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.
4\12 + 4
Problem 2: Translate these mathematical expressions into Matlab expressions, and then evaluate them.
cube root of 19
3 to the 1.2
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
(adapted from a problem in Introduction to Matlab Programming by Siauw and Bayen)