ECIV 201 Numerical Methods Lecture Help

Lectures and Notes

Week 1

Here is the power point notes for your viewing pleasure

Lecture 1 Power Point

Summary Excel Spreadsheet ---the spreadsheet I handed out

Summary of Excel Conventions --- the short handout on addressing cells etc..

This week we will look at several examples of number methods and computer applications. They include solutions to simple and complex problems. Computational tools you have used in the past and will use in the future include:

1. Computer-aided design. This may consist of automated (you wish) data gathering, data verification, and model construction. This follows with different iterations of design options and analyses. Finally a decision-making process is invoked. The design is then finalized with details and construction sequencing.
2. Finite Element Analysis. This may be a component of the design process (1) or an independent analysis of a particular problem. Finite elements are linearized versions of the differential equations used to describe many engineering phenomena: Strucutres and Solid Mechanics, Fluid Mechanics and Groundwater Flow, Contaminant Transport. Most problems are very complex and would be intractable otherwise.
3. Statistical and Probabilistic Methods. In order to better capture the variability of natural phenomena, engineers resort to methods that better quantify not only a particular set of quatities, but also how those quantities may vary over time and distance.

A simple example of how an engineer may use numerical tools to examine several design possibilities is started for you in the handout below:

Using Spreadsheets for Parametric Analysislang="en-us">-html version  pdf version

Week 2

 Lecture 2 Power Point

The subject of Error Analysis is a difficult one. It is unfamiliar territory for most students. Please keep in mind that it really is so difficult but does involve a very carefully-chosen set of terms and procedures. It is difficult to slap together a thoughtful analysis of how to evaluate errors in numerical computation. Looking at it one way; it is the most important aspect of Computational Methods. Have a look at the power point slides, especially the example at the end using Taylor's Series approximations. This concept is perhaps the most fundamental idea underlying most of your future livlihood, so it may do you well to think about it and try to get your brain around these concepts.

Week 3

Lecture  3 Power Point

Lecture 3a Supplemental Power Point

Working with matrices and linear simultaneous equations are probably the most difficult and time consuming numerical tasks you will face. This is because a lot of what you analyze is formulated this way. An entire universe of finite element analyses has grown from these concepts and are the fundamental analysis method for engineers today. So, the more you know about these methods, the better prepared you will be in the future to face these issues. I made a separate page for Matrices and Linear Equations

Week 7

Here is a study sheet for you for the test on Wednesday

Study Sheet

Week 8

Here is the lecture powerpoint on Integration   Integration Lecture