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gibson:teaching:spring-2016:math445:lab1

# 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.

2/3

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.   cube root of 19

3 to the 1.2

tangent of Problem 3: Are any of your answers for problems 1 and 2 surprising? Which, and why?

Problem 4: Wind chill factor: The WCF supposedly 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 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

(b) T = 45 F and V = 0 mph.

Problem 5: The geometric mean g of n numbers is given by This is useful, for example, in finding the average rate of return on an investment with varying yearly return.

(a) If an investment returns 15% its first year, 5% its second, and 10% its third, the average rate of return is Compute the average rate of return, expressed as a percent.

(b) Which is better for the investor, a steady 5% per year return on investment, or alternating between 0% and 10% year by year?

Problem 6: The astoundingly brilliant but short-lived mathematician Srinivasa Ramanujan devised the following very powerful formula for for  You can get an approximation of using only arithmetic operations by evaluating and summing a finite number of terms of this series. What is the numerical approximation of using just the first term ( )? Using the first and second ( and )? 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) 