming experience.


Objectives

By the end of the course students should be able to model problems mathematically and use mathematical software to solve or simulate these problems; to develop algorithms and implement them in the appropriate software or programming language; to present algorithms and solutions to problems in a mathematically sophisticated manner using a scientific documentation environment; and to know the benefits and drawbacks of each of the computational tools used during the semester.

Text

This course has no text book. Instead, handouts will be provided and documents can be download from the class web sites.

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Course Outline

• Learning Latex (approximately 8 days)
• Some Basics
• List Environments
• Tables
• Figures
• Mathematics
• Referencing
• Formatting and Special Environments
• Discrete and Continuous Mathematical Modeling and Simulation (throughout the course)
• Population Models (discrete and continuous)
• Stochastic Models (Environmental and Demographic Stochasticity)
• Using Excel in Modeling and Iteration (approximately 5 days)
• Graphing
• Formulas
• Parameterization
• Slider Bars
• Including Stochasticity
• Linear Programming
• IEEE Floating Point Number Representation and Arithmetic (approximately 5 days)
• IEEE Number Representation
• Machine Epsilon
• Proving Stability of Arithmetic Calculations
• K-Digit Arithmetic
• Mathematical Computations with MATLAB (approximately 2 days)
• Scalar Calculations
• Matrix and Vector Arithmetic
• Functions
• Plotting
• M-Files
• Algorithm Development and Programming in MATLAB (approximately 13 days)
• Variables
• Algorithm Development
• Conditional Statements and Looping
• Textual Output from MATLAB
• Variables and Arrays
• Programming Exercises
• Computer Algebra Systems (approximately 6 days)
• Basic Calculations
• Expressions and Parameters
• Functions
• Plotting
• Number Theory in Mathematica
• Differential Equations in Mathematica
• Individual Based Modeling and NetLogo (approximately 3 days)
• A predator-prey example
• NetLogo Models