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ME2001 - Elementary Mechanical Engineering Analysis

Syllabus, lecture notes, and other materials for ME2001-002, Spring 2008.
File Course Syllabus
Lec. 01 Reading: Solving Nonlinear Equations: Real-Life Example
To shrink fit a cylinder into a hollow hub, the cylinder needs to be cooled down. To find out how much cooling needs to be done, you need to solve a nonlinear equation.
Lec. 01 Reading: Solving Nonlinear Equations with Bisection Method
Lec. 01 Reading: Powerpoint Presentation on Bisection Method
File Lec. 01 Handouts
Course Information, Overview of Numerical Methods, Types of Problems Solved with Numerical Methods.
Lec. 02 Reading: Getting Started with MATLAB 7
Introductory materials on MATLAB.
File Lec. 02 Handouts
Solution of Nonlinear Equations. Graphical and Incremental Search Methods. Fluid Mechanics Example.
File Lec. 03 Handouts
Bisection and Newton-Raphson methods -- these are actually old slides from ME2000. I may rework them later, but these are the actual slides I showed on Jan. 28.
Octave
Free Software version of MATLAB
Octave-Forge
Main site for Octave development, including easy binary installers for Octave 3.0 for Windows and MacOS X.
File Lec. 04: Introduction to MATLAB
File Lec. 05 and 06 Handouts
More MATLAB materials: control structures, including if/then/else, for loops, and while loops; working with plots; loading and saving data with text and binary files. These also are technically old slides from ME2000 from Fall 2004, but I used them on Feb. 4 and 6, 2008.
File Lec. 07 Handouts
Incremental Search Method in MATLAB -- bolted plate stiffness problem, two different versions. These are old ME 2000 slides from September 2004, but were reused on Feb. 11, 2008.
File Lec. 08 Handouts
Introduction to systems of linear equations
File Lec. 09 Handouts
Solution of Linear Algebraic Equations: graphical interpretation, solvable and unsolvable problems, linear dependence and independence, ill-conditioning. Part 1 of material from February 18, 2008.
File Lec. 10 Handouts
Cramer's Rule and Gauss Elimination. Part 2 of material from February 18, 2008.
File Lec. 11 Handouts
Jacobi and Gauss-Seidel Iteration Methods, use of MATLAB and Excel to solve systems of equations.
File Matrix Inversion in Excel
I really don't recommend using this over MATLAB or Octave, but if you're just dying to know how to do matrix solutions with Excel, here you go.
File Lec. 12 Handouts
Introduction to curve fitting and interpolation. Overview of types of fits, step spline fits, linear spline fits, and quadratic spline fits.
File Heat Transfer Conduction Homework
Due 5pm Friday, March 14. Set up the equations for the nodes using the cases shown in Table 4.2. Nodes 1-6 are interior nodes, Nodes 7-8 are on a plane surface with convection. Perform one solution via Cramer's rule, one via Gauss elimination, and a third solution via Gauss-Seidel iteration: 1. The determinants for Cramer's rule aren't difficult, since most of the diagonals and antidiagonals have zeros on them. 2. The Gauss elimination solution is mildly tedious, but if you arrange the equations properly, you'll have 10 non-zero values below the main diagonal to start, and a total of 13 elimination operations to perform. 3. For the Gauss-Seidel iteration, set your initial guesses for nodal temperatures to a constant 400K. Iterate through until no nodal temperature changes more than 5K from iteration to iteration.
File Lec. 14 Handouts
Cubic Spline Interpolation, Least Squares Curve Fitting, Use of Software
File Lec. 14 Addendum: How Excel's R^2 Value Can Lie To You
Two examples of abusing Excel's least-squares curve fitting features. Just because R^2 is nearly or exactly 1.0 doesn't mean you found the function that drives your data!
File Lec. 15 Handouts
Solution of Matrix Eigenvalue Problem