This second semester study of the field of numerical analysis will  investigate numerical techniques in:

• First-Order Differential Equations and Modeling (Chapter 1)
• First-Order Systems of Differential Equations (Chapter 2)
• Linear Systems of Differential Equations (Chapter 3)
• Special Equations of Second Order (Chapter 4 - a portion)
• Non-linear Systems (Chapter 5 - a portion)
• Laplace Transforms (Chapter 6 - a portion)
• Using MATLAB to generate numerical approximations solutions of differential equations and the errors associated with each of these techniques.

Here are a few handouts that have been distributed in class:

• Syllabus
• Section 1.1: (Modeling) Handout
• Maple Example of Slope Fields
• Excel Example of Euler's Method
• MATLAB code for Euler's Method
• Existence Uniqueness Handout
• Bifurcations Handout
• Review Topics for Test 1
• Jeopardy questions for Test 1 material and corresponding answers.
• MATLAB Files for Graphing Numerical Approximations to Linear Systems of Differential Equations:
• dYdt.m (the file defining the system of differential equations)
  
• PredPrey.m (the script file)
• Maple Files for creating Slope Fields and Direction Fields
• SlopeDirFields.mws
• MATLAB Files for creating Direction Fields
• dirfield.m
• dxdt_eqn.m
• dydt_eqn.m
• DirFieldScript.m
• Modeling via Systems Handout
  
• The Geometry of Systems Handout
  
• Euler's Method (2D) Handout with Excel Spreadsheet Demo
• Project #1:  Euler's Method in 1 & 2-D
  
• Additional MATLAB files for Project 1
• Euler.m and script file PlotEulerSol_1d.m
  
• Euler2d.m and script file PlotEulerSol_2d.m
• Jeopardy Questions and Solutions for Chapter 2
• Instructions for Installing Client Software for MATLAB and Maple on a PC on campus
• Handout on Straight-Line Solutions (Section 3.2)
• Handout on Saddles, Sinks, and Sources (Section 3.3)
• Project 2: Romeo & Juliet (MATLAB Project)
• Handout on Complex Eigenvalues (Spiral Sinks, Spiral Sources, and Centers)
• Handout for Special Cases of Eigenvalues (Repeated and Zero-Valued) (Section 3.5)
• Handout for Forced Harmonic Oscillators (Section 4.1)
• Topics for Test 3 Handout
• Project 3: (Optional) on Nonlinear Systems -- Due at the time of the Final