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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 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 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 