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--- gibson:teaching:fall-2013:math445:lab1 [2013/08/26 18:23]
gibson
+++ gibson:teaching:fall-2013:math445:lab1 [2013/08/28 18:33] (current)
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@@ Line 1: / Line 1: @@
 ====== Math 445 Lab #1 ======
-These problems are taken from Attaway chapter 1, both 2nd and 3rd editions.
+These problems are taken from Attaway chapter 1, both 2nd and 3rd editions. Remember, Matlab's //help// function is your friend.
 **Problem 1:** Evaluate these expressions in your head and write down the answer. Then evaluate them with Matlab. If you made a mistake, figure out what it was.
@@ Line 16: / Line 16: @@
-**Problem 2:** What is the type of the answers in problem 5?
+**Problem 2:** What is the type of the answers in problem 1?
-**Problem 3:** Use //intmin// and //intmax// to determine the range of values that can be stored in the types //uint32// and //unint64//? Express the answer both as an integer and in scientific notation.
+**Problem 3:** Use //intmin// and //intmax// to determine the range of values that can be stored in the types //uint32// and //unint64//. Express the answers as integers and in scientific notation.
 **Problem 4:** Wind chill factor: The WCF conveys how cold it feels with a given air
@@ Line 34: / Line 34: @@
-**Problem 12.** Use Matlab help to understand the following questions, and then answer them based on your understanding. Then use Matlab to check your answers. Rethink any questions you answered incorrectly.
+**Problem 5:** Use Matlab help to understand the following questions, and then answer them based on your understanding. Then use Matlab to check your answers. Rethink any questions you answered incorrectly.
  is fix(3.5) == floor(3.5)?
@@ Line 44: / Line 44: @@
  is fix(-3.2) == floor(-3.2)?
- is fix(-3.2) === ceil(-3.2)?
+ is fix(-3.2) == ceil(-3.2)?
-**Problem 13.** Find Matlab expressions for
+What is the type of //fix(-3.2) == ceil(-3.2)//?
- square root of 19
+**Problem 6:** Find Matlab expressions for
+ cube root of 19
 to the 1.2
@@ Line 54: / Line 56: @@
  tangent of pi
-**Problem 17.** Generate random numbers
+Evaluate the expressions. Do you notice anything unexpected? Can you explain it?
+**Problem 7:** Generate random numbers
  real in range 0-1
@@ Line 68: / Line 72: @@
  integer in range 50-100
-** Problem 18.** Get into new Command window and type rand to get a random real number.
+**Problem 8:** Get into new Command window and type rand to get a random real number.
 Make a note of the number. Then exit and restart matlab, and repeat. The
 random number should be the same. Exit and restart matlab again. This time,
 change the random number seed before generating a new random number. The
 random number should be different this time.
+**Problem 9:** Evaluate these expressions in your head, and then check your answers by evaluating them with Matlab. If you made any mistakes, figure out why.
+  'b' >= 'c' + 1
+== 2 + 1
+  (3 == 2) + 1
+  xor(5 < 6, 8 > 4)
+What is the type of each of the answers?
+**Problem 10:** The geometric mean g of n numbers $x_1, x_2, \ldots, x_n$ is given by
+<latex>
+  g = \sqrt[n]{x_1 x_2 \ldots x_n}
+</latex>
+This is useful, for example, in finding the average rate of return on an investment with varying yearly return. If an investment returns 15% its first year, 5% its second, and 10% its third, the average rate of return is
+<latex>
+  \sqrt[3]{1.15 \cdot 1.05 \cdot 1.10}
+</latex>
+Compute the average rate of return, expressed as a percent.

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