# Lectures

PDF lecture slides, in printable handout form.

- 2004-08-31: Intro to Numerical Methods in Mechanical Engineering
- Course Information, Overview of Numerical Methods (relevance of numerical methods, types and sources of error, significiant digits, rounding), Types of Problems Solved with Numerical Methods (natural frequencies of a vibrating bar, static analysis of a scaffolding, critical loads for buckling a column, realistic design properties for materials)
- 2004-09-02: Solution of Nonlinear Equations - Graphical and Incremental Search Methods
- Sample Problems Solved With Numerical Methods (natural frequencies of a vibrating bar, static analysis of a scaffolding, critical loads for buckling a column, realistic design properties of materials), Solution of Nonlinear Equations (introduction, fluid mechanics example, incremental search method)
- 2004-09-14: Writing MATLAB Programs
- Control Structures (if/then/else, for loops, while loops, vectorized loops), Working with Data and Graphics (loading/saving data with text files, loading/saving data with MATLAB binary files, x-y plots)
- 2004-09-09: Introduction to MATLAB
- Introduction to MATLAB: Starting, Exiting, Getting Help; Major Elements of the MATLAB Environment; MATLAB as a Calculator. Writing Functions: Function Example - Projectile Motion; Rules for Writing Functions; Functions with Multiple Returned Variables
- trendlines.xls
- Examples of data with poorly-chosen trendlines. Just because R^2 is a number near 1.0 doesn't mean that you have a legitimate fit function.
- 2004-09-07: Bisection and Newton-Raphson Methods
- Bisection Method (problem setup, procedure, advantages and disadvantages, example), Newton-Raphson Method (problem setup, procedure, advantages/disadvantages)
- 2004-09-21: Solution of Simultaneous Linear Algebraic Equations
- Introduction (basic form of the equations, multiplication in matrix algebra, solution types), Applications and Problem Setup: Scaffolding, Basic Concepts of Solution (determinants and rank, rank and determinants example: scaffolding)
- 2004-09-23: Solution of Simultaneous Linear Algebraic Equations
- Graphical Interpretation, Solvable and Unsolvable Problems, Linear Dependence and Independence, Ill-Conditioning
- 2004-09-28: Cramer's Rule and Gauss Elimination
- Cramer's Rule (introduction, example, advantages/disadvantages), Gauss Elimination (introduction and rules, example, matrix version and example, advantages/disadvantages)
- 2004-09-16: Incremental Search Method in MATLAB
- An Incremental Search Problem (problem analysis, problem restatement, problem strategy), Incremental Search Program Solution (function to calculate stiffness of fastened plates, a program to find bolt diameter, a better program to find bolt diameter)
- matrix inversion.xls
- An example of performing matrix inversion in Excel to solve a system of equations.
- least squares example.xls
- Example data for performing least-squares curve fits
- 2004-09-30: Jacobi and Gauss-Seidel Iteration Methods, Use of Software Packages
- Jacobi Iteration Method (introduction, example, notes on convergence criteria), Gauss-Seidel Iteration Method (introduction, example), Use of Software Packages (MATLAB, Excel)
- 2004-10-14: Curve Fitting, Interpolation
- Curve Fitting and Interpolation: Introduction, Spline Interpolation (step function spline, linear spline, quadratic spline)
- 2004-10-21: Cubic Spline Interpolation, Least-Squares Curve Fitting, Use of Software
- Cubic Spline Interpolation (basics, piecewise cubic constraint equations, Lagrangian option to reduce number of equations), Least-Squares Curve Fitting (linear regression, example, nonlinear regression), Use of Software (Excel, MATLAB)
- 2004-10-12: Solution of Matrix Eigenvalue Problem
- Standard Eigenvalue Problem (introduction, other forms of the problem, solvability), General Eigenvalue Problem (introduction, example), Eigenvalue Solutions in MATLAB (standard problems, general problems)
- cubicspline.m
- 2004-11-02_handouts.pdf
- 2004-11-04_handouts.pdf
- 2004-11-09_handouts.pdf
- 2004-11-30_handouts.pdf
- 2004-12-02_handouts.pdf