Arithmetic Expressions

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• Misc
  • Colloquium
    • “Is the Set of Knots Fractal?”
    • Dr. Arunima Ray, Brandeis University (and Geneseo math alumna)
    • Friday, Jan. 29, 2:45; Newton 204
    • Extra credit (up to 1/5 of a lab) for going and writing ca 1 paragraph to 1 page on intellectual connections you make to the talk
      • “Due” any time before final exam
• Questions?
• Arithmetic Expressions
  • Variables?
    • “substitute” values, namely in two ways
      • Put values into variables
        • x = 8
      • Use variable’s value in expression
        • x + 3
  • Section 2.1
    • Scalar arithmetic operators
    • Precedence order: exponentiation(^), multiplication(*)/division(/), addition(+)/subtraction(-)
      • Equal precedence done left-to-right
      • Use parentheses to make intended order clear
        • But realize that too many parentheses can make code hard to read
    • Remember to use symbol for multiplication
    • Can use ... to continue expression over multiple lines
  • Examples / questions
    • Average height of some volunteers
      

      >> megan = 5 * 12 + 5
      megan =
          65
      >> maureen = 5*12+2
      maureen =
          62
      >> grace = 5*12 + 10;
      (megan + maureen+grace)/3 
      ans =
         65.6667

    • Sum of the powers of 2 from 2⁰ through 2⁴, i.e., first 5 powers of 2 (counting from 0)
      • Also think about how these sums compare to the next powers of 2
        

        >> (2^0) + (2^1) + (2^2) + (2^3) + (2^4)
        ans =
            31
        >> ans + (2^5)
        ans =
            63
        >> (2^0) + (2^1) + (2^2) + (2^3) + (2^4) + (2^5)
        ans =
            63
        >> 2^5
        ans =
            32
        >> 2^6
        ans =
            64

      • Suggests a theorem about sums of powers of 2, which you could prove by induction
        
      • Example of how computation complements other mathematical insight
    • Exam question re 1st 3 terms of Taylor series for cos x
      • i.e., write a Matlab expression for those terms
        

        >> x = pi/2
        x =
            1.5708
        >> 1 - ((x^2)/2) + ((x^4)/24)
        ans =
            0.0200
        >> 1 - ((x^2)/2) + ((x^4)/(4*3*2))
        ans =
            0.0200

      • Note importance of parenthesizing products in the denominator of a fraction
      • Easy to overlook because standard math notation for such a fraction makes order of evaluation obvious
        
    • Hypotenuse of right triangle with sides of length 1 and 2
      

      >> (1^2 + 2^2)^(1/2)
      ans =
          2.2361

• Next
  • Numeric functions
  • Read section 2.2

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