## Objectives

1. Numerical Error, Taylor Series

• Recognize types of error: truncations vs. round-off
• Apply Taylor series to error estimation

2. Solution of Single Algebraic Equations

• Classify equations: linear vs. nonlinear, algebraic vs. differential, etc.
• Understand the mechanics of a variety of bracketing and open solution methods: bisection, false position, Newton-Raphson, modified Newton-Raphson, and secant.
• Recognize the relative strengths and weaknesses of each method.
• Be able to choose an appropriate solution technique.
• Apply these techniques in the context of modern computational tools -- specifically, MATLAB.

3. Solution of Systems of Algebraic Equations

• Understand the mechanics of a variety of exact and iterative methods: Gauss Elimination, Gauss-Jordan, LU Decomposition, Gauss-Seidel, iterative refinement.
• Recognize the relative strengths and weaknesses of each method.
• Be able to choose an appropriate solution technique, including evaluation of system condition.
• Apply these techniques in the context of modern computational tools -- specifically, MATLAB.

4. Data Analysis

• Incorporate models into linear regressions
• Perform interpolation, splines
• Recognize and apply appropriate data analysis techniques for engineering purposes
• Perform numerical differentiation and integration.

5. Solution of Ordinary Differential Equations

• Classify ODE problems as initial, boundary value or eigenvalue problems.
• Reduce higher order equations to systems of first order equations.
• Solve first order initial value problems using Euler’s method up through 4th order Runge- Kutta.
• Solve first order boundary value problems using the shooting method and finite difference techniques.
• Recognize the relative strengths and weaknesses of each method.
• Be able to choose an appropriate solution technique
• Apply these techniques in the context of modern computational tools -- specifically, MATLAB.

6. Solution of Partial Differential Equations

• Classify PDEs as parabolic, hyperbolic or elliptic. Recognize these types in the context of common engineering physics.
• Apply explicit (Crank-Nicholson) and implicit finite difference techniques to the solution of parabolic and hyperbolic systems. Be aware of finite element techniques.
• Recognize the relative strengths and weaknesses of each method.
• Be able to choose an appropriate solution technique
• Apply these techniques in the context of modern computational tools -- specifically, MATLAB.
• Concept Integration
• Carry out a full problem solution, from problem definition, to selection of solution technique, application of technique, data analysis and physical interpretation of results.

Catalog Description

Studies fundamental numerical techniques for the solution of commonly encountered engineering problems. Includes overview of programming techniques in addition to methods for linear and nonlinear algebraic equations, data analysis, numerical differentiation and integration, ordinary and partial differential equations.

Prerequisites: GEEN 1300 or equivalent, including a working knowledge of Matlab, APPM 2360.