Analysis is crucial skill for both learning and the practice of engineering. The heart of engineering analysis is the use of mathematical models that allow us to predict the behavior of physical systems. Models allow us to test ideas, and explore the effects of design choices before we commit resources (time, money, materials) to building physical artifacts.
Algebra Review and Practice
Engineering analysis draws upon many branches of mathematics. The crucial fundamental mathematical skill is algebra because algebra allows us to rearrange and combine formulas.
Here are some practice problems for algebra. Hint: Don't look at the answers until you have worked the problems! Also note that some of the practice problems involve least squares curve fitting that will be covered later in the term.
Working with Units
Tracking the units of terms is crucial for avoiding silly mistakes. Sometimes analysis of units will give you clues about how to solve solve a problem.
- Notes on working with units includes some practice problems.
Least Squares Fitting of a Curve to Data
Working with data from experiments forces us to deal with uncertainty and variability. When we plot data from an experiment, there is often some scatter about a trend. Least squares curve fitting is a technique for finding an equation that follows the trend in data.
- Lecture slides on least squares line fitting (PDF)
- Lecture slides on R^2 metric (PDF)
- Lecture slides on polynomial curve fitting of pump data (PDF)
Curve fitting with Excel