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====== Math 445 Lab #1 ====== Most of 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 Matlab expressions in your head and write down the answer. Then type them into Matlab and see how Matlab evaluates them. If you made a mistake, figure out what it was. 25/4*4 3+4^2 4\12 + 4 3^2 (5-2)*3 **Problem 2:** Translate these mathematical expressions into Matlab expressions, and then evaluate them. $e^{3/4}$ $\sqrt[5]{7}$ $e^{\pi i}$ cube root of 19 3 to the 1.2 tangent of $\pi$ **Problem 3:** Wind chill factor: The WCF conveys how cold it feels with a given air temperature T (degrees Farenheit) and wind speed V (miles per hour). A formula for WCF is <latex> WCF = 35.7 + 0.6 T - 35.7 V^{0.16} + 0.43 \; T \; V^{0.16} </latex> Create variables for temperature T and wind speed V and then using this formula, calculate the WCF for (a) T = 45 F and V = 10 mph and (b) T = 45 F and V = 0 mph. **Problem 4:** The geometric mean g of n numbers $x_1, x_2, \ldots, x_n$ is given by \begin{eqnarray*} g = \sqrt[n]{x_1 x_2 \ldots x_n} \end{eqnarray*} 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 \begin{eqnarray*} \sqrt[3]{1.15 \cdot 1.05 \cdot 1.10} \end{eqnarray*} Compute the average rate of return, expressed as a percent. **Problem 5:** The astoundingly brilliant but short-lived mathematician Srinivasa Ramanujan devised the following very powerful formula for for $1/\pi$ \begin{eqnarray*} \frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum_{k=0}^{\infty} \frac{(4k)!\, (1103 + 26390\,k)}{(k!)^4 \, 396^{4k}} \end{eqnarray*} You can get an approximation of $\pi$ using only arithmetic operations by evaluating and summing a finite number of terms of this series. What is the numerical approximation of $\pi$ using just the first term ($k=0$)? Using the first and second ($k=0$ and $k=1$)? How many digits of accuracy does each of these approximation have? Be sure to use ''format long''. (adapted from a problem in //Introduction to Matlab Programming// by Siauw and Bayen) **Problem 6:** Translate the following Matlab logical expressions into English. x < y x < y || y < z x <= y && y <= z **Problem 7:** Translate the following mathematical expressions into Matlab and evaluate for $x=3, y=4, z=5$. $x < y < z$ $x < y$ and $x < z$ $y < z$ or $x == z$ **Problem 8:** Evaluate the following Matlab expressions and explain the results. 3 == 4 ~(5 >= 2) 2 < 3 < 5 2 > 3 > 5 2 > 3 < 5 xor(5 < 6, 8 > 4) (3 == 2) + 1
