MATH 224 - Mathematical Methods for Civil Engineers
News and Updates
Welcome! 20 September 2010 Welcome to Math 224!!! Here is the course syllabus. I've constructed some fill-in notes that will be used for the first half of the course.
Statistics Project, first take 21 September 2010
- Data presentation is important. Here is a website with some guidlines for effective data presentation. Never make pie charts. Of course, you can present data any way you like. Afterall, you may want to bend public opinion.
Statistics Project, first take 1 October 2010
- Here is the statistics project.
- Like I said in class, you shouldn't play the lotto.
Some Normal Distribution Goodies 6 October 2010
- Here is a normal distribution table. It's a little different than the one I used in class on Monday. The numbers in the body of the chart represent the area under the distribution from negative infinity to z.
- Here's the dice rolling example I used in class to demonstrate the Central Limit Theorem.
That was random 8 October 2010
- Are your numbers random? Random.org's are.
- What does catbert have to say about randomness?
- Why Most Published Research Findings Are False. A great quote from the abstract: "...for many current scientific fields, claimed research findings may often be simply accurate measures of the prevailing bias."
Correlation and causality 15 October 2010 Remember: only you can avoid the 'cum hoc ergo propter hoc' fallacy.
A Line of Best Fit 19 October 2010 Here is an example of a line of best fit to actual data on spiders.
A Polynomial of Best Fit 22 October 2010 I never really had time to talk about polynomial regression. Here is some data that you may try fitting a polynomial to. This can easily be done in Matlab. Save the data file in your Matlab directory and load the data with the command A=xlsread('heatdata.xls'). This will put the data into the matrix A. You can pick off the first column of A, the x data, with x=A(:,1). Similarly, y=A(:,2). Finally, scatter(x,y) will plot the data. Once plotted, you can use the GUI plot window to fit a line and polynomial of best fit: Tools->Basic Fitting. Try a few of the options. Here is what you get when you fit a line, quadratic, cubic, and all three of these options. Of course, you could keep fitting polynomials of higher and higher degree, but for practical purposes a cubic may be more insightful than a polynomial of degree 57.
And now for something completely different... 26 October 2010 Paul's Online Math Notes are probably the best reference on differential equations around. You should also practice your integration skills. You'll need at least some of them for this part of the course. Here are the answers and explanations on how to get them. I didn't provide solutions, but I'm willing to meet with you if you cannot solve any of the integrals.
Final Practice 22 November 2010 Here's the final exam practice! Roughly 80% of the final will be questions from this list.
Trace-determinant Plane 24 November 2010 Here's what Hirsch, Smale, and Devaney have to say about the trace-determinant plane. You'll notice that the left most and right most phase portraits on the plane are different than the ones I drew in class. Both theirs and my pictures are correct, but I placed mine in the wrong part of the plane. Where should they have gone? Hint: I was really close. As in, I drew them overlapping the region they belong in.
Classic 'Dynamical Systems' 30 November 2010 We only breifly covered some really interesting examples of systems of differential equations. The two we did cover are classic examples:
- The Lotka-Volterra system, or the Predator-Prey system, describes the interactions between two species, one food for the other.
- The Lorenz system resulted from an effort to predict weather. Some videos can be found here: Video 1, Video 2, Video 3.