MATH 224 Mathematical Methods for Civil Engineers

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MATH 224Mathematical Methods forCivil Engineers

• Instructor Alan Ableson

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Course Description

• Half statistics, half differential equations
• MATLAB use in both halves
• there will be tests in computer lab
• Start with Statistics

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Course Parts

• Lectures using slides, and MATLAB
• will post in advance
• Labs on computer, with TA available for
  assistance
• Tutorials will be for questions on the
  assignments

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Course Parts
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Mark Distribution

• Assignments 25
• 11 assignments, best 10 counted
• can work/submit in groups of 1-3 students
• Lab Tests
• One in statistics 25
• One in Diff. Eqs 25
• will be done in a computer lab
• no group work for these
• Final Exam 25
• Will be shorter than standard exam
• will be used to test theory, understanding

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Texts and Resources

• MATH 224 text in Bookstore
• new this year
• combination of stats and DE textbook
• should be resaleable next year
• MATLAB for home use
• will use/demonstrate MATLAB in class
• MATLAB will be used in later CIVL courses

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Statistics

• The word statistics brings to mind

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Definition

• A statistic is any quantity whose value can be
  calculated from sample data.
• Text, pg. 204
• Statistics of typical interest can be informally
  grouped
• descriptive
• comparative
• predictive

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Describing Sample Data

• A colleague presents you with the following data
  with water sediment measurements in the
  Sacramento River

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About the Data

• Before doing any analysis, what questions should
  you ask?

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Source of Sample

• Real statistics is not always about crunching
  numbers
• In many instances, knowing the properties of the
  sample can be more important than any later
  analysis!

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Describing/Summarizing the Data

• What techniques could you use to describe or
  summarize the data?

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Describing/Summarizing the Data

• Continued

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Data in MATLAB

• To read simple data from Excel,
• Make sure MATLAB is in the directory with the
  Excel spreadsheet
• data xlsread(ltfilenamegt')
• To plot a histogram
• hist(data)
• To find the mean
• mean(data)

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Interpreting Histogram
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Histogram Informing Mean
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Risk of the Mean

• Mean (add up numbers, divide by N) is sometimes a
  poor estimate of what we mean by average
• small number of extreme values can have a large
  distorting effect on mean
• Other alternative averages or measure of
  central tendency include
• median
• trimmed mean
• geometric mean
• Calculations on data should always be combined
  with graphical approaches

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Moving on

• By next class,
• open MATLAB, try some of the functionality
• download first assignment (up by this afternoon)
• read Sections 1.1 1.4 in the text